NCERT Solutions Class 6th Maths Chapter – 7 Fractions All Examples

Example 1. Express the following as mixed fractions-

(a) 17/4
(b) 11/3
(c) 27/5
(d) 7/3

Solution –

(a) 17/4

i.e. 4 whole and 1/4 more, or 4 1/4

(b) 11/3

i.e. 3 whole and 2/3 more, or 3 2/3

[Alternatively, 11/3 = 9 + 2/3 = 9/3 + 2/3 = 3 + 2/3 = 3 2/3]

Try (c) and (d) using both the methods for yourself.
Thus, we can express an improper fraction as a mixed fraction by dividing the numerator by denominator to obtain the quotient and the remainder. Then the mixed fraction will be written as Quotient Remainder/Divisor.

Example 2. Express the following mixed fractions as improper fractions-

(a) 2 3/4
(b) 7 1/9
(c) 5 3/7

Solution –

(a) 2 3/4 = 2 + 3/4 = 2 × 4/4 + 3/4 = 11/4

(b) 7 1/9 = (7 × 9) + 1/9 = 64/9

(c) 5 3/7 = (5 × 7) + 3/7 = 38/7

Thus, we can express a mixed fraction as an improper fraction as
(Whole × Denominator) + Numerator/Denominator.

Example 3. Find the equivalent fraction of 2/5 with numerator 6.

Solution –

We know 2 × 3 = 6. This means we need to multiply both the numerator and the denominator by 3 to get the equivalent fraction.

Hence, 2/5 = 2 × 3/5 × 3 = 6/15 ; 6/15 is the required equivalent fraction.

Example 4. Find the equivalent fraction of 15/35 with denominator 7.

Solution –

We have 15/35 = ▢/7

We observe the denominator and find 35 ÷ 5 = 7. We, therefore, divide both the numerator and the denominator of 15/35 by 5.

Thus, 15/35 = 15 ÷ 5/35 ÷ 5 = 3/7.

Example 5. Find the equivalent fraction of 2/9 with denominator 63.

Solution –

We have 2/9 = ▢/63
For this, we should have, 9 × ▢ = 2 × 63.
But 63 = 7 × 9, so 9 × ▢ = 2 × 7 × 9 = 14 × 9 = 9 × 14
or 9 × ▢ = 9 × 14
By comparison, ▢ = 14.
Therefore, 2/9 = 14/63.

Example 6. Compare 4/5 and 5/6.

Solution –

The fractions are unlike fractions. Their numerators are different too. Let us write their equivalent fractions.

4/5 = 8/10 = 12/15 = 16/20 = 20/25 = 24/30 = 28/35 = ………..
and 5/6 = 10/12 = 15/18 = 20/24 = 25/30 = 30/36 = ………..

The equivalent fractions with the same denominator are-
4/5 = 24/30 and 5/6 = 25/30
Since, 25/30 > 24/30 so, 5/6 > 4/5

Note that the common denominator of the equivalent fractions is 30 which is 5 × 6. It is a common multiple of both 5 and 6.

So, when we compare two unlike fractions, we first get their equivalent fractions with a denominator which is a common multiple of the denominators of both the fractions.

Example 7. Compare 5/6 and 13/15.

Solution –

The fractions are unlike. We should first get their equivalent fractions with a denominator which is a common multiple of 6 and 15.

Now, 5 × 5/6 × 5 = 25/30, 13 × 2/15 × 2 = 26/30
Since 26/30 > 25/30 we have 13/15 > 5/6.

Example 8. Subtract 3/4 from 5/6.

Solution –

We need to find equivalent fractions of 3/4 and 5/6, which have the same denominator. This denominator is given by the LCM of 4 and 6. The required LCM is 12.

Therefore, 5/6 – 3/4 = 5 × 2/6 × 2 – 3 × 3/4 × 3
= 10/12 – 9/12 = 1/12.

Example 9. Add 2/5 to 1/3.

Solution –

The LCM of 5 and 3 is 15.
Therefore, 2/5 + 1/3 = 2 × 3/5 × 3 + 1 × 5/3 × 5
= 6/15 + 5/15 = 11/15.

Example 10. Simplify 3/5 = 7/20

Solution –

The LCM of 5 and 20 is 20.
Therefore, 3/5 – 7/20 = 3 × 4/5 × 4 – 7/20 = 12/20 – 7/20
= 12 – 7/20 = 5/20 = 1/4.

Example 11. Add 2 ⅘  and 3 ⅚

Solution – 

2 ⅘ + 3 ⅚
= 2 + 4/5 + 3 + 5/6 = 5 + 4/5 + 5/6

Now 4/5 + 5/6 = 4 × 6/5 × 6 + 5 × 5/6 × 5
(Since LCM of 5 and 6 = 30)

24/30 + 25/30 = 49/30 = 30 + 19/30 = 1 + 19/30
Thus, 5 + 4/5 + 5/6 = 5 + 1 + 19/30 = 6 + 19/30 = 6 19⁄30

And, therefore, 2 ⅘ + 3 ⅚ = 6 19⁄30. 

Example 12. Find 4 ⅖ – 2 ⅕

Solution –

The whole numbers 4 and 2 and the fractional numbers
2/5 and 1/5 can be subtracted separately.
(Note that 4 > 2 and 2/5 > 1/5)
So, 4 ⅖ – 2 1⅕ = (4 – 2) + (2/5 – 1/5) = 2 + 1/5 = 2 ⅕.

Example 13. Simplify- 8 1⁄4 = 2 5⁄6

Solution –

Here 8 > 2 but 1/4 < 5/6. We proceed as follows-
8 1⁄4 = (8 × 4) + 1/4 = 33/4 and 2 5⁄6 = 2 × 6 + 5/6 = 17/6

Now, 33/4 – 17/6 = 33 × 3/12 – 17 × 2/12 (Since LCM of 4 and 6 = 12)
= 99 – 34/12 = 65/12 = 5 5⁄12.