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.