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Page 1 Exercise 6.5 page: 6.15 1. Write the fractions and check whether they are equivalent or not: Solution: (i) We know that Fraction = ½ Fraction = 2/4 = 1/2 Fraction = 3/6 = ½ Fraction = 4/8 = ½ Hence, they are equivalent. (ii) We know that Fraction = 5/15 = 1/3 Fraction = 3/9 = 1/3 Fraction = 2/6 = 1/3 Fraction = 1/3 Hence, they are equivalent. 2. Write the fractions and match fractions in Column I with the equivalent fractions in Column II. Page 2 Exercise 6.5 page: 6.15 1. Write the fractions and check whether they are equivalent or not: Solution: (i) We know that Fraction = ½ Fraction = 2/4 = 1/2 Fraction = 3/6 = ½ Fraction = 4/8 = ½ Hence, they are equivalent. (ii) We know that Fraction = 5/15 = 1/3 Fraction = 3/9 = 1/3 Fraction = 2/6 = 1/3 Fraction = 1/3 Hence, they are equivalent. 2. Write the fractions and match fractions in Column I with the equivalent fractions in Column II. Solution: (i) (b) (ii) (c) (iii) (a) (iv) (d) 3. Replace ? in each of the following by the correct number: (i) 2/7 = 6/ ? (ii) 5/8 = 10/? (iii) 4/5 = ?/20 (iv) 45/60 = 15/ ? (v) 18/24 = ?/4 Solution: (i) 2/7 = 6/21 (ii) 5/8 = 10/16 (iii) 4/5 = 16/20 (iv) 45/60 = 15/20 (v) 18/24 =3/4 4. Find the equivalent fraction of 3/5, having: (i) numerator 9 (ii) denominator 30 (iii) numerator 21 (iv) denominator 40 Solution: (i) The given fraction = 3/5 By considering numerator = 9 We know that 3 × 3 = 9 Multiply the numerator and denominator of the fraction by 3 3/5 × 3/3 = 9/15 (ii) The given fraction = 3/5 By considering denominator = 30 We know that 5 × 6 = 30 Multiply the numerator and denominator of the fraction by 6 3/5 × 6/6 = 18/30 (iii) The given fraction = 3/5 By considering numerator = 21 Page 3 Exercise 6.5 page: 6.15 1. Write the fractions and check whether they are equivalent or not: Solution: (i) We know that Fraction = ½ Fraction = 2/4 = 1/2 Fraction = 3/6 = ½ Fraction = 4/8 = ½ Hence, they are equivalent. (ii) We know that Fraction = 5/15 = 1/3 Fraction = 3/9 = 1/3 Fraction = 2/6 = 1/3 Fraction = 1/3 Hence, they are equivalent. 2. Write the fractions and match fractions in Column I with the equivalent fractions in Column II. Solution: (i) (b) (ii) (c) (iii) (a) (iv) (d) 3. Replace ? in each of the following by the correct number: (i) 2/7 = 6/ ? (ii) 5/8 = 10/? (iii) 4/5 = ?/20 (iv) 45/60 = 15/ ? (v) 18/24 = ?/4 Solution: (i) 2/7 = 6/21 (ii) 5/8 = 10/16 (iii) 4/5 = 16/20 (iv) 45/60 = 15/20 (v) 18/24 =3/4 4. Find the equivalent fraction of 3/5, having: (i) numerator 9 (ii) denominator 30 (iii) numerator 21 (iv) denominator 40 Solution: (i) The given fraction = 3/5 By considering numerator = 9 We know that 3 × 3 = 9 Multiply the numerator and denominator of the fraction by 3 3/5 × 3/3 = 9/15 (ii) The given fraction = 3/5 By considering denominator = 30 We know that 5 × 6 = 30 Multiply the numerator and denominator of the fraction by 6 3/5 × 6/6 = 18/30 (iii) The given fraction = 3/5 By considering numerator = 21 We know that 3 × 7 = 21 Multiply the numerator and denominator of the fraction by 7 3/5 × 7/7 = 21/35 (iv) The given fraction = 3/5 By considering denominator = 40 We know that 5 × 8 = 40 Multiply the numerator and denominator of the fraction by 8 3/5 × 8/8 = 24/40 5. Find the fraction equivalent to 45/60, having: (i) numerator 15 (ii) denominator 4 (iii) denominator 240 (iv) numerator 135 Solution: (i) The given fraction = 45/60 By considering numerator = 15 We know that 45 ÷ 3 = 15 Dividing the numerator and denominator of the fraction by 3 45/60 ÷ 3/3 = 15/20 (ii) The given fraction = 45/60 By considering denominator = 4 We know that 60 ÷ 15 = 4 Dividing the numerator and denominator of the fraction by 15 45/60 ÷ 15/15 = 3/4 (iii) The given fraction = 45/60 By considering denominator = 240 We know that 60 × 4 = 240 Multiply the numerator and denominator of the fraction by 4 45/60 × 4/4 = 180/240 (iv) The given fraction = 45/60 By considering numerator = 135 We know that 45 × 3 = 135 Multiply the numerator and denominator of the fraction by 3 45/60 × 3/3 = 135/180 6. Find the fraction equivalent of 35/42, having: (i) numerator 15 (ii) denominator 18 (iii) denominator 30 (iv) numerator 30 Solution: The given fraction = 35/42 In order to reduce the fraction, divide the numerator and denominator by the HCF of 35 and 42 Page 4 Exercise 6.5 page: 6.15 1. Write the fractions and check whether they are equivalent or not: Solution: (i) We know that Fraction = ½ Fraction = 2/4 = 1/2 Fraction = 3/6 = ½ Fraction = 4/8 = ½ Hence, they are equivalent. (ii) We know that Fraction = 5/15 = 1/3 Fraction = 3/9 = 1/3 Fraction = 2/6 = 1/3 Fraction = 1/3 Hence, they are equivalent. 2. Write the fractions and match fractions in Column I with the equivalent fractions in Column II. Solution: (i) (b) (ii) (c) (iii) (a) (iv) (d) 3. Replace ? in each of the following by the correct number: (i) 2/7 = 6/ ? (ii) 5/8 = 10/? (iii) 4/5 = ?/20 (iv) 45/60 = 15/ ? (v) 18/24 = ?/4 Solution: (i) 2/7 = 6/21 (ii) 5/8 = 10/16 (iii) 4/5 = 16/20 (iv) 45/60 = 15/20 (v) 18/24 =3/4 4. Find the equivalent fraction of 3/5, having: (i) numerator 9 (ii) denominator 30 (iii) numerator 21 (iv) denominator 40 Solution: (i) The given fraction = 3/5 By considering numerator = 9 We know that 3 × 3 = 9 Multiply the numerator and denominator of the fraction by 3 3/5 × 3/3 = 9/15 (ii) The given fraction = 3/5 By considering denominator = 30 We know that 5 × 6 = 30 Multiply the numerator and denominator of the fraction by 6 3/5 × 6/6 = 18/30 (iii) The given fraction = 3/5 By considering numerator = 21 We know that 3 × 7 = 21 Multiply the numerator and denominator of the fraction by 7 3/5 × 7/7 = 21/35 (iv) The given fraction = 3/5 By considering denominator = 40 We know that 5 × 8 = 40 Multiply the numerator and denominator of the fraction by 8 3/5 × 8/8 = 24/40 5. Find the fraction equivalent to 45/60, having: (i) numerator 15 (ii) denominator 4 (iii) denominator 240 (iv) numerator 135 Solution: (i) The given fraction = 45/60 By considering numerator = 15 We know that 45 ÷ 3 = 15 Dividing the numerator and denominator of the fraction by 3 45/60 ÷ 3/3 = 15/20 (ii) The given fraction = 45/60 By considering denominator = 4 We know that 60 ÷ 15 = 4 Dividing the numerator and denominator of the fraction by 15 45/60 ÷ 15/15 = 3/4 (iii) The given fraction = 45/60 By considering denominator = 240 We know that 60 × 4 = 240 Multiply the numerator and denominator of the fraction by 4 45/60 × 4/4 = 180/240 (iv) The given fraction = 45/60 By considering numerator = 135 We know that 45 × 3 = 135 Multiply the numerator and denominator of the fraction by 3 45/60 × 3/3 = 135/180 6. Find the fraction equivalent of 35/42, having: (i) numerator 15 (ii) denominator 18 (iii) denominator 30 (iv) numerator 30 Solution: The given fraction = 35/42 In order to reduce the fraction, divide the numerator and denominator by the HCF of 35 and 42 We get 35/42 ÷ 7/7 = 5/6 (i) So the fraction = 5/6 By considering numerator = 15 We know that 5 × 3 = 15 Multiply the numerator and denominator of the fraction by 3 5/6 × 3/3 = 15/18 (ii) So the fraction = 5/6 By considering denominator = 18 We know that 6 × 3 = 18 Multiply the numerator and denominator of the fraction by 3 5/6 × 3/3 = 15/18 (iii) So the fraction = 5/6 By considering denominator = 30 We know that 6 × 5 = 30 Multiply the numerator and denominator of the fraction by 5 5/6 × 5/5 = 25/30 (iv) So the fraction = 5/6 By considering numerator = 30 We know that 5 × 6 = 30 Multiply the numerator and denominator of the fraction by 6 5/6 × 6/6 = 30/36 7. Check whether the given fractions are equivalent: (i) 5/9, 30/54 (ii) 2/7, 16/42 (iii) 7/13, 5/11 (iv) 4/11, 32/88 (v) 3/10, 12/50 (vi) 9/27, 25/75 Solution: (i) We know that 5/9 × 6/6 = 30/54 Therefore, 5/9 is equivalent to 30/54. (ii) We know that 2/7 × 8/8 = 16/56 Therefore, 2/7 is not equivalent to 16/42. (iii) We know that 7/13 × 5/5 = 35/65 The same way 5/11 × 7/7 = 35/77 Therefore, 7/13 is not equivalent to 5/11. Page 5 Exercise 6.5 page: 6.15 1. Write the fractions and check whether they are equivalent or not: Solution: (i) We know that Fraction = ½ Fraction = 2/4 = 1/2 Fraction = 3/6 = ½ Fraction = 4/8 = ½ Hence, they are equivalent. (ii) We know that Fraction = 5/15 = 1/3 Fraction = 3/9 = 1/3 Fraction = 2/6 = 1/3 Fraction = 1/3 Hence, they are equivalent. 2. Write the fractions and match fractions in Column I with the equivalent fractions in Column II. Solution: (i) (b) (ii) (c) (iii) (a) (iv) (d) 3. Replace ? in each of the following by the correct number: (i) 2/7 = 6/ ? (ii) 5/8 = 10/? (iii) 4/5 = ?/20 (iv) 45/60 = 15/ ? (v) 18/24 = ?/4 Solution: (i) 2/7 = 6/21 (ii) 5/8 = 10/16 (iii) 4/5 = 16/20 (iv) 45/60 = 15/20 (v) 18/24 =3/4 4. Find the equivalent fraction of 3/5, having: (i) numerator 9 (ii) denominator 30 (iii) numerator 21 (iv) denominator 40 Solution: (i) The given fraction = 3/5 By considering numerator = 9 We know that 3 × 3 = 9 Multiply the numerator and denominator of the fraction by 3 3/5 × 3/3 = 9/15 (ii) The given fraction = 3/5 By considering denominator = 30 We know that 5 × 6 = 30 Multiply the numerator and denominator of the fraction by 6 3/5 × 6/6 = 18/30 (iii) The given fraction = 3/5 By considering numerator = 21 We know that 3 × 7 = 21 Multiply the numerator and denominator of the fraction by 7 3/5 × 7/7 = 21/35 (iv) The given fraction = 3/5 By considering denominator = 40 We know that 5 × 8 = 40 Multiply the numerator and denominator of the fraction by 8 3/5 × 8/8 = 24/40 5. Find the fraction equivalent to 45/60, having: (i) numerator 15 (ii) denominator 4 (iii) denominator 240 (iv) numerator 135 Solution: (i) The given fraction = 45/60 By considering numerator = 15 We know that 45 ÷ 3 = 15 Dividing the numerator and denominator of the fraction by 3 45/60 ÷ 3/3 = 15/20 (ii) The given fraction = 45/60 By considering denominator = 4 We know that 60 ÷ 15 = 4 Dividing the numerator and denominator of the fraction by 15 45/60 ÷ 15/15 = 3/4 (iii) The given fraction = 45/60 By considering denominator = 240 We know that 60 × 4 = 240 Multiply the numerator and denominator of the fraction by 4 45/60 × 4/4 = 180/240 (iv) The given fraction = 45/60 By considering numerator = 135 We know that 45 × 3 = 135 Multiply the numerator and denominator of the fraction by 3 45/60 × 3/3 = 135/180 6. Find the fraction equivalent of 35/42, having: (i) numerator 15 (ii) denominator 18 (iii) denominator 30 (iv) numerator 30 Solution: The given fraction = 35/42 In order to reduce the fraction, divide the numerator and denominator by the HCF of 35 and 42 We get 35/42 ÷ 7/7 = 5/6 (i) So the fraction = 5/6 By considering numerator = 15 We know that 5 × 3 = 15 Multiply the numerator and denominator of the fraction by 3 5/6 × 3/3 = 15/18 (ii) So the fraction = 5/6 By considering denominator = 18 We know that 6 × 3 = 18 Multiply the numerator and denominator of the fraction by 3 5/6 × 3/3 = 15/18 (iii) So the fraction = 5/6 By considering denominator = 30 We know that 6 × 5 = 30 Multiply the numerator and denominator of the fraction by 5 5/6 × 5/5 = 25/30 (iv) So the fraction = 5/6 By considering numerator = 30 We know that 5 × 6 = 30 Multiply the numerator and denominator of the fraction by 6 5/6 × 6/6 = 30/36 7. Check whether the given fractions are equivalent: (i) 5/9, 30/54 (ii) 2/7, 16/42 (iii) 7/13, 5/11 (iv) 4/11, 32/88 (v) 3/10, 12/50 (vi) 9/27, 25/75 Solution: (i) We know that 5/9 × 6/6 = 30/54 Therefore, 5/9 is equivalent to 30/54. (ii) We know that 2/7 × 8/8 = 16/56 Therefore, 2/7 is not equivalent to 16/42. (iii) We know that 7/13 × 5/5 = 35/65 The same way 5/11 × 7/7 = 35/77 Therefore, 7/13 is not equivalent to 5/11. (iv) We know that 4/11 × 8/8 = 32/88 Therefore, 4/11 is equivalent to 32/88. (v) We know that 3/10 × 4/4 = 12/40 Therefore, 3/10 is not equivalent to 12/50. (vi) We know that 9/27 = 1/3 and 25/75 = 1/3 Therefore, 9/27 is equivalent to 25/75. 8. Match the equivalent fractions and write another 2 for each: (i) 250/400 (a) 2/3 (ii) 180/200 (b) 2/5 (iii) 660/990 (c) ½ (iv) 180/360 (d) 5/8 (v) 220/550 (e) 9/10 Solution: (i) 250/400 By dividing numerator and denominator by HCF of 250 and 400 = (250/50)/ (400/ 50) = 5/8 So the match is (d) (ii) 180/200 By dividing numerator and denominator by HCF of 180 and 200 = (180/20)/ (200/20) = 9/10 So the match is (e) (iii) 660/990 By dividing numerator and denominator by HCF of 660 and 990 = (660/90)/ (990/90) = 2/3 So the match is (a) (iv) 180/360 By dividing numerator and denominator by HCF of 180 and 360 = (180/180)/ (360/180) = ½ So the match is (c) (v) 220/550 By dividing numerator and denominator by HCF of 220 and 550 = (220/11)/ (550/11) = 2/5 So the match is (b) 9. Write some equivalent fractions which contain all digits from 1 to 9 once only. Solution: The equivalent fractions which contain all digits from 1 to 9 once only are 2/6 = 3/9 = 58/174, 2/4 = 3/6 = 79/158Read More
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