## Chapter 2 Fractions and Decimals Exercise 2.2

**Question 1: Which of the drawings (a) to (d) show:(i) 2 × (1/5) (ii) 2 × 1/2 (iii) 3 × 2/3 (iv) 3 × 1/4 **

**Answer:**

(i) 2 × 1/5 represents figure (d).

(ii) 2 × 1/2 represents figure (b).

(iii) 3 × 2/3 represents figure (a).

(iv) 3 × 1/4 represents figure (c).**Question 2: Some pictures (a) to (c) are given below. Tell which of them show:(i) 3 × (1/5) = (3/5) (ii) 2 × (1/3) = (2/3) (iii) 3 × (3/4) = 2 1/4**

**Answer:**

(i) 3 × 1/5 = 3/5 represents figure (c).

(ii) 2 × 1/3 = 2/3 represents fig (a).

(iii) 3 × 3/4 = 2 1/4 represents figure (b).

**Question 3: Multiply and reduce to lowest form and convert into a mixed fraction:**

(i) 7 × (3/5)

Answer:

(i) 7 × (3/5)

Answer:

= 7/1 × 3/5

= 7 × 3/1 × 5

= 21/5

= 4 1/5

**(ii) 4 × (1/3)**

Answer:

Answer:

= 4/1 × 1/3

= 4 × 1/1 × 3

= 4/3

= 1 1/3

**(iii) 2 × (6/7)**

Answer:

Answer:

= 2/1 × 6/7

= 2 × 6/1 × 7

= 12/7

= 1 5/7

**(iv) 5 × (2/9)**

Answer:

Answer:

= 5/1 × 2/9

= 5 × 2/1 × 9

= 10/9

= 1 1/9

**(v) (2/3) × 4**

Answer:

Answer:

= 2/3 × 4/1

= 2 × 4/3 × 1

= 8/3

= 2 2/3

**(vi) (5/2) × 6**

Answer:

Answer:

= 5/2 × 6/1

= 5 × 6/2 × 1

= 30/2

= 15

**(vii) 11 × (4/7)**

Answer:

Answer:

= 11/1 × 4/7

= 11 × 4/1 × 7

= 44/7

= 6 2/7

**(viii) 20 × (4/5)**

Answer:

Answer:

= 20/1 × 4/5

= 20 × 4/1 × 5

= 80/5

= 16

**(ix) 13 × (1/3)**

Answer:

Answer:

= 13/1 × 1/3

= 13 × 1/1 × 3

= 13/3

= 4 1/3

**(x) 15 × (3/5)**

Answer:

Answer:

= 15/1 × 3/5

= 15 × 3/1 × 5

= 45/5

= 9

**Question 4: Shade:**

(i) 1/2 of the circles in box (a)

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

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

(i) 1/2 of the circles in box (a)

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

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

**Answer:**(i) 12 × 1/2 = 12/2 = 6

(ii) 9 × (2/3) = 18/3 = 6

(iii) 15 × 3/5 = 45/5 = 9

**Question 5: Find:(a) 1/2 of (i) 24 (ii) 46Answer:**(i) 24

= 1/2 × 24

= 24/2

= 12

(ii) 46

= 1/2 × 46

= 46/2

= 23

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

Answer:

Answer:

(i) 18

= 2/3 × 18

= 2 × 6

= 12

(ii) 27

= 2/3 × 27

= 2 × 9

= 18

**(c) 3/4 of (i) 16 (ii) 36**

Answer:

Answer:

(i) 16

= 3/4 × 16

= 3 × 4

= 12

(ii) 36

= 3/4 × 36

= 3 × 9

= 27

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

Answer:

(i) 20

Answer:

= 4/5 × 20

= 4 × 4

= 16

(ii) 35

= 4/5 × 35

= 4 × 7

= 28

**Question 6: Multiply and express as a mixed fraction:**

(a) 3 × 5 1/5

Answer:

= 5 1/5 = 26/5

(a) 3 × 5 1/5

Answer:

= 3 × 26/5

= 78/5

= 15 3/5

**(b) 5 × 6 3/4**

Answer:

Answer:

= 6 3/4 = 27/4

= 5 × 27/4

= 135/4

= 33 3/4

**(c) 7 × 2 1/4**

Answer:

Answer:

= 2 1/4 = 9/4

= 7 × 9/4

= 63/4

= 15 3/4

**(d) 4 × 6 1/3**

Answer:

Answer:

= 6 1/3 = 19/3

= 4 × 19/3

= 76/3

= 25 1/3

**(e) 3 1/4 × 6**

Answer:

Answer:

= 3 1/4 = 13/4

= 13/4 × 6

= 13/2 × 3

= 39/2

= 19 1/2

**(f) 3 2/5× 8**

Answer:

Answer:

= 3 2/5 = 17/5

= 17/5 × 8

= 136/5

= 27 1/5

**Question 7: Find:**

(a) 1/2 of (i) 2 3/4 (ii) 4 2/9

Answer:

(a) 1/2 of (i) 2 3/4 (ii) 4 2/9

Answer:

(i) 2 3/4

= 2 3/4 = 11/4

= 1/2 × 11/4

= 1/2 × 11/4

= 1 × 11/2 × 4

= 11/8

= 1 3/8

(ii) 4 2/9

= 4 2/9 = 38/9

= 1/2 × 38/9

= 1/2 × 38/9

= 1 × 38/2 × 9

= 38/18

= 19/9

= 2 1/9

**(b) 5/8 of (i) 3 5/6 (ii) 9 2/3**

Answer:

Answer:

(i) 3 5/6

= 3 5/6 = 23/6

= 5/8 × 23/6

= 5/8 × 23/6

= 5 × 23/8 × 6

= 115/48

= 2 19/48

(ii) 9 2/3

= 9 2/3 = 29/3

= 5/8 × 29/3

= 5/8 × 29/3

= 5 × 29/8 × 3

= 145/24

= 6 1/24

**Question 8: Vidya and Pratap went for a picnic. Their mother gave them a water bottle that contained 5 litres water. Vidya consumed 2/5 of the water. Pratap consumed the remaining water.**

(i) How much water did Vidya drink?

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

Answer:

(i) How much water did Vidya drink?

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

Answer:

(i)

Amount of water in the water bottle = 5 litres

Amount of water consumed by Vidya = 2/5 of 5 litres

= 2/5 × 5

= 2 litres

Therefore, the total amount of water drank by Vidya is 2 litres

(ii)

Amount of water in the water bottle = 5 litres

Amount of water consumed by Pratap = ?

= (1 - water consumed by Vidya)

= 1 - (2/5)

= 5-2/5

= 3/5

Therefore, total amount of water consumed by Pratap = 3/5 of 5 litres

= 3/5 × 5

= 3 litres

Therefore, the total amount of water drank by Pratap is 3 litres.

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