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.