RD Sharma Solutions: Ratio, Proportion & Unitary Method (Exercise 9.2)

# Ratio, Proportion & Unitary Method (Exercise 9.2) RD Sharma Solutions | Mathematics (Maths) Class 6 PDF Download

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Exercise 9.2                                                                                  page: 9.9
1. Which ratio is larger in the following pairs?
(i) 3: 4 or 9: 16
(ii) 15: 16 or 24: 25
(iii) 4: 7 or 5: 8
(iv) 9: 20 or 8: 13
(v) 1: 2 or 13: 27
Solution:

(i) 3: 4 or 9: 16
It can be written as
3: 4 = 3/4 and 9: 16 = 9/16
LCM of 4 and 16 is 16
Multiplying both numerator and denominator of the term ¾ by 4 to make the denominator 16
3/4 = (3/4) × (4/4) = 12/16 and 9/16
We know that 12 > 9
So we get 12/16 > 9/16
We can write it as
3/4 > 9/16

Hence, 3: 4 > 9: 16.

(ii) 15: 16 or 24: 25
It can be written as
15: 16 = 15/16 and 24: 25 = 24/25
LCM of 16 and 25 is 400
Multiplying both the terms by relevant numbers to make denominator as 400
15/16 = (15/16) × (25/25) = 375/400 and 24/25 = (24/25) × (16/16) = 384/400
We know that 384 > 375
So we get 384/400 > 375/400
We can write it as 24/25 > 15/16

Hence, 24: 25 > 15: 16.

(iii) 4: 7 or 5: 8
It can be written as
4: 7 = 4/7 and 5: 8 = 5/8
LCM of 7 and 8 is 56
Multiplying both the terms by relevant numbers to make denominator as 56
4/7 = (4/7) × (8/8) = 32/56 and 5/8 = (5/8) × (7/7) = 35/56
We know that 35 > 32
So we get 35/56 > 32/56
We can write it as 5/8 > 4/7

Hence, 5: 8 > 4: 7.

(iv) 9: 20 or 8: 13
It can be written as
9: 20 = 9/20 and 8: 13 = 8/13
Page 2

Exercise 9.2                                                                                  page: 9.9
1. Which ratio is larger in the following pairs?
(i) 3: 4 or 9: 16
(ii) 15: 16 or 24: 25
(iii) 4: 7 or 5: 8
(iv) 9: 20 or 8: 13
(v) 1: 2 or 13: 27
Solution:

(i) 3: 4 or 9: 16
It can be written as
3: 4 = 3/4 and 9: 16 = 9/16
LCM of 4 and 16 is 16
Multiplying both numerator and denominator of the term ¾ by 4 to make the denominator 16
3/4 = (3/4) × (4/4) = 12/16 and 9/16
We know that 12 > 9
So we get 12/16 > 9/16
We can write it as
3/4 > 9/16

Hence, 3: 4 > 9: 16.

(ii) 15: 16 or 24: 25
It can be written as
15: 16 = 15/16 and 24: 25 = 24/25
LCM of 16 and 25 is 400
Multiplying both the terms by relevant numbers to make denominator as 400
15/16 = (15/16) × (25/25) = 375/400 and 24/25 = (24/25) × (16/16) = 384/400
We know that 384 > 375
So we get 384/400 > 375/400
We can write it as 24/25 > 15/16

Hence, 24: 25 > 15: 16.

(iii) 4: 7 or 5: 8
It can be written as
4: 7 = 4/7 and 5: 8 = 5/8
LCM of 7 and 8 is 56
Multiplying both the terms by relevant numbers to make denominator as 56
4/7 = (4/7) × (8/8) = 32/56 and 5/8 = (5/8) × (7/7) = 35/56
We know that 35 > 32
So we get 35/56 > 32/56
We can write it as 5/8 > 4/7

Hence, 5: 8 > 4: 7.

(iv) 9: 20 or 8: 13
It can be written as
9: 20 = 9/20 and 8: 13 = 8/13

LCM of 20 and 13 is 260
Multiplying both the terms by relevant numbers to make denominator as 260
9/20 = (9/20) × (13/13) = 117/260 and 8/13 = (8/13) × (20/20) = 160/260
We know that 160 > 117
So we get 160/260 > 117/260
We can write it as 8/13 > 9/20

Hence, 8: 13 > 9: 20.

(v) 1: 2 or 13: 27
It can be written as
1: 2 = 1/2 and 13: 27 = 13/27
LCM of 2 and 27 is 54
Multiplying both the terms by relevant numbers to make denominator as 54
1/2 = (1/2) × (27/27) = 27/54 and 13/27 = (13/27) × (2/2) = 26/54
We know that 27 > 26
So we get 27/54 > 26/54
We can write it as 1/2 > 13/27

Hence, 1: 2 > 13: 27.

2. Give two equivalent ratios of 6: 8.
Solution:

The given ratio = 6: 8
It can be written as = 6/8
Dividing the fraction by 2 we get
6/8 = (6/8) ÷ (2/2) = 3/4
Hence, 3: 4 is an equivalent ratio of 6: 8

Multiply the fraction by 2 we get
6/8 = (6/8) × (2/2) = 12/16
Hence, 12: 16 is an equivalent ratio of 6: 8

So, 3: 4 and 12: 16 are the equivalent ratios of 6: 8.

3. Fill in the following blanks:
12/20 = ?/5 = 9/ ?
Solution:

It is given that
12/20 = ?/5 = 9/ ?
We know that LCM of 20 and 5 is 20
It can be written as 20/4 = 5

Dividing the fraction by 4
12/20 = (12/20) × (4/4) = 3/5
So the first number is 3 and the ratio is 3/5.

In the same way,
Page 3

Exercise 9.2                                                                                  page: 9.9
1. Which ratio is larger in the following pairs?
(i) 3: 4 or 9: 16
(ii) 15: 16 or 24: 25
(iii) 4: 7 or 5: 8
(iv) 9: 20 or 8: 13
(v) 1: 2 or 13: 27
Solution:

(i) 3: 4 or 9: 16
It can be written as
3: 4 = 3/4 and 9: 16 = 9/16
LCM of 4 and 16 is 16
Multiplying both numerator and denominator of the term ¾ by 4 to make the denominator 16
3/4 = (3/4) × (4/4) = 12/16 and 9/16
We know that 12 > 9
So we get 12/16 > 9/16
We can write it as
3/4 > 9/16

Hence, 3: 4 > 9: 16.

(ii) 15: 16 or 24: 25
It can be written as
15: 16 = 15/16 and 24: 25 = 24/25
LCM of 16 and 25 is 400
Multiplying both the terms by relevant numbers to make denominator as 400
15/16 = (15/16) × (25/25) = 375/400 and 24/25 = (24/25) × (16/16) = 384/400
We know that 384 > 375
So we get 384/400 > 375/400
We can write it as 24/25 > 15/16

Hence, 24: 25 > 15: 16.

(iii) 4: 7 or 5: 8
It can be written as
4: 7 = 4/7 and 5: 8 = 5/8
LCM of 7 and 8 is 56
Multiplying both the terms by relevant numbers to make denominator as 56
4/7 = (4/7) × (8/8) = 32/56 and 5/8 = (5/8) × (7/7) = 35/56
We know that 35 > 32
So we get 35/56 > 32/56
We can write it as 5/8 > 4/7

Hence, 5: 8 > 4: 7.

(iv) 9: 20 or 8: 13
It can be written as
9: 20 = 9/20 and 8: 13 = 8/13

LCM of 20 and 13 is 260
Multiplying both the terms by relevant numbers to make denominator as 260
9/20 = (9/20) × (13/13) = 117/260 and 8/13 = (8/13) × (20/20) = 160/260
We know that 160 > 117
So we get 160/260 > 117/260
We can write it as 8/13 > 9/20

Hence, 8: 13 > 9: 20.

(v) 1: 2 or 13: 27
It can be written as
1: 2 = 1/2 and 13: 27 = 13/27
LCM of 2 and 27 is 54
Multiplying both the terms by relevant numbers to make denominator as 54
1/2 = (1/2) × (27/27) = 27/54 and 13/27 = (13/27) × (2/2) = 26/54
We know that 27 > 26
So we get 27/54 > 26/54
We can write it as 1/2 > 13/27

Hence, 1: 2 > 13: 27.

2. Give two equivalent ratios of 6: 8.
Solution:

The given ratio = 6: 8
It can be written as = 6/8
Dividing the fraction by 2 we get
6/8 = (6/8) ÷ (2/2) = 3/4
Hence, 3: 4 is an equivalent ratio of 6: 8

Multiply the fraction by 2 we get
6/8 = (6/8) × (2/2) = 12/16
Hence, 12: 16 is an equivalent ratio of 6: 8

So, 3: 4 and 12: 16 are the equivalent ratios of 6: 8.

3. Fill in the following blanks:
12/20 = ?/5 = 9/ ?
Solution:

It is given that
12/20 = ?/5 = 9/ ?
We know that LCM of 20 and 5 is 20
It can be written as 20/4 = 5

Dividing the fraction by 4
12/20 = (12/20) × (4/4) = 3/5
So the first number is 3 and the ratio is 3/5.

In the same way,

Consider 2/3 + 3/5 = 9/ ?
We know that 9/3 = 3
Multiply the fraction by 3
3/5 = (3/5) × (3/3) = 9/15
So the second number is 15 and the ratio is 9/15.

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## Mathematics (Maths) Class 6

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## Mathematics (Maths) Class 6

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