# EXERCISE – 2.2

Q1. Which of the drawings (a) to (d) show:

(i) 2 x 1/5

SOLUTION:-

2 X (1/5) Represents the addition of 2 figures each represents 1 shaded part out of given 5 equal parts .

2 x (1/5) is represented by figure(d).

(ii) 2 x 1/2

SOLUTION:-

2 x 1/2  represents the addition of 2 figures each represents 1 shaded parts out of given 2 equal

parts.

2 x 1/2   is represented by fig (b).

(iii) 3 x 2/3

SOLUTION:-

3 X (2/3) represents the addition of 3 figures each represents 2 shaded parts out of the given 3 equal parts

3 x (2/3) is represented by fig (a).

Q3. Multiply and reduce to lowest form and convert into a mixed fraction:-

(i) 7 x 3/5

SOLUTION:-

By the rule of multiplication of fraction

Product of fraction = ( product of numerator) /( product of denominator)

Then,

= (7/1) x (3/5)

= ( 7 x 3 ) / (1 x5 )

= (21/5)

= 4.2

(ii) 4 x (1/3)

SOLUTION:-

By the rule multiplication of faction,

Product of fraction= ( product of numerator)/ ( product of denominator)

Then,

= (4/1) x (1/3)

= (4 x 1 ) / (1 x 3 )

= (4/3)

=  1.3

(iii) 2 x (6/7)

SOLUTION:-

= 12/7

= 1.7

(iv) 5 x (2/9)

SOLUTION:-

= (10/9)

= 1.1

(v) (2/3) x 4

SOLUTION:-

= (8/3)

= 2.6

(vi) (5/2) x 6

SOLUTION:-

= (30/2)

= 15

(vii) 11 x 4/7

SOLUTION:-

= (44/7)

= 6.2

(viii) 20 x 4/5

SOLUTION:-

= 80/5

= 16

(ix) 13 x (1/3)

SOLUTION:-

= (13/3)

= 4.3

(x) 15 x (3/5)

SOLUTION:-

= (45/ 5)

= 9

(a) ½ of the circles in box (a)

(b) 2/3 of the triangles in box (b)

(c) 3/5 of the squares in the box (c)

SOLUTION:-

(i) From the question,

We may observe that there are 12 circles in the given box. So, we have to shade ½ of the circles in the box.

= 12 x ½  = 12/2

= 6

So we have to shade any 6 circles in the box.

(ii) From the question,

We may observes that there are 9 triangles in the given box. so, we have to shade 2/3 of the triangles in the box.

= 9 x (2/3)

= 18/3

= 6

(iii) From the question,

We may observes that there are 15 squares in the given box. So, we have to shade 3/5 of the squares in the box.

= 15 x(3/5)

= 45/5

= 9

Q5. Find:

(a) ½ of (i) 24 (ii) 46

SOLUTION:-

(i) 24

We have,

= ½ x 24

= 24/2

=12

(ii) 46

We have,

= ½ x 46

= 46/2

= 23

(b) 2/3 of (i) 18 (ii) 27

SOLUTION:-

(i) 18

We have,

= 2/3 x 18

= 2 x 6

= 12

(ii) 27

We have,

= 2/3 x 27

= 2 x 9

= 18

(c) ¾ of (i) 16 (ii) 36

SOLUTION:-

(i) 16

We have,

= ¾ x 16

= 3 x 4

= 12

(ii) 36

We have,

= ¾ x 36

= 3 x 9

= 27

(d) 4/5 of (i) 20 (ii) 35

SOLUTION:-

(i) 20

We have,

= 4/5 x 20

= 4 x 4

= 16

(ii) 35

We have,

= 4/5 x 35

= 4 x 7

= 28

Q6. Multiply the express as a mixed fraction:

(a) 3 x 26/5

SOLUTION:-

= 78/5

(B) 5 X 27/4

SOLUTION:-

= 135/4

(C) 7 X 9/4

SOLUTION:-

= 63/4

(D) 4 X 19/3

SOLUTION:-

= 76/3

(E) 13/4 X 6

SOLUTION:-

= 78/4

(F) 17/5 X 8

SOLUTION:-

= 136/5

Q7. Find:

(a) ½ of (i) 11/4 (ii) 38/9

SOLUTION:-

By the rule of multiplication of fraction,

Product of fraction = (product of numerator) / ( product of denominator)

Then,

= ½ x (11/4)

= (1×11) / (2 x 4)

= (11/8)

(ii) By the rule of multiplication of fraction

Product of fraction = (product of numerator)/(products of denominator)

Then,

= ½ x (38/9)

= (1 x 38) / (2x 9)

= (38/18)

= 19/9

(b) 5/8 of (i) 23/6 (ii) 29/3

SOLUTION:-

(i) By the rule multiplication of fraction,

Product of fraction = ( product of numerator) / ( product of denominator)

Then,

= (5/8) x (23/6)

= (5 x 23) /(8 x 6)

= (115/48)

(ii) By the rule of multiplication of fraction,

Product of fraction = (product of numerator ) / (product of denominator)

Then,

= (5/8) x (29/3)

= (5 x 29) / (8×3)

= (145/24)

Q8. Vidya  and pratap went for a picnic . their mother gave then a water bottle that contained 5 liters of water . vidya consumed 2/5 of the water . pratap consumed the remainning the water .

(i) How much water did vidya drink ?

(ii) What fraction of the total quantity of water did pratap drink ?

SOLUTION:-

(i) From the question , it is given that ,

Amount of water in the water bottle = 5 liters

Amount of water consumed by vidya = 2/5 of 5 liters

= (2/5) x5

= 2 liters

So the total amount of water drank by vidya  is 2 liters

(ii) From the question it is given that

Amount of water in the water bottle = 5 litres

Then ,

Amount of water consumed by pratap = (1-water consumed by vidya)

= ( 1 – (2/5))

= (5 – 2) /5

= 3/5

Total amount of water consumed by pratap = 3/5 of 5 liters

= (3/5) x 5

= 3 liters