Fractions

In grade IV, we have learnt equivalent fractions, comparison of fractions, addition and subtraction of fractions.

Let's Learn these fraction topics in detail.

• Fraction as Division
• Mixed Numbers and Improper Fractions
• Express Improper Fractions as Mixed Numbers
• Express Mixed Numbers as Improper Fractions
• Equivalent Fractions
• Fractions in the lowest terms
• Comparison of Fractions
• Addition and Subtraction of Fractions with Unlike Denominators
• Multiplying a Fraction and a Whole Number
• Multiplying a Fraction by Another Fraction
• Division of Fractions

Fraction as Division

We know, Division is equal sharing. If we share 10 toffees among 5 children equally, each of them will get 2 toffees.
That is 10 ÷ 5 = 2 or 10/5 = 2.
If we share 1 toffee between 2 children equally, each of them will get half of a toffee.
That is 1 ÷ 2 or ¹⁄₂ toffee.

Mixed Numbers and Improper Fractions

A combination of a whole number and a proper fraction is called a mixed number.

2 1/2, 5 2/3, 10 1/3 are mixed numbers
A fraction whose numerator is greater than or equal to its denominator is called an improper fraction.

3/2, 5/2, 7/7, 10/4 are improper fractions.

Express Improper Fractions as Mixed Numbers

To express an improper fraction as a mixed number, divide the numerator by its denominator. The quotient will be the whole number part of the mixed number and the remainder so obtained will be the numerator of the fractional part. The denominator of the fractional part will be the same as the denominator of the improper fraction.

Numerator = 13,
Denominator = 3
when we divide 13 by 3, we get quotient as 4 and remainder as 1.
Hence, 13/3 = 4 1/3

More Examples

Express Mixed Numbers as Improper Fractions

To express mixed numbers as improper fractions, multiply the whole number with the denominator of the proper fraction, and add that product to the numerator. The result will be the numerator of the mixed number. The denominator is unchanged.

Numerator of the improper fraction = (whole number x denominator of the Mixed Number) + Numerator of the Mixed Number
Denominator of the improper fraction = denominator of the Mixed Number

5 1/3 = (5 x 3) + 1/3 = 16/3

More Examples

Equivalent Fractions

In the first image, 1/3 portion is shaded. In the second picture, 2/6 portion is shaded.
We can see that, even though, number of cells are different, the size of the shaded portion is same.
So, the fraction representing the shaded portion also same.
Hence, 1/3 = 2/6

Hence, all the below fractions are Equivalent Fractions.
Multiply the numerator and the denominator of the first fraction with 2, 3, 4 and 5

1/3 = 2/6 = 3/9 = 4/12 = 5/15

Divide the numerator and the denominator of the first fraction with 2, 3

6/12 = 3/6 = 2/4 = 1/2

Fractions in the lowest terms

A fraction is said to be in its lowest term or the simplest form, when its numerator and the denominator do not have any common factor other than 1.
So, to convert a fraction to its lowest term, just divide the numerator and the denominator with their highest common factor.

Comparison of Fractions

When two fractions have the same denominator, then the fraction having the greater numerator is greater than the other.
We use the below symbols to compare.
> (is greater than),
< (is less than) and
= (is equal to)
Let's compare 4/9 and 7/9
Both the fractions have the same denominator. since 4 < 7, we can say, 4/9 < 7/9
Let's compare 5/7 and 2/7
Both the fractions have the same denominator. since 5 > 2, we can say, 5/7 > 2/7
(ii) Comparison of fractions with the same numerator

When two fractions have the same numerator, then the fraction having the smaller denominator is greater than the other.

We learnt how to compare fractions with the same numerator and fractions with the same denominator. To compare fractions with unlike numerator and denominator, as a first step, we need to convert the given fractions into either same numerator or same denominator.
In the following example, we will convert the fractions into equivalent fractions of same denominator.

Here both fractions have unlike numerator and denominator. To convert these two fractions into equivalent fractions having same denominator, we need to multiply the numerator and the denominator with a number so the denominator becomes the Least Common Multiple (LCM) of those denominators.
LCM of 5 and 4 is 20,
so, we need to multiply 1/5 with 4 (both numerator and denominator) and multiply 3/4 with 5 (both numerator and denominator).
So, 1/5 and 3/4 becomes 4/20 and 15/20
Since, 4 < 15, 4/20 < 15/20
Hence, 1/5 < 3/4
Compare 3/11 and 5/7

Here both fractions have unlike numerator and denominator.
LCM of 11 and 7 is 77,
so, we need to multiply 3/11 with 7 (both numerator and denominator) and multiply 5/7 with 11 (both numerator and denominator).
So, 3/11 and 5/7 becomes 21/77 and 55/77
Since, 21 < 55, 21/77 < 55/77
Hence, 3/11 < 5/7

Addition and Subtraction of Fractions with Unlike Denominators

In previous classes, we learnt the addition and subtraction of fractions with like denominator.
To add or subtract two fractions with unlike denominators, we first convert them into fractions with like denominators. We learnt how to do that in the above section.
Example 1: Add 1/12 and 5/6
1/12 + 5/6 = 1/12 + 5 x 2/6 x 2
= 1/12 + 10/12
= 1 + 10/12
= 11/12
(12 is the LCM of 12 and 6, the denominators.)

Multiplying a Fraction and a Whole Number

We know, multiplication is the process of repeated addition.
So, multiplying a Fraction and a Whole Number is the process of adding that fraction to itself that many number of times as represented by the whole number.
Multiply 3 and 1/2
3 x 1/2 = 1/2 + 1/2 + 1/2
= 1 + 1 + 1/2
= 3 x 1/2
= 3/2

Multiplying a Fraction by Another Fraction

To multiply a group of fractions, we need to multiply the numerators and denominators separately. The product of the numerators will form the numerator of the result and the product of the denominators will form the denominator of the result.

Division of Fractions

To divide a fraction by another fraction or a whole number, we just need to multiply the first fraction with the multiplicative inverse of the second fraction (or the whole number).