What is GCF in Math

Introduction to gcf in math:

In mathematics, Gcf is used to simplify the common fractions and carrying out basic operations. The greatest common divisor (gcd), as well-known as the greatest common factor (gcf), greatest common denominator, or highest common factor (hcf), of two or more non-zero integers, is the largest positive integer that divide the numbers without a remainder. In mathematics “Greatest Common Factor” short form gcf. GCF of those numbers is largest factor which commonly divides the specified set of numbers (two or more).


Examples problem for gcf in math:


1. Find the gcf of 8, 10, 6, 14 and 16.

Solution:

Given numbers are 8, 10, 6, 14 and 16.

The Greatest Common Factor (GCF) of the numbers 8, 10, 6, 14 and 16 is 2.

2 is the greatest number that divides common into all of them.

Gcf of this problem is 2.

2. Find the gcf of 150, 250,300 and 350.

Solution:

Given numbers are 150, 250, 300 and 350.

The Greatest Common Factor (GCF) of the numbers 150, 250, 300 and 350 is 50.

50 is the greatest number that divides common into all of them.

Gcf of this problem is 50.

3. Find the gcf of 25, 55, 17, 16 and 50.

Solution:

Given numbers are 25, 55, 17, 16 and 50.

The Greatest Common Factor (GCF) of the numbers 25, 55, 17, 16 and 50 is 1.

1 is the greatest number that divides common into all of them.

Gcf of this problem is 1.

4. Find the gcf of 15, 45, 18, 27 and 60.

Solution:

Given numbers are 15, 45, 18, 27 and 60.

The Greatest Common Factor (GCF) of the numbers 15, 45, 18, 27 and 60 is 3.

3 is the greatest number that divides common into all of them.

Gcf of this problem is 3.

5. Find the gcf of 10, 30, 50, 70 and 80.

Solution:

Given numbers are 10, 30, 50, 70 and 80.

The Greatest Common Factor (GCF) of the numbers 10, 30, 50, 70 and 80 is 10.

10 is the greatest number that divides common into all of them.

Gcf of this problem is 10.

6. Find the Greatest Common Factor (gcf) of 14, 24 and 42.

lowest Factors of 14: 1,2,7,14
lowest Factors of  24 : 1, 2,4, 6,8,12,24
lowest Factors of  42  : 1, 2, 3, 6, 7, 14, 21, 42

Common Factors: 1, 2.
1, 2 divides 14, 24, 42 therefore they are common factors.

Answers for gcf = 2

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Practice problems for gcf in math:


1. Find the gcf of 20, 52, 10, 16 and 50.

Answers for gcf = 2

2. Find the gcf of 25, 55, 15, 35 and 50.

Answers for gcf = 5

3. Find the gcf of 6, 12, 15, 21 and 30.

Answers for gcf = 3

Help Kids in Math

Introduction to help kids in math:
Mathematics is a group of terms which is used to declare various functions. In general mathematics is always based on the number system formats .
The following areas are covered in mathematics,they are integers, fractions, number types,algebra problems, geometry problems, measurement of shapes, trigonometry and calculus an etc.. Here, in this article will help kids to learn math.

Math topics with examples to help kids:


Here are some basic math topics to help kids.

Number system:

In number system we have many numbers to describe,they are

Positive number:

Positive number is a number which identified by the symbol  '+' . Generally the number starts with 1,2,3...

Example: 4+ 6 = 10   ( the result is also a positive number)

Negative number:

Negative number is a number which identified by the symbol ' - '. These numbers are starting with  -1 , -2 , -3 ....

Example : -4 + -6 = -10.

Fractions:

Fraction is a whole number which consist of two parts, they are numerator ( top part )  and the denominator ( the bottom part)

normally the numerator is greater than the denominator.

Example: 10 / 2.

Arithmetic operations:

The following operations are called arithmetic operations, they are , Addition, subtraction, multiplication and division.

Examples:

Addition:

Its a normal addition, just add the given values and place the larger number symbol

10 + 20 = 30

Subtraction:

Its a normal subtraction, just subtract the smaller number from the larger number and place the larger number symbol at the result.

10 - 20 = -10 .

Multiplication:

multiplication is a process of product the given values.

5 * 4 = 20 ( positive * positive =positive )

5 * (-4) =  -20 ) ( positive * negative = negative )

- 5 * 4 = -20 ( negative * positive = negative )

-5 * -4 20 ( negative * negative =positive )

Division:

Division properties also same like multiplication.

Example: 10 / 2  = 5.


Example math problems to help kids:


Let we see some algebra problems to help kids:

Solve the problem using order of operation method.

5( 2+3) - 10 +3( 5-2)

Solution:

step1 : As per the order of operations rule, we need to take the parentheses values

= 5 ( 2+3) - 10 + 3 (5-2)

= 5(5) - 10 +3 (3)

step2 : Multiply the values

= 25 - 10 +9

step3: add the values

= 25 +9 -10

= 34 - 10

step4 : subtract the values

= 24.

Math problem 2 ) 3x  - 5  =  25 where x = 10, check whether the x value satisfy the equation

solution: apply the x value in the above equation

3x - 5 = 25

3 ( 10 ) - 5  = 25

30 -5 =25

25 = 25 .

Answer : The x value is true and its satisfy the equation.

Solve : 3x + 6 = 12 -3x, find x value.

Solution:

step1: group the terms,we get

3x +3x = 12 - 6

6x = 6

step2:  divide by 6 on both sides,we get

6x / 6 = 6/6

x =1 .

Math problem3 )  a+ 2a+3a+4a+5a+6a -84 = 0 find the value of a.

Solution:

step1 : add all the coefficients of a ,we get

= a + 2a+3a+4a+5a+6a -84=0

21a - 84 = 0

step2: add 84 on both sides, we get

21a - 84 +84 = 0+ 84

21a = 84

step3: divide by 21 on both sides,we get

21a /21 = 84 / 21

a = 4

Math Grade Six Probability

Introduction math grade six probability:

Generally probability is defined as the ratio of the number do ways of an event occur to the total number of possible outcomes, probability is used in the area of statistics, finance, gambling and science.

Probability formula for math grade six probabilities

The probability of event P (A)  =no of possible events n (a) /the total number of the events n(s)


Example problem 1 - math grade six probability


Suppose a bag contains the number up to 1 to 10, find the probability of sleeting a prime number?

Solution:

Bag contains the number from 1 to 10 here we have to know which the prime number between the numbers 1 to 10 is

So the prime number is 2.3,5,7

So the probability p (prime) =4/10 or 2/5

Example problem 2 - math grade six probability

A quiz competition is conducted by the royal club there are 25 members are attended in the competition, in that 7 members are selected in the competition find the probability of the selected members

Solution:

There are 25 members are attended in the quiz competition (total number), 7 members are selected so the probability of the past person is 7/25

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Example problem 3 - math grade six probability

Find the probability of the red, blue and green color ball?

Solution:

From the given diagram w e can calculate the total number of balls.
So total number of balls=number of red color ball + blue color ball + green color ball

Total number of red color ball=5

Total number of blue color ball=4

Total number of green color ball=2

So the total number of red, blue and yellow color ball is

Probability of taking red color ball=5/11

Probability of taking blue color ball=4/11

Probability of taking green color ball=2/11

Example problem 4 - math grade six probability:

Find the probability of blue, yellow and pink color?

Solution:

Here the rectangle is divided into 8 parts, so the total number of divided part is 8

Here pink color is 2

Number of part colored with blue color is 2

Number of part colored with yellow color is 4

So the probability of pink color 2/8

Probability of blue color 2/8

Probability of blue color 4/8

Range in Math Terms

Introduction to range in math terms:

In math terms range is a difference between the maximum and minimum value in the set of numbers or elements. In math terms, group of numbers or elements is called set. A set can have finite number of elements. There are two steps to calculate the range the range of set of numbers.

Step 1: Arrange the numbers in ascending order by size.

Step 2: Subtract minimum value by maximum value.

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Range in Math Terms - Examples


Example 1: Calculate the range of set of numbers: {20, 30, 32, 51, 56, 64, 33, 35, 61, 27}

Solution:

Arrange the set of numbers in ascending order

{20, 27, 30, 32, 33, 35, 51, 56, 61, 63}

Range = Maximum value – Minimum value

= 63 – 20 = 43

Therefore range of set of numbers is 43.

Example 2: Calculate the range of set of numbers: {38, 44, 49, 57, 23, 54, 124, 158, 264, 142}

Solution:

Arrange the set of numbers in ascending order

{23, 38, 44, 49, 54, 57, 124, 142, 158, 264}

Range = Maximum value – Minimum value

= 264 – 23 = 241

Therefore range is 241.

Example 3: Ten student’s weight is as follows {37, 47, 87, 76, 99, 48, 75, 62, 57, 62}. Calculate the range.

Solution:

Arrange the set of numbers in ascending order

{37, 47, 48, 57, 62, 62, 75, 76, 87, 99}

Range = Maximum value – Minimum value

= 99 – 37 = 62

Therefore range of ten student’s height is 62.

Example 4: Ten student’s heights as follows {135, 122, 162, 172, 173, 142, 167, 144, 137, 160}.  Calculate the range of set of numbers:

Solution:

Arrange the set of numbers in ascending order

{122, 135, 137, 142, 144, 160, 162, 167, 172, 173}

Range = Maximum value – Minimum value

= 173 – 122 = 51

Therefore range of ten student’s height is 51.

Example 5: Calculate the range of set of numbers: {9.52, 7.25, 5.65, 10.47, 9.52, 12.60, 8.29, 5.20, 7.68, 4.34}

Solution:

Arrange the set of numbers in ascending order

{4.34, 5.2, 5.65, 7.25, 7.68, 8.29, 9.52, 10.52, 11.47, 12.6}

Range = Maximum value – Minimum value

= 12.6 – 4.34 = 8.26

Therefore range of set of numbers is 8.26.

Example 6: Twelve students’ marks in math as follows {37, 45, 100, 99, 75, 83, 67, 97, 39, 44, 48, 59}. Calculate the range of set of numbers:

Solution:

Arrange the set of numbers in ascending order

{37, 39, 44, 45, 48, 59, 67, 75, 83, 97, 99, 100}

Range = Maximum value – Minimum value

= 100 – 37 = 63

Therefore range of set of numbers is 63.

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Range in Math Terms - Practice


Problem 1: Ten students’ marks in math as follows {33, 55, 77, 51, 79, 48, 61, 76, 99, 27}. Calculate the range of marks.

Answer: 72

Problem 2: Calculate the range of set of numbers: {29, 29, 27, 29, 24, 54, 26, 42, 27, 95}

Answer: 71

Problem 3: Calculate the range of set of numbers: {3.45, 5.27, 8.25, 4.47, 8.52, 23.6, 14.9, 34.3, 27.87, 4.04}

Answer: 30.85

Distance and Rate Word Problems Math

Introduction to distance and rate word problem:

In mathematics education, the term word problem is often used to refer to any mathematical exercise where significant background information on the problem is presented as text rather than in mathematical notation. As word problems often involve a narrative of some sort, they are occasionally also referred to as story problems.

Here, we are going to see about word problems on distance and rate measurement in math. A few examples of word problems on distance and rate is given below which helps you for learning distance and rate word problems in math.

(Source: Wikipedia)

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Example of word problems on distance and rate:


Word problem 1:

Rohit left office and drove his car at the rate of 55 miles per hour for 3 hours. He stopped his car for few minutes and then he drove it for another 2 hours at the rate of 50 miles per hour to reach his home. Calculate how many miles did Rohit drive?

Solution:

The total distance travelled by Rohit is given by

Distance, D = (55 * 3) + ( 50 * 2)

= 165 + 100

= 265

So, total distance travelled by Rohit is 265 miles.

Word problem 2:

Nick travelled from place A to place B by bike in 4 hours. Chan travelled the same distance in 3 hours at a rate 30 miles per hour greater than Nick's. Calculate the distance between the two places.

Solution:

Let X be the rate at which Nick travelled between the two places.

Therefore, X + 30 be the rate at which Chan travelled between the two places.

So, the distance travelled by Nick is given by

Distance, D = Rate * Time = 4X ....................... (1)

Distance travelled by Chan is given by

Distance, D = Rate * Time = 3(X + 30) ............... (2)

From equation (1), we get

X = D/4

Substitute X = D/4 in equation (2).

D = 3(X + 30)

D = 3(D/4 + 30)

4D = 3(D + 120)

4D = 3D + 360

D = 360

Therefore, the distance between the two places is 360 miles.

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Homework problems:


1) Mick left from city A and drove his car at the rate of 70 miles per hour for 4 hours. He stopped his car for few minutes and then he drove it for another 4 hours at the rate of 60 miles per hour to reach city B. Calculate how many miles did Mick drive?

2) Morkel travelled from City A to City B by car in 3 hours. Joseph travelled the same distance in 2 hours at a rate 20 miles per hour greater than Morkel's. Calculate the distance between the two cities.

Solutions:

1) Total distance travelled by Mick is 520 miles.

2) Distance between the two cities 120 miles.

Math Word Problems Grade 9

Introduction to math word problem grade 9:

In mathematics, especially in the area of abstract algebra known as combinatorial group theory, the word problem for a recursively presented  group G is the algorithmic problem of deciding whether two words represent the same element. Although it is common to speak of the word problem for the group G strictly speaking it is a presentation of the group that does or does not have solvable word problem. (Source: Wikipedia)

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Example problems for math word problems grade 9:


Math word problems grade 9 – Example: 1

In the box 12 cards are placed as 1 to 12, mixed up thoroughly and  then a card is drawn at random from the box. if it is known that the number on the card is more than 3, find the probability that it is an even number.

Solution:

Let S be the sample space. then,

S = {1, 2, 3, 4, ......10, 11, 12}

Let A = Event of getting a card having a number more than 3.

And B = Event of getting a card having an even number.

Then, A = {4,5,6,7,8,9,10,11,12} and B = {2,4,6,8,10,12}

Therefore A B ={4,6,8,10,12}.

Therefore P(A) = `(n(A))/(n(S))` = `9/12` = `3/4`

P(B) = `(n(B))/(n(S))` = `6/12` = `1/12`

and P(A`nn` B) =`(P(AnnB))/(n(S))` = `5/12`

Suppose A has already occured and then B occurs.

Then, We have to find P(`B/A` )

Therefore P(`B/A` ) = P(A`nn` B) = `(P(AnnB))/(P(A))` = `(5/12)/(3/4)` = `(5/12 * 4/3)` = `5/9`

Math word problems grade 9 – Example: 2

The odds in favor of occurrence of an event 5:13. Find the odds against the occurrence of the event. Find the probability that it will occur.

Solution:

Odds in favor = `5/13`

Therefore Odds against = `13/5`

Number of favorable outcomes = 5

Number of unfavorable outcomes = 5 + 13

Required probability = `5/18`

Math word problems grade 9 – Example: 3

One card is drawn from a well shuffled deck of cards. Find the probability that the card is red ace.

Solution:

The number of possible outcomes n(s) = 52

Let A: getting a red ace card.

There are 2 red ace cards in the deck of the  cards n(A)  = 2.

P(ace) = P(A) = `(n(A))/(n(S))`

= `2/52`

= `1/26`

Math word problems grade 9 – Example: 4

A pair of dice is thrown. Find the probability of getting a doublet.

Solution:

When two dice are thrown, there are 36 sample points  n(S) = 36

A = {(1,1), (2,2), (3,3), (4,4), (5,5), (6,6)}

n(A) = 6

P(a doublet) = `(n(A))/(n(S))`

= `6/36`

= `1/6`

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Practice problems for math word problems grade 9:


1. A, B and C shoot to hit a target. If A hits the target 4 times in 5 trials; B hits it 3 times in 4 trials and C hits it 2 times in 3 trials, what is the probability that the target is hit by at least 2 persons?

[Answer: The required probability is 5/6]

2.A card is drawn from a well-shuffled deck of 52 cards and without replacing this card, a second card is drawn. Find the probability that the first card is a club and the second card is spade.

[Answer: `13/204` ]

Grade 10 Math Elimination

Introduction to Grade 10 math elimination:

Elimination method is used to solve if we have two unknown variables. In grade 10 math elimination we are going to solve word problems. In grade 10 math elimination problems we have to use the multiplication operation to eliminate the variables. After eliminating we will get the equation with one variable. Using that we have to find the x and y values. Here we will see an example problem for grade 10 math elimination method.

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Example problems grade 10 math elimination methods:


Example:

Solve the following equation using elimination method.

5x + y = 10

2x + 3y = - 9

Solution:

Given equations are,

5x + y = 10    ………………… (1)

2x + 3y = - 9     ...……………....  (2)

Here both variables having different co – efficient. So multiply the first equation with 3 for eliminating y.

15x + 3 y = 30   …………………. (3)

2x + 3 y = - 9    ………………… (4)

Now subtract 3 and 4

We get,

13x = 39

Now we have to divide by 13 on both side of the equation,

So x = 3

Now plug the value in any of the equation.

5(3) + y = 10

15 + y = 10

So y = - 5

In this the variables with values given in the equation directly. Now we will see an example to make an equation and then we have to solve.

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Example 2:


Alex and Jerry is have the total age is 30. Three years ago, the sum of twice Alex's age and three times Tom's age was 60 years. Find both of their ages using elimination method.

Solution:

Sum of Alex and Jerry’s age is 30

x + y = 30 ……………….. (1)

Three years ago gives x -3 and y – 3

2 (x – 3) + 3 (y – 3) = 60

2x – 6 + 3y – 9 = 60

2x + 3y - 15 = 60

2x + 3y = 75    ……………………. (2)

Multiply (1) with 2

2x + 2y = 60   .......................... (3)

2x + 3y = 75    ......................... (4)

Now subtract the equation

We get,

-y = - 15

So y = 15 (Jerry’s age)

From this Alex’s age x + 15 = 30 than x = 15

So Alex age = 15 and Jerry’s age = 15

These are the some example problems for grade 10 math elimination.

Fifth Grade Math Terms

Introduction to fifth grade math terms:

Learning fifth grade math terms is very necessary because it provides the foundation for solving various mathematical problems and also for learning basic operations in math.

In this article of fifth grade math terms, various fifth grade math terms are given.


Fifth grade math terms:


Algebraic equation

It refers to any equation that contains only algebraic expressions and signs of operations.

Algebraic expression

It consists of various algebraic terms connecting with the help of signs of operations.

Angles

Two rays form an angle with a common end point called the vertex.

Binomial

When an algebraic expression consists of two terms, it is called a binomial.

Circle

A circle is path traced by a point, which moves in a plane in such a way that its distance from a fixed point remains constant.

Collinear points

If three or more points lie on a line, then the points are called collinear points.

Complementary  angles

Two angles are said to be complementary if the sum is equal to 90o

Concurrent lines

If two or more straight lines pass through the same point, then they are called concurrent lines. The point through which the lines pass is known as point of concurrency.

Equivalent fractions

Fractions that show the same amount are called equivalent fractions.

Even numbers

The numbers, which are divisible by two are called even numbers

Fractions

A fraction whose numerator is less than its denominator is called a proper fraction. A fraction whose numerator is equal to or greater than the denominator is called improper fraction. The sum of a whole number and a proper fraction is called as mixed fraction. Fractions that show the same amount are called equivalent fractions.

Irrational numbers

A number which cannot be put in the form a/b, where a and b are integers and a is not equal to zero, is called an irrational number.

Like terms

Terms that differ in their numerical coefficients but do not differ in symbol are called like terms.

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Additional Fifth grade math terms:


Mixed fraction

The sum of a whole number and a proper fraction is called as mixed fraction.

Monomial

When an algebraic expression consists of only one term, it is called a monomial.

Natural Numbers

To count a given number of objects, we use numbers, which we call counting numbers or natural numbers. The numbers 1,2,3,4... are called natural numbers.

Obtuse angle

An angle, which is greater than 90o but less than 180o is called an obtuse angle.

Odd numbers

The numbers, which are not divisible by two, are called odd numbers.

Parallel lines

The lines that lie in the same plane and never intersect are called as Parallel lines.

Perpendicular lines

If two lines lie in the same plane and intersect at right angles, they are called perpendicular lnes.

Rational numbers

The numbers of  the form a/b , where a and b are integers and a is not equal to zero, are known as rational numbers.

Supplementary angles

The two angles are said to be Supplementary if the sum is equal to180o.

Trinomial

When an algebraic expression consists of three terms, it is called a trinomial.

Unlike terms

Terms may or may not differ in their numerical coefficient are called unlike terms.

Whole numbers

All natural numbers together with 0 form whole numbers.

Probability in Math

Introduction to Probability

In math,Probability is used to get the feasible outcomes in an event. It is definite as the ratio between the numbers of positive outcomes to the total number of outcomes. The importance of probability lies only between 0 and 1. The Conditional probability and  the Theoretical probability is the types of  the probability in math.


Example1:


In math the examples of probabilities is as follows.

1)In a vehicles parking area 200 vehicles are parked. There are 50 are cars, 40 are vans and the remaining are lorries. If all vehicles are similarly possible to leave, find the probability in math of.

a) First leaving the lorry.

b) First leaving the van.

c) First leaving the car.

Solution:

a) Let s be the sample space and A be the event of a lorry leaving first.

n(S) =200

n(A)= 200-50-40= 110

probability of a lorry leaving first:

P(A)= 110/200

=11/20

b) Let B be the event of a van leaving first

n(S)=200

n(B) =40

Probability of a van leaving first:

P(B)=40/200

= 4/50

c) Let c be the event of a car leaving first

n(S)=200

n(C)=50

Probability of a car leaving first:

P(C)=50/200

=5/40.

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Example2:


In math, the another example of probability is as follows,

2)An analysis was taken on 20 groups at a college to find the total number of left-handed students in each class.

Math 10.5 Answers

Introduction to Math 10.5 Answers:
The decimal numbers are one of the types of numbers in math. The decimal number system with digits before and after the decimal point should be named as in the form of place values. The place values of decimals before the decimal point is one’s, ten’s, hundred’s, and thousands, etc. The place values after the decimal point starts with ten’s, hundreds and thousands, etc. Here, shall we study about 10.5 math answers in this article.


Example Problems for Math 10.5 Answers


Decimal 10.5 Using Addition Operation in Math:

Problem 1:

Add 4.4 and 6.1?

Solution:

Let us add the two decimals in the given problem and the result should be the sum of the two decimals.

4.4 (addend)

6.1 (addend)

-------------

10.5 (sum)

-------------

The sum for adding 4.4 and 6.1 is 10.5.

Decimal 10.5 Using Subtraction Operation in Math:

Problem 2:

Subtract 43.8 and 33.3?

Solution:

Let us subtract the two decimals in the given problem and the result should be difference of the two decimals.

43.8 (minuend)

33.3 (subtrahend)

---------------

10.5 (difference)

---------------

The difference for subtracting 43.8 and 33.3 is 10.5.

Decimal 10.5 Using Multiplication Operation in Math:

Problem 3:

Multiply 21 and 0.5?

Solution:

Let us multiply the two decimals in the given problem and the result should be the product of the two decimals.

21 ×

0.5

-----------------

10.5

-----------------

The product of multiplying 21 and 0.5 is 10.5.

Decimals 10.5 Using Division Operation in Math:

Problem 4:

Multiply 9.45 and 0.9?

Solution:

Let us divide the two decimals in the given problem and the result should be the quotient of the two decimals.

0.9)9.45(

First we write the given decimals as by multiplying the decimals with 10 for dividend and divisor. Multiply the divisor 0.9 with 10 gives 9 and the dividend with 10 gives 94.5.

Let us continue with the division method.

9)94.5(1

9

-----------------

04

-----------------

The number 4 cannot go into 4. So, it can go into 45 for 5 times.

Number 9 go into 45 for 5 times.

9)94.5(105

9

--------------------

045

045

-------------------

0

--------------------

In the dividend, there is a decimal point after before one digit from the right hand side, so put the decimal point one digit before in the answer.

So, the quotient 105 should be 10.5.

The quotient for dividing 9.45 by 0.9 is 10.5.

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Practice Problems for Math 10.5 Answers


1. Add 9.5 and 1?

Answer: 10.5

2. Subtract 37.9 and 27.4?

Answer: 10.5

3. Multiply 4.2 and 2.5?

Answer: 10.5

4. Divide 68.25 by 6.5?

Answer: 10.5

6th Grade Math Practice

6th grade math practice:

In this article we discuss about 6th grade math practice problems and solutions. In this article we are going to discuss for 6th grade math topics. In each day life we are using arithmetical concepts often. 6th grade math practice cover following chapters

Numbers
Measures
Algebra
Geometry
Handling data.
The 6th  grade math practice solutions problems are given below.

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Example problems for 6th grade math practice:


Example 1:

Addition of integers: (+ 5) + (+10) =?

Solution:

The sum of positive number is a positive integer obtained by adding the two integers.

(+10) + (+10) = +20

Solution is 20

Example 2:

Subtraction of integers:

(+15) – (+4) =?

Solution:

To subtract an integer from another number, add the additive inverse of the second number to the first number.

(+15) – (+4) = 15 – 4 = 11

Solution is 11

Example 3:

Multiplication of integers:

(+18) * (+8) =?

Solution:

The product of two positive integers is a positive integer.

(+18) * (+8) = 18 * 8 = 144

Solution is 144

Example 4:

Division of integers:

(+50)/ (+5) =?

Solution:

Positive integer / positive integer = positive value

(+50)/ (+5) = 50/5 = 20

Solution is 10

Example 5:

Find the area of a rectangle with length 8.5 cm and breadth 8.4cm.

Solution:

Given length = 8.5 cm

Breadth = 8.4 cm

Area of a rectangle = l * b square unit

= 8.5 * 8.4 square unit

= 71.6

Area = 71.4 cm2

Example 6:

Find the area and perimeter of a rectangle with length 6.5 cm and breadth 5.4cm.

Solution:

Given length = 6.5 cm

Breadth = 5.4 cm

Area of a rectangle = l * b square unit

= 6.5 * 5.4 square unit

= 35.1

Area = 35.1 cm2

Perimeter of rectangle = 2 (l + b) unit

= 2 (6.5 + 5.4)

= 2 * 11.9

= 23.8

Perimeter = 23.8 cm

Example 7:

Solve 4a -10 = 30

Solution:

Given expression 4a -10 = 30

Add 10 on both sides

4a + 10 – 10 = 30+10

4a = 40

Divide 4 on both sides

4a/4 = 40/ 4

a = 10

Solution is 10

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Practice problems for 6th grade math :


Problem 1: Addition of integer (+5) + (+2) =?

Solution: 7

Problem 2: Subtraction of integer (+15) – (+12) =?

Solution: 3

Problem 3: Multiplication of integer (+8) * (+5) =?

Solution: 40

Problem 4: Division of integer (+20) / (+10) =?

Solution: 2

Problem 5: solve the area of a rectangle with length 5 cm and breadth 7cm.

Solution: 35cm2

Problem 6: Find the perimeter of a rectangle with length 5 cm and breadth 7cm.

Solution: 24 cm

Quick Probability Math

Quick Probability math Introduction:

Quick Probability is study of math. Probability is number of outcomes is divided into total number of events. The probability is also the expected value of the math. These are the two kinds of distribution are used discrete and continuous distribution.  The general format of the formula for quick probability

The probability of Event P (A) =` ("Number of outcomes na(a)")/("Total Number of events n(s)")`

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Quick Probability math Examples:


Quick Probability math– Example 1:

Toss three coins and find the probability of two tails. The possible outcomes are:

Solution:

Step 1:

n (s) = {TTT, TTH, THT, THH, HTT, HTH, HHT, HHH}=8

Step 2:

There are 3 tosses with only two tails:

n (a) = {TTH, THT, HTT}=3

Step 3:

Formula:

P (A) = n(a)/n(s)

Answer:

P (A) =` 3/8.`

Quick Probability math– Example 2:

To toss three coins and get the probability of two head and so one tails. The possible outcomes are:

Solution:

Step 1:

n (s) = {TTTT, TTTH, TTHT, TTHH, HTTT, HTTH,THHT, HTHH, THTT, TTHH, THHT, HTHH, HTHT, HTHH,HHHT, HHHH }=16

Step 2:

There are 3 tosses with only one head:

n (a) = { TTHH, HHTT, HTTH, THHT, HTHT, THTH}=6

Step 3:

Formula:

P (A) = n(a)/n(s)

Answer:

P (A) = `6/16.`

Quick Probability math Example 3:

Roll a dice; find the probability of obtain number 5.

Solution:

Total Number of possible = n (a) = {1, 2, 3, 4, 5, 6}

n (s) = 6

The number of outcomes n (a) = {5}

n (a) = 1

The probability of getting value = `1/6` .

Quick Probability math Example 4:

A coin is tossed. If the coin land on top of a container is filled with one black globe and three white spheres. If the coin landed on tails the container is filled with one black sphere and nine white spheres. A sphere is then selected from the container. What is the probability that the sphere selected is black?

Solution

Let H = Heads, T = Tails and B = Black sphere selected. Then by the law of total probability

P(B) = P(B|H)P(H) + P(B|T)P(T)

= (0.25)(0.5) + (0.1)(0.5)

P (B) = 0.175

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Quick Probability math practice problems:


Quick Probability math Practice problem 1:

To tossing the coin in one time what is the probability of get Head?

Quick Probability math Practice Problem 2;

If through the dice in one time what is the probability of get 6?

Quick Probability math Practice Problem 3:

If the probability of being correct is .95

Answer key:

½

`1/6`

0.05

How to do Percents in Math

Introduction to how to do percents in math:

How many hundreds are in a number is called its Percent. Express a number as a fraction part of 100 is known as percent.  The symbol used to denote the percent is %. For example 34/100 is 0.34 %.  In this article we will see about how to do percents in math with some example problems.

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How to do percents in math steps:


To solve percent for a single number that means how many percent is particular number we have to simple divide that umber by 100.
Example:

What is the percent of 45?

45 = `45/100 ` = 45%

To solve what percent “of p is q”:

We have to express the numbers as proportions


Keep the unknown number (that is how many %) as x.


Write percent as` x/100 `


Multiply the “of” quantity (that is p) with `x/100 `


Equate the above term with “is” quantity (that is q). Otherwise we can also write as `x/100` = is/of (`q/p` )

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Example problems on How to do percents in math:


Example 1:

What percent of 175 is 60?

Solution:

Percent = x%

`x/100 ` * 175 = 60

(or)

`x/100` = `60/175`

x= 34.28%

Hence 34.28% of 175 is 60.

Example 2:

What percent of 45 is 10?

Solution:

`x/100` = `10/45`

x= `10/45` *100

= 22. 22

Hence 22. 22% of 45 is 10.

Example 3:

What is 34% of 150?

Solution:

Here the unknown value is “is” quantity = x

(`34/100` ) *150 = x

(Or)

34 % = `x/150`

Rewriting the equation,

`x/150` = `34/100`

x = (`34/100` )* 150

= 51

Hence 34% of 150 is 51.

Example 4:

16 % of what number is 56?

Solution:

Now the equation becomes,

`16/100 ` * x = 56

X = 56 *(`100/16` )

X = 350

Hence 16% of 350 is 56

Example 5:

There are 55 balloons with Rajul. 18 of them blew away in air.  What percent of balloons are with him now?

Solution:

Total number balloons = 55

Number of balloons blew away = 18

Then,

The number of balloons remaining = 55-18

=37

Now we need to find how many percent is 37 in 55

(`X/100` ) * 55 = 37

`x/100` =` 37/55`

x = (`37/55 ` )*100

= 67.27

Hence 67.27% of balloons are with Rajul in hand

Basic Math Pre Algebra

Introduction of basic math pre algebra:

Basic math pre-algebra is a general name for a course in middle school mathematics. In the United States, it is normally taught between the seventh and ninth grades, although it may be necessary to take this course as early as sixth grade in order to advance to Calculus BC by twelfth grade. The purpose of pre-algebra is to prepare the student for the study of algebra.

[Source: wikipedia]

Addition & Subtraction

This part will help you better understand, work with and solve equations when they include addition and/or subtraction in them. Please express your views of this topic What is Dependent Variable by commenting on blog.


Explanation of basic math Pre algebra :


Important Things to Remember

Associative property: Three or more numbers are involved in associative property. Its nothing but a grouping of numbers.

Equation: 1

a + (b + c) = (a + b) + c

Any number plus 0 (zero) equals itself.

Equation: 2

a + 0 = a

Identity Property: If the value is added to the number the value remains unchanged.

Equation: 3

a = b

a + c = b + c

a - c = b - c

When answering equations remember to addition and subtraction are inverse operations they undo each other (i.e. 10 + 9 - 9 = 10). To answer equations by addition and subtracting, first decide which operation has be applied, then use the inverse operation to undo this (remember to add or subtract from both sides of the equation).

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Example and practice problems for basic math Pre algebra :


Some examples problem for learn basic math pre algebra concepts

1. The example for pre algebra to find x value x + 56 = 128

Solution:

x + 56 = 128 To variable through itself

(Isolate the variable).

x + 56 - 56 = 128 - 56 To undo adding 56, subtract

56 from both sides.

x = 72

2. Solve: x - 34 = 345

Solution:

x - 34 = 345You need to isolate the variable.

x - 34 + 34 = 345+ 34 To undo subtracting 34, add

34 to both sides.

x = 379

These are basic math pre algebra example problem

Math Fraction Problems

Introduction of math fraction problems:

Study fraction math (from the Latin fractus, broken) is a number that can represent part of a whole. The earliest fractions were reciprocals of integers: ancient symbols representing one part of two, one part of three, one part of four, and so on. A much later development were the common or "vulgar" fractions which are still used today (½, ?, ¾, etc.) and which consist of a numerator and a denominator in study fraction math.

Source: Wikipedia


Definition of math fraction problems:


In fraction are usually used in mathematics, science and the world impressive like us. They have been used by human sovereign while the time of the original Egyptians and are still used by public to solve problems in their day-by-day lives.

In study, fraction math came into regular use in the 16th century. Look at this study fraction math:

`4/8`

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Example problem for math fraction problems:


Example 1:

Alex had 130 teddy bears in his toy store. He sold `5/2`of them at $13 each. How much did he receive?

Solution:

Step 1: Find the number of teddy bears sold.

`5/2`*130=`(5*130)/(2)`

=`150/2`

= 75

He sold 75 teddy bears.

Step 2: Find how much money he received.

75 × 13 = 975

He received $975.

Example 2:

If Sam earns $15 in a week and spend $8, what part of his weekly salary did he save?

Solution:

Step 1: Numerator: amount saved=15-8=7

Step 2: Denominator: salary = $15

Step 3: Part or fraction

=`(15-8)/(15)`

=`(7)/(15)`

Answer is `7/15`

Example 3:

15 is `1/3`of what number?

Solution:

Step 1: Assign variables:

Let x = number

Step 2: Solve the equation

15=`1/3`x

Isolatevariable x
x=15*3=45

Answer: The number is 45.

Example 4:

Nick spent `5/9`of her allowance on foodstuff and shopping. What fraction of his allowance had he left?

Solution:

=1-`5/9`

=`9/9`-`5/9`

=`(9-5)/(9)`

=`4/9`

He had`4/9`of his allowance left.

Practice problem for math fraction problems:

Problem 1:

A class has 30 girls and 30 boys. What part of the class are boys?

Answer: `1/2` of the class are boys

Problem 2:

18 is 2 of what number?

Answer: The number is 9.

Functions of Math

Introduction for functions of math:

Before giving the explanation of the function in math, we have to know, what are functions of math? The function is nothing that gives the result for the given argument. The argument is also know and element of the function from the given set. Function is associated with domain and co domain. The element exists in domain is also exactly one element in co domain. Having problem with Definition of a Function keep reading my upcoming posts, i will try to help you.


Pre-requisite for functions of math:


Constant and Variable:

The value will not be changed during the mathematical process is called constant. The value will be changed during the mathematical process is called variable.

Interval:

The subset of real number is called interval

Neighborhood.

In a number line the neighborhood of a real number is defined as an open interval of very small length.

Independent / Dependent Variable:

A variable is an independent variable when it has any arbitrary value. A variable is said to be dependent when its value depends on other variables.

Cartesian product:

The Cartesian product of the two sets A and B is denoted by A x B and is denoted as

Let A={ a1,a2,a3} B={b1,b2}

A x B={ (a1,b1),(a1,b2)(a2,b1)(a2,b2)(a3,b1)(a3,b2)}


Explanation for functions of math:

A function is a special type of relation. If no two ordered pairs have same first element and deferent second element, the relation is called function. If two ordered pairs have same first element and deferent second element, the relation is called not a function. If the element x in the set A is associated with element x in the set B is called image of the function. The set of images is called range of the function. If the range of function in not equal to the co domain, those functions are called mapping. Please express your views of this topic Triple Integrals by commenting on blog.


Types in functions of math:


1. Identity function:

A function from a set A to the same set A is said to be an identity

2. Inverse of a function:

To define the inverse of a function f i.e. f−1 (read as ‘f inverse’), the

function f must be one-to-one and onto.

3. Constant function:

If the range of a function is a singleton set, the function is called a

constant function.

4. Linear function:

If a function f : R → R is defined in the form f(x) = ax + b then the function

is called a linear function. Here a and b are constants.

5. Polynomial function:

If f : R→R is defined by f(x) = an xn + an − 1 xn − 1+ …+ a1x + a0, where

a0, a1,…, an are real numbers, an≠0 then f is a polynomial function of degree n.

Solve Math Percent Problem

Introduction to solve math percent:

In mathematics, a percentage is a way of expressing a number as a fraction of 100 (per cent meaning "per hundred" in French). It is often denoted using the percent sign, "%", or the abbreviation "pct". For example, 45% (read as "forty-five percent") is equal to 45 / 100, or 0.45. Let us see how to computing percentages.                                                       - Source from Wikipedia


Solve math percent problem:


For converting a fraction and a decimal to a Percentage, multiply it by hundred.
For converting a percentage to a fraction and decimal, divide by hundred.
We can write a fraction and a decimal as a percentage.

Having problem with Converting a Decimal to a Fraction keep reading my upcoming posts, i will try to help you.

Examples for solve math percent problem:


Problem 1:

What is the percentage of 79%?

Solution:

` 79 /100` = 0.79

71% is 0.79

Problem 2:

What is the percentage of 93%?

Solution:

` 93/ 100` = 0.93

93% is 0.93

Problem 3:

How to add 22% to 89?

Solution:

22% + 89 = 0.22 + 89 = 89.22

Problem 4:

Solve 2`1/ 2` % as a fraction

Solution:

2`1 / 2 ` % =  `(2 (1 / 2)) / 100 ` = `5 / (2 * 100)` = `1 / 40`

Problem 5:

A basket contains 250 eggs. 150 were not broken. What percentages of the eggs were broken?

Solution:

Number of eggs                       = 250

Number of eggs not broken    = 150

Total No. of eggs broken        = 250 – 150 = 100

Broken egg's Percentage       = `100 / 250` * 100 = 40%

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Problem 6:

A school hall has 900 seats. 450 of them are occupied. What percentages of the seats are occupied?

Solution:

Number of seats of a school hall    = 900

Number of seats occupied              = 450

Percentage of the seats occupied   = `450 / 900` * 100 = 50%

Problem 7:

What is the percentage of 84.5% of 46?

Solution:

= 84.5 =` (84.5) / 100` = 0.845 * 46

= 38.87

Problem 8:

What is the percentage of 88% of 22?

Solution:

= 88% = 88 /100 = 0.88

0.88 * 22 = 19.36

Therefore 19.36 is 88% of 22.

Problem 9:

What percentage of 2.75 is 25?

Solution:

Percentage = `25 / 275` * 100 = 9.09%

Problem 10:

What percentage of 50 is 10?

Solution:

Percentage = `10 / 50` * 100 = 20%

Practice problem for solve math percents:

Problem 1:

What is the percentage of 28%?

Solution:

= 0.28.

Problem 2:

What is the percentage of 64%?

Solution:

= 0. 64

Problem 3:

What is the percentage of 22% of 72?

Solution:

= 15.84

Therefore 15.84 is 22% of 72.

Problem 4:

What is the percentage of 24% of 68?

Solution:

= 16.32

Therefore 16.32 is 24% of 68.

Commutative Math

Commutative Math Introduction:

Commutative math is the property. The commutative is change the order but cannot change the answer. More math problems and theorems are depends on commutative math. The commutative math is simple operations, it is such that addition and multiplication. The following formulas for using the commutative math,

Commutative Math Formulas:

X + Y = Y + X

X .Y = Y. X

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Commutative Math Problems:


Using Math commutative law Example 1:

You can commutative math when you add:

3 + 6 = 6 + 3

9       =      9

Answer is same but the order is different. That is called commutative math.

You can commutative math when you multiply:

2 × 4 = 4 × 2

8      =      8

Answer is same but the order is different. That is called commutative math.

The math Commutative Law of Addition Example 2:

Write an equivalent expression for 8 + 6x

The math Commutative Law is swap of the addition so 6x + 8 would be an equivalent expression.

The math Commutative Law of Multiplication Example 3:

Write and equivalent expression for x (2 + z)

The math Commutative Law is swap of the multiplication so (2 + z) x would be an equivalent expression.

Using Math commutative law Example 4:

You can commutative math when you add:

7 + 3 = 3 + 7

10 = 10

Answer is same but the order is different. That is called commutative math.

You can commutative math when you multiply:

7 × 3 = 3 × 7

21    =    21

Answer is same but the order is different. That is called commutative math.

The math Commutative Law of Addition Example 5:

Write an equivalent expression for 6 + 8x

The math Commutative Law is swap of the addition so 8x + 6 would be an equivalent expression.

The math Commutative Law of Multiplication Example 6:

Write and equivalent expression for y (15 + z)

The math Commutative Law is swap of the multiplication so (15 + z) y would be an equivalent expression.

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Practice Problems for Commutative Math:


Identify which law is being used.

x (yz) = x (zy)

Identify which law is being used.

(x + y) + z = (y + x) + z

Answer key:

Multiplication Law

Addition Law

Math Subtraction Word Problems

Introduction to math subtraction word problems
Subtraction is one of the fundamental arithmetic operations in math. Subtraction is the inverse of addition. In math subtraction is denoted by minus (-) sign. If ‘a’ and ‘b’ are real numbers then the expression ‘a-b’ is called difference. Here ‘a’ is called the minuend and b is subtrahend. Consider this expression ‘c-b=a’ then ‘c’ is called minuend, ‘b’ is called subtrahend, and ‘a’ is called difference. Understanding Find the Probability is always challenging for me but thanks to all math help websites to help me out.


Examples for word problems on subtraction in math


Ex 1: Jack has $2154 . Jack and John has $3156 . Find the amount John has.

Sol:

(Amount of Jack and John) - (Amount of Jack) = (Amount of John)

3156 – 2154 = 1002

John has$1002 .

Ex 2: The price of a fridge is 542 dollar and the price of an oven is 4814 dollar. What is the difference between the prices of the two products?

Sol:

Price of a fridge – Price of a oven = difference between the price of 2 products

4814 – 542 = 4272

The difference between the prices of the two products is 4272 dollar.

Ex 3: There are 245 balls in a bag. During an event, 185 balls were taken. How many balls were not taken?

Sol:

245 – 185 = 60

60 balls were not taken.

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More word problems on subtraction in math


Solved  subtraction (of fraction )word problems

Ex 1: A cement mixture needs 2/5 bucket of water and 3/5 cement. How much more water does the cement mixture need?

Sol:

The fact that the problem is asking how much more water the mixture needs is an indication that

3/5 is bigger than 2/5

3/5 - 2/5 = 1/5

The water is 1/5 of a bucket more than the cement.

Ex 2: A basket ball player advances 3/4 of a yard. A second player in the same team advances 6/5 of a yard. How much more yard did the second player advance?

Sol

6/5 - 3/4 = 9/20

9/12 is just a bit less than half.

So, the second player advanced by about half of a yard more.

Ex 3: Rosy lives 4/9 mile from the Museum of Arts. Sheba leaves 2/5 mile from the Museum of Arts. How much closer is Sheba from the museum?

Sol:

The fact that the word problem is saying how much closer Sheba is an indication that 2/5 is smaller than 4/9

4/9 - 2/5 = 2/45

Sheba is closer to the museum by 2/45 mile.

You can also say that Roy is further away by 2/45 mile.

Math Division Decimals

Steps for math division decimals:

Given: how do math division (decimals) positive integers x and y.

Result: non-negative integers q and r such that x=yq+r, and 0=r
Steps you need to do for math division decimals:

Step 1: Begin by setting Q=0 and R=x.

Step 2: if R
Step 3: If R=y, subtract b from R, increase Q by 1, and go back to step 2.

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Introduction of math division decimals:


I think, you are interested in the math division decimals of integers, so you need to do task consists of finding the quotient and the remainder in the math division decimals of two positive integers. Do most of ”quotients, remainders” and you bring to mind a picture like this:

24
50 | 1200
100
200
200
0
In this example, we are dividing 1200 by 50 and we are find the quotient to be 24 and the remainder to be 0 using dividing 1200 by 50. The algorithm has the dividend and the divisor as its given value; in the example these are, respectively, 1200 and 50. The result consists of the quotient and the remainder, which, in the example, are 24 and 0, respectively.

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Concept of math division decimals:


Consider the division decimals 203 % 5= 20 remainder 3. It may also be written as

`203/5` =20+(`3/5`)

In math division decimals using algorithm, 203 is called the dividend, 5 the divisor, 20 the quotient, and 3 the remainder. The relation between these four quantities can also be expressed as 203=10x20+3.

In fact, given any positive integers x and y (y not equal to 0) there exist unique integers q and r, where 0= r
x=yq+r

This theorem is referred to as the math division decimals or the division identity.

If you need to do divide x by y (y not equal to 0), we get `x/y`=q=`r/y`, which makes the algorithm almost self-evident:

When x is divided by y we get x quotient q and x remainder r, 0 =r

Math Related Articles

Introduction to math related articles:

Mathematics is the study of quantity, structure, space, and change. Mathematicians seek out patterns, formulate new conjectures, and establish truth by rigorous deduction from appropriately chosen axioms and definitions.(Source: From Wikipedia). Now, we are going to discuss about the following math related articles:

1) Simultaneous equations article and

2) General slope form article.


Some math related articles explanation:


Simultaneous equations article:

In algebra, the simplest technique of linear system involves two equations and two variables:

3x+3y=6

4x+2y=5

Here, x and y are the two variables. Generally, a letter is used to denote the variable in the expression or equation.

The following methods are used to solve the simultaneous equations:

1) Substitution method

2) Elimination method

3) Matrix method

4) Graphing method.

Article on general slope form:

The slope (m) of a line in the plane containing the x and y axes is generally represented as

m = Δy / Δx

Δy = y2-y1

Δx = x2-x1

When the two points (x1, y1) and (x2, y2) are known, then the general formula to find the slope, m = (y2-y1) / (x2-x1)

Slope Intercept Form is used to create the straight line equation with a y-intercept (b) and slope m of the line.

General slope Intercept Form:  y = m x + b

b = y-intercept of the line,

m = Slope of the line.

The graph of this equation is a straight line.

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Worked math related articles examples:


Example problem related to Simultaneous equations:

Solve the simultaneous equations by substitution method:

x + y = 20 -------equation (1)
3x + 11y = 100 ------equation (2)

Step 1: From equation (1)

x + y = 20

Subtract x on both sides of the equation

x + y –x = 20 –x

y = -x +20------------------Equation (3)

Substitute the equation (3) in equation (2)

3x + 11y = 100

3x + 11(-x +20)=100

3x -11x +220=100

-8x +220=100

Subtract 220 on both sides of the equation

-8x +220 -220=100 – 220

-8x=-120

Divide by -8 on both sides of the equation

-8x/-8=-120/-8

x = 15

Step 2: Substitute the value x in equation (1)

x + y = 20

15+y=20

y=5

So, the solution is (15, 5).

Example problem related to general slope form:

Find the slope of the equation and then find the slope-intercept form of an Equation through the given points (0, 2) and (3, 8)?

Solution:

(x1 , y1)= (0, 2)

(x2 , y2)= (3, 8)

From the slope formula,

m= (y2-y1)/(x2-x1)

m= (8-2)/(3-0)

m=6/3

m=2

Substitute m=2 and one point (0,2)  in the below equation,

y - y1 = m(x - x1)

y - 2= 2*(x - 0)

y - 2 = 2x

y = 2x + 2

This is the general slope intercept form for the given two points.

Here, m= slope =2 and y-intercept b=2.

Math Decimal Division

Introduction to math decimal division:

Decimal:

The decimal number system is defined as the number system in which it has 10 as its base.Example for decimal number system is 0, 1, 2, 3, 4, 5,……..

Division:

The division is defined as the splitting of a number or any objects into the (equal)same part or into groups, the symbol used for division in math is ‘ / ’.Example for division is as follows,

24/2 = 12.


Math decimal division:


In math decimal division , the basic and the standard division type is Long division.Using long division we can divide numbers with complex or multi complex digit numbers.The following math problem shows the example problem for long division. I like to share this Decimal Calculator with you all through my article.

125.5

5)627.5

5

12

10

27

25

2.5

2.5

--------

0

-------

Explanation:

step 1: 5x1 = 5.

step 2: 6 - 5 = 1.

step 3: 5x2 = 10.

step 4: 12 - 10 =2.

step 5: 5x5 = 25.

step 6:27.5-25 = 2.5.

step 7:5x0.5 = 2.5

0step 8:2.5-2.5 = 0.

So the answer is 125.5.

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Example and practice problems for math decimal division:


Example problems:

Example 1:

Compute the math decimal division 36.3 by 6.

Solution:

Step 1 : 360.3 can be written as 6x6x10+3.

Step 2 : So 6x6x10/6 = 6x10.

Step 3 : 6x10 = 60.

Step 4 : Then divide 0.3/6 = 0.05.

Step 5: The answer is 60+0.05 =60.0.5

Example 2:

Compute the math decimal division 4201.50 by 3.

Solution:

Step 1 : 4200.50 can be written as 2x3x7x10x10+1.5

Step 2 : So 2x3x7x10x10/ 3 = 14x10x10

Step 3 : 14x100 = 1400.

Step 4 : Then divide 1.5/3 = 0.5

Step 5 : The answer is 1400+0.5=1400.5.

Example 3:

Compute the math decimal division 56.25 by 2.

Solution:

Step 1 : 56.25 can be written as 2x4x7+0.25.

Step 2 : So 2x4x7/2= 4x7.

Step 3 : 4x7 = 28.

Step 4 :Then divide 0.25/2 = 0.125

Step 5 : The answer is 280+2.5=282.5.

Example 4:

Compute the math decimal division 366.6 by 6.

Solution:

Step 1 : 366.6 can be written as 2x3x61+0.6

Step 2 : So 2x3x61/6 = 61.

Step 3 : Then divide 0.3/6 = 0.05

Step 4 : 61+0.05 = 61.05

Step 5 : The answer is 610.5.

Example 5:

Compute the math decimal division 440.32 by 8.

Solution:

Step 1 : 440.32 can be written as 2x2x11xx10+0.32.

Step 2 : So 2x2x2x5x11/8 = 5x8x11/8.

Step 3 : 5x11 = 55.

Step 4 :  Then divide 0.32/8= 0.04

Step 5 : 55+0.04 = 55.04.

Step 6 : The answer is 55.04.

Practice problems:

Problem 1:

Compute the math decimal division 433.75/2.

Solution:

The answer is 216.875

Problem 2:

Compute the math decimal division 481.650/3.

Solution:

The answer is 160.55

Problem 3:

Compute the math decimal division 765.88/6

Solution:

The answer is 127.647

Problem 4:

Compute the math decimal division 95.90/10

Solution:

The answer is 9.59.

Inference and Predictions

Introduction:

Inference is the process of sketching a conclusion by pertaining hints. That is based on anonym or hypotheses; or by interpolating the next rational step in an intuited model. This conclusion drawn is said to be an inference. The laws of suitable inference are deliberated in the field of logic.

The prediction is a statement that is about the things will happen in future. And these can be frequently but not based on experience or knowledge forever. I like to share this Mann Whitney Wilcoxon Test with you all through my article.


Description of inference:


Human inference:

It is studied within the field of cognitive psychology.
Artificial intelligence researchers developing the automated inference systems to emulate human inference.


Accuracy of inductive inferences:

Inductive reasoning is the process that a conclusion is inferred from multiple annotations.
Conclusion may be correct or incorrect and correct to within an assured extent of accuracy, or correct in certain situations.
Conclusions inferred from multiple observations may be tested by supplementary annotations.


Examples of deductive inference:

Greek philosophers explained a number of syllogisms should be correct three-part deduction. And that can be used as building blocks for more composite logic. Few of them from that will be shown below:

All men are mortal
Socrates is a man
Therefore, Socrates is mortal


Validity of inference is to be depends on form of inference. That is word "valid" could not refer to the reality of the locations or the conclusion. These can be rather to the form of the inference. An inference is valid even if parts should be false. And should be invalid even when the parts are true. But valid form with true premises will have a true conclusion forever. Understanding Solve Partial Fractions is always challenging for me but thanks to all math help websites to help me out.


Description of prediction:


The overlapping between prediction and forecast should be a statement.
In this, some outcome is predictable, while a forecast may wrap a range of possible outcomes.


Informal prediction from hypothesis:

Outside the meticulous framework of science, prediction is confused with informed guess or opinion always.
A prediction of this type may be valid when the forecaster is a knowledgeable person in the field and is utilizing sound analysis and accurate data.
Large corporations spend deeply in this type of activity to help focus concentration on possible events, risks and business opportunities, using futurists.

Finding Quadratic Functions

Introduction:

In mathematics, quadratic equations are the polynomial equation of the second degree. The general form is,

ax^2 + bx + c = 0

where x represents the variable, and a, b, and c, constants, with a ? 0. (If a = 0, the equation becomes a linear equation.)

The constants a, b, and c respectively known as the quadratic coefficient, the linear coefficient and the constant term or free term. The term "quadratic" came from quadratus, which is the Latin word for "square." Quadratic equations could be solved by factoring, completing the square, graphing, Newton's method, and using the quadratic formula (given below). One common use of quadratic equations are to compute trajectories in projectile motion.


Quadratic Formula Explanation:


Often, the simplest way to solve "ax^2 + bx + c = 0" for the value of x is to factor the quadratic, set each factor equal to zero, and then solve each factor. While factoring could not always be successful, the Quadratic Formula can always find the solution.

The Quadratic Formula uses the co-efficient "a", "b", and "c" from "ax^2 + bx + c", where "a", "b", and "c" are just numbers; they are the "numerical coefficients". The Formula is derived from the process to complere the square, and is formally stated as:

For ax^2 + bx + c = 0, the value of x is given by: x = (-b ± v(b2 - 4ac)) / 2a

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Discriminant:


In the above formulae, the expression underneath the square root sign is called the discriminate of the quadratic equation, and is often represented using an upper case Greek Delta:

? = b^2 - 4ac

A quadratic equation with real co-efficients can have either one or two distinct real roots, or two distinct complex roots. In this case the discriminant defines the number and nature of the roots. There are three cases:

(1) If the discriminant is positive, then there should be two distinct roots, both of which are real numbers. For quadratic equations with integer co-efficients, if the discriminant is a perfect square, then the roots are rational numbers in other cases they may be quadratic irrationals.

(2) If the discriminant is zero, then there must be exactly one distinct real root, sometimes called a double root:

x = -b/2a.

(3) If the discriminant is negative, then there is no real roots. Rather, there are two distinct complex roots, which are complex conjugates of each other.

Thus the roots may distinct if and only if the discriminant is non-zero, and the roots are real if and only if the discriminant is non-negative.

Discrete Math Solution

Introduction to discrete math solution

Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous. In contrast to real numbers that have the property of varying "smoothly", the objects studied in discrete mathematics – such as integers, graphs, and statements. Discrete objects can often be enumerated by integers. More formally, discrete mathematics has been characterized as the branch of mathematics dealing with countable sets. (Source: wikipedia)

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Discrete math solution example problem

Example 1:

Prove that (Z, +) is an infinite abelian group.

Solution:

(i) Closure axiom:

We know that sum of two integers is again an integer.

(ii) Associative axiom:

Addition is always associative in Z i.e., ?a, b, c ? Z, (a + b) + c = a + (b + c)

(iii) Identity axiom:

The identity element O ? Z and it satisfies O + a = a + O = a, ? a ? Z Identity axiom is true.

(iv) Inverse axiom:

For every a ? Z, ? an element - a ? Z such that - a + a = a + (- a) = 0

Therefore Inverse axiom is true.

Therefore (Z, +) is a group.

(v) ? a, b ? Z, a + b = b + a

Therefore Addition is commutative. ? (Z, +) is an abelian group.

(vi) Since Z is an infinite set (Z, +) is infinite abelian group.

Example 2: Let G be the set of all rational numbers except 1 and * be defined on G by a * b = a + b - ab for all a, b ? G. Show that (G, *) is an infinite abelian group.

Solution: Let G = Q - {1}

Let a, b ? G. Then a and b are rational numbers and a ? 1, b ? 1.

(i) Closure axiom: Clearly a * b = a + b - ab is a rational number. But to prove a * b ? G, we have to prove that a * b ? 1.

On the contrary, assume that a * b = 1 then

a + b - ab = 1

? b - ab = 1 - a

? b(1 - a) = 1 - a

? b = 1 (‡ a ? 1, 1- a ? 0)

This is impossible, because b ? 1. ? Our assumption is wrong.

Therefore a * b ? 1 and hence a * b ? G.

Therefore Closure axiom is true.

(ii) Associative axiom:

a * (b * c) = a * (b + c - bc)

= a + (b + c - bc) - a (b + c - bc)

= a + b + c - bc - ab - ac + abc

(a * b) * c = (a + b - ab) * c

= (a + b - ab) + c - (a + b - ab) c

= a + b + c - ab - ac - bc + abc

Therefore a * (b * c) = (a * b) * c ? a, b, c ? G

Therefore Associative axiom is true.

(iii) Identity axiom: Let e be the identity element.

By definition of e, a * e = a

By definition of *, a * e = a + e - ae

? a + e - ae = a

? e(1 - a) = 0

? e = 0 since a ? 1

e = 0 ? G

Therefore Identity axiom is satisfied.

(iv) Commutative axiom:

For any a, b ? G, a * b = a + b - ab

= b + a - ba

= b * a

Therefore * is commutative in G and hence (G, *) is an abelian group. Since G is infinite, (G, *) is an infinite abelian group. Please express your views of this topic math tutor free online by commenting on blog.


Discrete math solution practice problem


Problem 1:

Show that the set G = {2n / n ? Z} is an abelian group under the multiplications.

Problem 2:

Show that the set of all positive even integers forms a semi-group under the usual addition and multiplication. Is it a monoid under each of the above operations?

Math Interactive Activity

Introduction to math interactive activity:

Interactive math activity provides the way of solving the basic math problems. This interactive activity deals with problems in calculus, pre-calculus and algebra problems with answers. All the problems are explained with step by step solutions and it provides interactive way of learning activity. Math comprises of all the topics, only certain category problems are discussed here. The following are some of the example problems which show the interactive math activity with answers. I like to share this Statistics Hypothesis Testing with you all through my article.


Math interactive activity example problems:


Example 1:

Reduce the expression

4(g -1) + 2k - 5(g -d -4) + 5

Solution:

Given algebraic expression is

4(g -1) + 2k - 5(g -d -4) + 5

Multiplying the integer terms

= 4g - 4 + 2k -5g + 5d + 20 + 5

Grouping the above terms

= -g + 7k + 21

Example 2:

Differentiate the given function and find the critical numbers.

f(a) = | a - 8 |

Solution:

The given function f has set of real numbers. Then substitute sqrt (s 2) = | s | to change function f as follows

f(a) = sqrt (s 2) , with s = a - 8

Using the chain rule, f '(a) is given by

f '(a) = (1/2) 2 s d'(z) / | s |

Since d '(a) = 1, f '(a) simplifies to

f '(a) = (a - 8) / | a - 8 |

Where f ' is undefined at a = 8 and 8 is in the domain of f. a = 8 is a critical number for the given function.

Example 3:

Determine s (4) and k(4) and s(4) / k(4) and the functions k and s is given as

s (z) = 3z - 8 and k (z) = z 2 - 12

Solution:

Calculate s(4)

s(4) = 3(4) - 8 = 4

Calculate k (4)

k (4) = 4 2 - 12
= 16 -12 = 4

s (4) / k (4) =4/4 =1

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Math interactive activity practice problems:


1) Determine s (4), k (4) and s (4) / k (4) and the functions s and k is given as

s (y) = 4y - 6 and k (y) = y 2 - 20

Answer: s (4) / k (4) = -5/2

2) Reduce the algebraic equation     6(-8z - 3) - (-5z - 5) = -8(2z + 4) + 9

Answer: z = 10/27

Math Question Solver

A thinker who focuses on the problem as started and tries to synthesize information and knowledge to achieve a solution. Learning how to solve problems in math knows what we look for. Math problem often requires established procedures and knowing what and when to apply them.

To identify procedures, we have to be familiar with the problem situation and should be able to collect appropriate information, identify a strategy and use the strategy appropriately. G. polya wrote a book in 1957 named ‘how to solve it’. Many of the ideas that worked are continue to work for us now.

Problem solving requires practice, the more you practice, the better you get. Please express your views of this topic First Derivative by commenting on blog.


Types of Math Question Solver

Math question solver uses four steps to solve problem, they are:

Clues
read the problem carefully.
Underline the clue words.
Ask yourself that you have seen a similar problem. If so what similarity about it?
What did you need to do further?
What facts are given?
What we need to find out?


2.   Game Plan

Define the game plan.
Have you ever came across a problem like this?
Define our strategies to solve the problem.
Try the defined strategies.
3.   Solve

Use the strategies to solve the problem
4.  Reflect

This part crucial. Look the solution which we got.
Does it seem to be probable?
Did you answered the question?
Are you sure of the result?
Did you answered using language in the question?
Same units?

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Instance of Math Question Solver


Clue words for addition are:

sum
total
in all
perimeter
Clue words for subtraction are:

difference
how much more
exceed
Clue words for multiplication are:

product
total
area
times


Clue words for division are:

share
distribute
quotient
average
Although clue words will vary slightly, we will find that it will guide us to the correct operation

Math Linear Algebra

Introduction to linear Algebra:

The bunch of mathematics that handles with the theory of systems of number systems , matrices, vector spaces, determinants, and linear equations.
A mathematical package and vector space with scalars from a related field, the multiplication of which is of the method (aA) (bB) = (ab) (AB), here scalars are a and b and vectors are A and B.

Description about linear algebra with application:


In linear algebra the following types are used, they are

Matrices and Systems of Equations

Determinants

Vector Spaces

Linear transformations

Orthogonally

Eigenvalues

Numerical linear algebra

Iterative methods

Descriptions:

Matrices and systems equations:

Its Rectangular array of real numbers
It contains m rows by n columns
It should be Named using capital letters
The First subscript is row, second subscript is column
Determinants

The determinant is defined as a special method related with any square matrix. The basic geometric, the determinant is defined as scale factor for calculating if the matrix is consider as a linear transformation.
Vector Spaces

It’s a mathematical calculated shaped by a group of vector: objects will be connected together and multiplied ("scaled") by figures, called scalars.
Orthogonality

It’s a relation of opposition between the things at right angles and it’s a quality of lying or intersecting at right angles
Numerical linear algebra

By using this technique we can easily perform the linear algebra calculations. Here we used some algorithms to find out the matrix operations. It is also used to perform the fundamental engineering concepts and some science related problems.

Application of linear algebra with solutions


The following applications are used in the linear algebra , they are

Application 1 - Its used to find the Least Square approximation
Application 2 -We can use the linear algebra in Traffic Flow, Electrical Circuits and Determinant
Application 3 -We can build the curves and surfaces which is passing the given the particular points.
Application 4 -In inheritance, its widely used to discover the solution,
Application 5 -We can use the technique in cryptography and graph theory.


Solve the solution for following linear equation.

1) 7x-6 = 3x-8

Step1: here subtract 3x from both the sides, we get

Solution:

7x-3x-6 = 3x-3x-8

4x-6 = -8

4x = -8+6

4x = -2

x= -1/2

x =-1/2

Input and Output Math

Input and Output Math:

The input and output in math means when we have some standard method, we have to substitute some value in the given standard method, in result we will get some other value. In this, the standard method is known as rule and the value we are substituting is input value and the value we are getting after substitution and deriving is result, that result is known as output.  We use most of the input and output in math is in function rule.


Input and output math In function:

In Function rules, we have some rule in terms of variables here we have to substitute different values for one variable from that we can get the output value.

Writing function rules from tables
Writing tables from Function rules
Graphing Tables and Function rules
Writing Function Rules from Graphs
In this table it contains two values one refers to input value and the other is output value. The output value can be obtained by substituting the input value in the given equation. The Graphing table it contains two values one is input and the other is output value. Using this graphing table we can mark the ordered pair in a graph and draw the corresponding graphs.


General guidelines about Input and Output math

In general,

Let us take this equation y=Ax+B ,

Where A and B are constant numbers, and  x and y are input and output variables and their value changes

With this equation we can get different output value for y when we substitute different  input values for x.

Sample problem:

Step 1: Let us consider we have the function rule as f(x) =x+2

Step 2: Let f(x) =y, so the given equation is y=x+2

Step 3: Now we have to substitute x=0, 1, 2, 3 and 4 we will get the y value as 2, 3, 4 ,5 and 6

Step 4: The x values are inputs and y values are output value

This is a graph for the function f(x)=x+2 that is y=x+2

Adding Algebraic Expressions

Introduction to Adding algebraic expression:

Adding algebraic expression mean nothing but  combine the like terms  should not change the dislike terms. Expressions are a central concept in algebra .We can group the variables and constants to make algebraic expressions. A simple algebraic expressions like x + 3, y – 5, 4x + 5,10y – 5.Algeberic expression contains variables and constants. A variable can take various values. The value is not fixed. On the other hand, a constant has a fixed value. Examples of constants are: 4, 100, and 17


Example for Adding algebraic expression and concepts:


Example for algebraic expression:

Algebraic Expressions are obtained:

x^ 2, 2y^2,

1. Given algebraic expression x^ 2 is obtained by multiplying the variable x by itself;

x × x = x^ 2

Just as 4 × 4 is written as 42, we write x × x = x^ 2. It is commonly read as x squared

2. The expression 2y^2 is obtained from y: 2y^2 = 2 × y × y

Here by multiplying y with y we obtain y^2 and then we multiply y^2 by the constant 2

Example for adding algebraic expression:

Example 1: Adding algebraic:

2x^ 2+3x^ 2=5x^ 2 (add the like terms)

4xy+6xy+3y+4=10xy+3y+4 (arrange the terms and then add the like terms)

7xy-5xy+4z+6yz=2xy+4z+6yz

=2xy+2z(1+3y)(Taking common outside)

Basic concept Terms in algebraic expression

Terms of algebraic expression:

An algebraic function contains  two terms those are the like terms and dislike terms For example, in the expression 8xy – 5x + 6xy – 4,look at the terms 8xy and 6xy. The factors of 8xy are 8, x and y. The factors of 6xy are 6,x and y.
On the other hand the terms 8xy and –5x, have different algebraic factors.They are unlike terms. Similarly, the terms, 8xy and 4, are unlike terms. Also, the terms –5x and 4 are unlike terms. Understanding Variables and Expressions is always challenging for me but thanks to all math help websites to help me out.

Example problems in adding algebraic expression:


Steps in adding algebraic expression:

Procedure for adding algebraic function:

1.       Add 4x+4 +7y+5x+6

STEP 1: First we can add the co-efficient of x values (4x+5x) (like terms)=>9x

STEP 2: Second step we can add the  co-efficient of y values (7y)=>7y   (4x+7y is the unlike terms)

Step 3: Third step we can add the constant values (4+6)=10

STEP 4:  Adding the whole expression 9x+7y+10

Example problems in adding algebraic expression:

Example 1:

Adding the expression:   5xy+7xy+7z+6y-2xy+4yz

Solution:

5xy+7xy+7z+6y-2xy+4yz (given terms)

=5xy+7xy-2xy+6y+4yz+7z (arranging the like and dislike terms)

=12xy-2xy+6y+4yz+7z (Adding the like terms)

=10xy+6y+4yz+7z (perform the operation)

=10xy+2y(1+2z)+7z(Taking common terms)

Solve Cosecant

Introduction to solve cosecant:

In trigonometry functions we study about the trigonometry terms to find weather the value of the right angle or any angle of the right angle triangle is found. These values are study through the trig terms like sine (sin), cos (cosine) and tan (tangent). We also have inverse trigonometry functions for sine as cosecant, cosine as secant and tangent as cotangent . By using solve trig terms we can solve the trigonometry terms and find the accurate values. Let us study about trig terms with some examples.

Formulas for Trigonometric Functions:

1. `sin^2theta + cos^2theta =1`

2.  `sin 2theta` = `2 sin theta cos theta`

3. `cos 2theta` =` 1 - 2 sin^2 theta`

4. `""1/(sec theta)` = `cos theta`

5. `sin (-theta)` = `- sin theta`

6. `" cos ` = `cos theta`

7.  `"e^(+-jtheta) ` = `cos theta`   ± `j sin theta`

8.` 1 + tan^2 theta ` = `sec^2 theta`

9.` tan (a +- b)` = `(tan a +- tan b)/(1+- tana tan b) `


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Solve Cosecant Problems:

Solve cosecant problem 1:

Solve trigonometric equation :  4 cosec x - 8 = 0

Solution:

Given trigonometric equation is  4 cosec x - 8 = 0

Add  by 8 on both sides.we get

4 cosecx - 8+ 8 = 8

4 cosecx = 8

Now, Both sides divided by 4. so we get the equation is

`(4cosec x)/4` = `8/4` .= 2

cosec x = 2.

So, x = cose-1 2 .

x = `(pi/6)` .

But the cosec term is positive in First and second quadrants. so , cosec`(pi - pi/6)` = cosec `((5pi)/6)`.

and   sin`((5pi)/6)` = 2 .

So, The solutions are . x = `(pi/6)`and x = `((5pi)/6)`

Solve cosecant problem 2:

Solve trigonometric equation :  5cosec x - 5 = 0

Solution:

Given trigonometric equation is  5cosec x - 5 = 0

Add  by 5 on both sides.we get

5 cosecx - 5+ 5 =5

5 cosecx = 5

Now, Both sides divided by 5. so we get the equation is

`(5cosec x)/5` = `5/5` .= 1

cosec x = 1.

So, x = cose-1 1 .

x = `(pi/2)`

So, The value of x = `(pi/2)` .