Class 6 Exam > Class 6 Notes > Mathematics (Maths) Class 6 > RD Sharma Solutions: Ratio, Proportion & Unitary Method (Exercise 9.2)
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Page 1 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.Read More
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