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Chapter 7 – Fractions

The following Topics and Sub-Topics are covered in this chapter and are available on MSVgo:

Introduction

With fractions, life becomes simple. Say on your friend’s birthday, you order a pizza for yourself and your friends. On receiving the pizza, you open the box and discover that it is not cut into slices. If you cut in 8 slices and have 8 friends, then there are 1/8 portions of pizza for friends. Thus, application of fractions is for our everyday lives. The simplest form of a fraction is just having a numerator and a denominator. Let’s read on to understand fractions in a better way.

Fractions can be represented on a number line. 

Steps to make a fraction number line:

  1. First, draw the number line with the whole numbers.
  2. Find the denominator of the fraction which we want to show or represent in the number line.
  3. Mark the points which are total as that of the denominator.
  4. Write the fractions with the denominator and the numerator.

 Figure showing fractions represented in the number line.

Fractions of the value more than the number 0 and less than 1 are called proper fractions. Here, the numerator is smaller than the denominator. But when a fraction has a greater or equal numerator to that of the denominator, then the fraction is improper. An improper fraction is 1 or more than 1. 

Example of a proper fraction is 2/3

Here 2 is the numerator and 3 is the denominator. 2 is less than 3 or numerator is less than the denominator.

  • A mixed fraction is an integer and also has a fractional part. 
  • An improper fraction is a form of the fraction, but here the numerator is larger than the denominator.

Let us consider this with an example. But remember that in the improper fraction the numerator is greater than the denominator.

In the fraction 8/7, 8 is greater than 7, so it is an improper fraction.

They can be converted among mixed fraction and improper fraction without altering the values of the numbers.

Equivalent fractions are those which have different numerator and denominator yet they have the same value.

Example, 4/8 and 5/10 are both equal to ½. So, they are comparable in nature. They depict the same parts of the whole.

Fractions can be compared if the denominators are common. If they are different denominators, then they need to be converted to a common denominator. Then the numerators can be compared. Two fractions are comparable only when they depict the same parts of a whole entity.

Addition and subtraction of fractions can be done in a few steps:

  1. The fractions need to have a common denominator.
  2. If they are different denominators, they need to be converted into a common denominator.
  3. With a common denominator, adding or subtracting the numbers in the numerator is possible.
  4. The solution is with the new numerator, which is over the denominator.

Addition and Subtraction also take place in mixed fractions.

Here are the steps:

  1. First, convert mixed fractions to improper fractions.
  2. Then add the improper fractions with a common denominator.

 

Like Fractions

When a group of two or more fractions have the same denominator, then they are known as like fractions.

Fractions are nothing but the numbers which show various parts of the whole. So when you have a whole number or a group or even a bunch of objects, and you divide them into several equal parts, each of the individual portions becomes a fraction. A fraction is usually written with a numerator and a denominator.

  • How do you work out a fraction?

Ans: For working on a fraction of any number, it is required for you to divide the number by the fraction and multiply this answer by its numerator.

Example: Working out 4/8 of 48.

First of all, let us divide 48 by the denominator:

So 48 ÷ 8 = 6 (this gives 1/8 of 48)

The next step is to multiply the solution by the numerator:

6 × 4 = 24 (this gives you 4/8 of 48)

  • What are the 3 types of fractions?

Ans: They are:-

  1. Proper fractions: Here the denominator is less than the denominator.
    For example, 5/12
  2. Improper fractions: Here, the numerator is greater than the denominator.
    For example, 15/12
  3. Mixed fractions: It is when the integer, as well as a proper fraction, are combined.
    For example, 1 3/8
  • What is a fraction for kids?

A fraction describes the parts of a whole number or even the number of several equal parts. So a fraction explains the number of parts of a number.

For example, 1/2, 7/8.

Another example, if you are two friends and you are dividing the apple into 2, then each portion of the apple is 1/2.

  •  What is an easy way to learn fractions?

The parts of a whole are fractioned. It is nothing but a ratio between two integers which are separated by / or _ sign. The upper part of this fraction is the numerator, and lower is the denominator.

  •  How do you find the 3/4 of a number?

Three portions of a number four are represented by ¾, or it is ¾ times the number. The number can be multiplied by the number by 3, and then it can be divided by 4 or if you can, divide the number by 4 and then multiply it by 3.

Example, 3/4 x 24 = 3 x (24 / 4) = 3 x 6 = 18.

  • What is a fraction in simple words?

Fractions illustrate the equal parts of a whole or a or collection. It can be obtained by dividing a whole or a collection into various equal parts, each part being a fraction of the whole. Example, if there are 10 cups, then 1 cup is 1/10 of the whole.

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