Chapter 2: Fractions and Decimals

Solution:-

Rani ate 2/7 part of a cake while her brother Ravi ate 4/5 of the remaining. Part of the cake left is 1/7.

Now, let us assume total part of cake be 1.

Then, from the question, given that Rani ate 2/7 part of a cake = 1 – (2/7)

= (7 – 2)/7

= 5/7

So, Ravi ate 4/5 of the remaining cake = (4/5) × (5/7)

= 4/7

Therefore, the part of the cake left = (5/7) – (4/7)

= 1/7

Solution:-

The reciprocal of 3/7 is 7/3

The reciprocal of a non-zero fraction is obtained by interchanging its numerator and denominator.

Solution:-

2/3 of 27 is 18.

= 2/3 × 27

= 2 × 9

= 18

Solution:-

4/5 of 45 is 36.

= 4/5 × 45

= 4 × 9

= 36

Solution:-

4 ×
is equal to 76/3

First we have to convert the mixed fraction into an improper fraction
= 19/3

Then, 4 × 19/3

= 76/3

Solution:-

½ of
is 15/7.

First we have to convert the mixed fraction into an improper fraction
= 30/7

Then, ½ × (30/7)

= 15/7

Solution:-

1/9 of 6/5 is 2/15.

= (1/9) × (6/5)

= (1/3) × (2/5)

= 2/15

Solution:-

The lowest form of the product
× (7/9) is (17/9) or

First we have to convert the mixed fraction into an improper fraction
= 17/7

Then, (17/7) × (7/9)

= 17/9

=

Solution:-

(4/5) ÷ 4 is equal to 1/5.

= (4/5) ÷ 4

= (4/5) × (¼)

= (1/5) × (1/1)

= 1/5

Solution:-

2/5 of 25 is 10

= 2/5 × 25

= 2 × 5

= 10