## Chapter 2 Fractions and Decimals Exercise 2.3

**Question 1: Find:(i) 1/4 of (a) 1/4 (b) 3/5 (c) 4/3 Answer:**

(a) 1/4

= 1/4 × 1/4

= 1/4 × 1/4

= 1 × 1/4 × 4

= 1/16

(b) 3/5

= 1/4 × 3/5

= 1/4 × 3/5

= 1 × 3/4 × 5

= 3/20

(c) 4/3

= 1/4 × 4/3

= 1/4 × 4/3

= 1 × 4/4 × 3

= 4/12

= 1/3

**(ii) 1/7 of (a) 2/9 (b) 6/5 (c) 3/10**

Answer:

(a) 2/9

Answer:

= 1/7 × 2/9

= 1/7 × 2/9

= 1 × 2/7 × 9

= 2/63

(b) 6/5

= 1/7 × 6/5

= 1/7 × 6/5

= 1 × 6/7 × 5

= 6/35

(c) 3/10

= 1/7 × 3/10

= 1/7 × 3/10

= 1 × 3/7 × 10

= 3/70

**Question 2: Multiply and reduce to lowest form (if possible):**

(i) (2/3) × 2 2/3

Answer:

= 2 2/3 = 8/3

(i) (2/3) × 2 2/3

Answer:

= 2/3 × 8/3

= 2 × 8/3 × 3

= 16/9

= 1 7/9

**(ii) (2/7) × (7/9)**

Answer:

= 2 × 7/7 × 9

Answer:

= 2 × 1/1 × 9

= 2/9

**(iii) (3/8) × (6/4)**

Answer:

= 3 × 6/8 × 4

Answer:

= 3 × 3/4 × 4

= 9/16

**(iv) (9/5) × (3/5)**

Answer:

Answer:

= 9 × 3/5 × 5

= 27/25

= 1 2/25

**(v) (1/3) × (15/8)**

Answer:

Answer:

= 1 × 15/3 × 8

= 1 × 5/1 × 8

= 5/8

**(vi) (11/2) × (3/10)**

Answer:

Answer:

= 11 × 3/2 × 10

= 33/20

= 1 13/20

**(vii) (4/5) × (12/7)**

Answer:

Answer:

= 4 × 12/5 × 7

= 48/35

= 1 13/35

**Question 3: Multiply the following fractions:**

(i) (2/5) × 5 1/4

Answer:

(i) (2/5) × 5 1/4

Answer:

= 5 1/4 = 21/4

= 2/5 × 21/4

= 2 × 21/5 × 4

= 1 × 21/5 × 2

= 21/10

= 2 1/10

**(ii) 6 2/5 × (7/9)**

Answer:

= 6 2/5 = 32/5

Answer:

= 32/5 × 7/9

= 32 × 7/5 × 9

= 224/45

= 4 44/45

**(iii) (3/2) × 5 1/3**

Answer:

= 5 1/3 = 16/3

Answer:

= 3/2 × 16/3

= 3 × 16/2 × 3

= 1 × 8/1 × 1

= 8

**(iv) (5/6) × 2 3/7**

Answer:

= 2 3/7 = 17/7

Answer:

= 5/6 × 17/7

= 5 × 17/6 × 7

= 85/42

= 2 1/42

**(v) 3 2/5 × (4/7)**

Answer:

= 3 2/5 = 17/5

Answer:

= 17/5 × 4/7

= 17 × 4/5 × 7

= 68/35

= 1 33/35

**(vi) 2 3/5 × 3**

Answer:

= 2 3/5 = 13/5

Answer:

= 13/5 × 3/1

= 13 × 3/5 × 1

= 39/5

= 7 4/5

**(vi) 3 4/7 × (3/5)**

Answer:

= 3 4/7 = 25/7

Answer:

= 25/7 × 3/5

= 25 × 3/7 × 5

= 5 × 3/7 × 1

= 15/7

= 2 1/7

**Question 4: Which is greater?**

(i) (2/7) of (3/4) or (3/5) of (5/8)

Answer:

= 2/7 × 3/4 and 3/5 × 5/8

(i) (2/7) of (3/4) or (3/5) of (5/8)

Answer:

= 2/7 × 3/4

= 2 × 3/7 × 4

= 1 × 3/7 × 2

= 3/14

= 3/5 × 5/8

= 3 × 5/5 × 8

= 3 × 1/1 × 8

= 3/8

LCM of 8, 14 = 56

= 3/14 × 4/4 = 12/56

= 3/8 × 7/7 = 21/56

Comparing 12/56 [] 21/56

= 12/56 < 21/56

= 3/14 < 3/8

**(ii) (1/2) of (6/7) or (2/3) of (3/7)**

Answer:

= 1/2 × 6/7 and 2/3 × 3/7

Answer:

= 1/2 × 6/7

= 1 × 6/2 × 7

= 1 × 3/1 × 7

= 3/7

= 2/3 × 3/7

= 2 × 3/3 × 7

= 2 × 1/1 × 7

= 2/7

Comparing 3/7 [] 2/7

= 3/7 > 2/7

**Question 5: Saili plants 4 saplings, in a row, in her garden. The distance between two adjacent saplings is 3/4 m. Find the distance between the first and the last sapling.**

Answer:

The distance between two adjacent saplings = 3/4 m

Answer:

Number of saplings planted by Saili in a row = 4

Number of gap in saplings = 3/4 × 4 = 3

The distance between the first and the last saplings = ?

= 3 × 3/4

= 9/4 m

= 2 1/4 m

Therefore, the distance between the first and the last saplings is 2 1/4 m.

**Question 6: Lipika reads a book for 1 3/4 hours every day. She reads the entire book in 6 days. How many hours in all were required by her to read the book?**

Answer:

Time taken by Lipika to read a book = 1 3/4 hours (7/4 hours)

Answer:

Number of days she took to read the entire book = 6 days

Total number of hours required by her to complete the book = 7/4 × 6

= 7/2 × 3

= 21/2

= 10 1/2 hours

Therefore, the total number of hours required by her to complete the book is 10 1/2 hours.

**Question 7: A car runs 16 km using 1 litre of petrol. How much distance will it cover using 2 3/4 litres of petrol.**

Answer:

The total number of distance travelled by a car in 1 litre of petrol = 16 km

Answer:

Total quantity of petrol = 2 3/4 litre (11/4 litre)

Total distance travelled by car in 11/4 litres of petrol = ?

= 11/4 × 16

= 11 × 4

= 44 km

Therefore, total distance travelled by car in 11/4 litres of petrol is 44 km.

**Question 8: (a) (i) provide the number in the box [ ], such that (2/3) × [ ] = (10/30)**

Answer:

Let the number be x.

Answer:

= 2/3 × x = 10/30

= x = 10/30 × 3/2

= x = 10 × 3/30 × 2

= x = 5 × 1/10 × 1

= x = 5/10

Therefore, the required number in the box is 5/10.

**(ii) The simplest form of the number obtained in [ ] is**

Answer:

Answer:

Let the number in the box be 5/10.

The simplest form of 5/10 = 1/2

**(b) (i) provide the number in the box [ ], such that (3/5) × [ ] = (24/75)**

Answer:

Answer:

Let the number be x.

= 3/5 × x = 24/75

= x = 24/75 × 5/3

= x = 24 × 5/75 × 3

= x = 8 × 1/15 × 1

= x = 8/15

Therefore, the required number in the box is 8/15.

**(ii) The simplest form of the number obtained in [ ] is**

Answer:

Let the number in the box be 8/15.

Answer:

The simplest form of 8/15 is 8/15

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