Page 1 Exercise 6.6 PAGE: 6.19 Reduce each of the following fractions to its lowest term (simplest form): 1. (i) 40/75 (ii) 42/28 (iii) 12/52 (iv) 40/72 (v) 80/24 (vi) 84/56 Solution: (i) 40/75 We know that Factors of 40 are 1, 2, 4, 5, 8, 10, 20 and 40 Factors of 75 are 1, 3, 5, 15 and 75 So the common factors are 1 and 5 We get HCF = 5 By dividing numerator and denominator by 5 40/75 ÷ 5/5 = 8/15 Hence, the simplest form of 40/75 is 8/15. (ii) 42/28 We know that Factors of 42 are 1, 2, 3, 6, 7, 14, 21 and 42 Factors of 28 are 1, 2, 4, 7, 14 and 28 So the common factors are 1, 2 and 14 We get HCF = 14 By dividing numerator and denominator by 14 42/28 ÷ 14/14 = 3/2 Hence, the simplest form of 42/28 is 3/2. (iii) 12/52 We know that Factors of 12 are 1, 2, 3, 4, 6 and 12 Factors of 52 are 1, 2, 4, 13, 26 and 52 So the common factors are 1, 2 and 4 We get HCF = 4 By dividing numerator and denominator by 4 12/52 ÷ 4/4 = 3/13 Hence, the simplest form of 12/52 is 3/13. Page 2 Exercise 6.6 PAGE: 6.19 Reduce each of the following fractions to its lowest term (simplest form): 1. (i) 40/75 (ii) 42/28 (iii) 12/52 (iv) 40/72 (v) 80/24 (vi) 84/56 Solution: (i) 40/75 We know that Factors of 40 are 1, 2, 4, 5, 8, 10, 20 and 40 Factors of 75 are 1, 3, 5, 15 and 75 So the common factors are 1 and 5 We get HCF = 5 By dividing numerator and denominator by 5 40/75 ÷ 5/5 = 8/15 Hence, the simplest form of 40/75 is 8/15. (ii) 42/28 We know that Factors of 42 are 1, 2, 3, 6, 7, 14, 21 and 42 Factors of 28 are 1, 2, 4, 7, 14 and 28 So the common factors are 1, 2 and 14 We get HCF = 14 By dividing numerator and denominator by 14 42/28 ÷ 14/14 = 3/2 Hence, the simplest form of 42/28 is 3/2. (iii) 12/52 We know that Factors of 12 are 1, 2, 3, 4, 6 and 12 Factors of 52 are 1, 2, 4, 13, 26 and 52 So the common factors are 1, 2 and 4 We get HCF = 4 By dividing numerator and denominator by 4 12/52 ÷ 4/4 = 3/13 Hence, the simplest form of 12/52 is 3/13. (iv) 40/72 We know that Factors of 40 are 1, 2, 4, 5, 8, 10, 20 and 40 Factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36 and 72 So the common factors are 1, 2, 4 and 8 We get HCF = 8 By dividing numerator and denominator by 8 40/72 ÷ 8/8 = 5/9 Hence, the simplest form of 40/72 is 5/9. (v) 80/24 We know that Factors of 80 are 1, 2, 4, 5, 8, 10, 16, 20, 40 and 80 Factors of 24 are 1, 2, 3, 4, 6, 8, 12 and 24 So the common factors are 1, 2, 4 and 8 We get HCF = 8 By dividing numerator and denominator by 8 80/24 ÷ 8/8 = 10/3 Hence, the simplest form of 80/24 is 10/3. (vi) 84/56 We know that Factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42 and 84 Factors of 56 are 1, 2, 4, 7, 8, 14, 28 and 56 So the common factors are 1, 2, 4, 7, 14 and 28 We get HCF = 28 By dividing numerator and denominator by 28 84/56 ÷ 28/28 = 3/2 Hence, the simplest form of 84/56 is 3/2. 2. Simplify each of the following to its lowest term: (i) 75/80 (ii) 52/76 (iii) 84/98 (iv) 68/17 (v) 150/50 (vi) 162/108 Solution: (i) 75/80 We know that Page 3 Exercise 6.6 PAGE: 6.19 Reduce each of the following fractions to its lowest term (simplest form): 1. (i) 40/75 (ii) 42/28 (iii) 12/52 (iv) 40/72 (v) 80/24 (vi) 84/56 Solution: (i) 40/75 We know that Factors of 40 are 1, 2, 4, 5, 8, 10, 20 and 40 Factors of 75 are 1, 3, 5, 15 and 75 So the common factors are 1 and 5 We get HCF = 5 By dividing numerator and denominator by 5 40/75 ÷ 5/5 = 8/15 Hence, the simplest form of 40/75 is 8/15. (ii) 42/28 We know that Factors of 42 are 1, 2, 3, 6, 7, 14, 21 and 42 Factors of 28 are 1, 2, 4, 7, 14 and 28 So the common factors are 1, 2 and 14 We get HCF = 14 By dividing numerator and denominator by 14 42/28 ÷ 14/14 = 3/2 Hence, the simplest form of 42/28 is 3/2. (iii) 12/52 We know that Factors of 12 are 1, 2, 3, 4, 6 and 12 Factors of 52 are 1, 2, 4, 13, 26 and 52 So the common factors are 1, 2 and 4 We get HCF = 4 By dividing numerator and denominator by 4 12/52 ÷ 4/4 = 3/13 Hence, the simplest form of 12/52 is 3/13. (iv) 40/72 We know that Factors of 40 are 1, 2, 4, 5, 8, 10, 20 and 40 Factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36 and 72 So the common factors are 1, 2, 4 and 8 We get HCF = 8 By dividing numerator and denominator by 8 40/72 ÷ 8/8 = 5/9 Hence, the simplest form of 40/72 is 5/9. (v) 80/24 We know that Factors of 80 are 1, 2, 4, 5, 8, 10, 16, 20, 40 and 80 Factors of 24 are 1, 2, 3, 4, 6, 8, 12 and 24 So the common factors are 1, 2, 4 and 8 We get HCF = 8 By dividing numerator and denominator by 8 80/24 ÷ 8/8 = 10/3 Hence, the simplest form of 80/24 is 10/3. (vi) 84/56 We know that Factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42 and 84 Factors of 56 are 1, 2, 4, 7, 8, 14, 28 and 56 So the common factors are 1, 2, 4, 7, 14 and 28 We get HCF = 28 By dividing numerator and denominator by 28 84/56 ÷ 28/28 = 3/2 Hence, the simplest form of 84/56 is 3/2. 2. Simplify each of the following to its lowest term: (i) 75/80 (ii) 52/76 (iii) 84/98 (iv) 68/17 (v) 150/50 (vi) 162/108 Solution: (i) 75/80 We know that Factors of 75 are 1, 3, 5, 15, 25 and 75 Factors of 80 are 1, 2, 4, 5, 8, 10, 12, 16, 20, 40 and 80 So the common factors are 1 and 5 We get HCF = 5 By dividing numerator and denominator by 5 75/80 ÷ 5/5 = 15/16 Hence, the simplest form of 75/80 is 15/16. (ii) 52/76 We know that Factors of 52 are 1, 2, 4, 13, 26 and 52 Factors of 76 are 1, 2, 4, 19, 38 and 76 So the common factors are 1, 2 and 4 We get HCF = 4 By dividing numerator and denominator by 4 52/76 ÷ 4/4 = 13/19 Hence, the simplest form of 52/76 is 13/19. (iii) 84/98 We know that Factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42 and 84 Factors of 98 are 1, 2, 7, 14, 49 and 98 So the common factors are 1, 2, 7 and 14 We get HCF = 14 By dividing numerator and denominator by 14 84/98 ÷ 14/14 = 6/7 Hence, the simplest form of 84/98 is 6/7. (iv) 68/17 We know that Factors of 68 are 1, 2, 4, 17, 34 and 68 Factors of 17 are 1 and 17 So the common factors are 1 and 17 We get HCF = 17 By dividing numerator and denominator by 17 68/17 ÷ 17/17 = 4/1 Hence, the simplest form of 68/17 is 4/1. (v) 150/50 We know that Factors of 150 are 1, 2, 3, 5, 6, 10, 15, 25, 50 and 150 Page 4 Exercise 6.6 PAGE: 6.19 Reduce each of the following fractions to its lowest term (simplest form): 1. (i) 40/75 (ii) 42/28 (iii) 12/52 (iv) 40/72 (v) 80/24 (vi) 84/56 Solution: (i) 40/75 We know that Factors of 40 are 1, 2, 4, 5, 8, 10, 20 and 40 Factors of 75 are 1, 3, 5, 15 and 75 So the common factors are 1 and 5 We get HCF = 5 By dividing numerator and denominator by 5 40/75 ÷ 5/5 = 8/15 Hence, the simplest form of 40/75 is 8/15. (ii) 42/28 We know that Factors of 42 are 1, 2, 3, 6, 7, 14, 21 and 42 Factors of 28 are 1, 2, 4, 7, 14 and 28 So the common factors are 1, 2 and 14 We get HCF = 14 By dividing numerator and denominator by 14 42/28 ÷ 14/14 = 3/2 Hence, the simplest form of 42/28 is 3/2. (iii) 12/52 We know that Factors of 12 are 1, 2, 3, 4, 6 and 12 Factors of 52 are 1, 2, 4, 13, 26 and 52 So the common factors are 1, 2 and 4 We get HCF = 4 By dividing numerator and denominator by 4 12/52 ÷ 4/4 = 3/13 Hence, the simplest form of 12/52 is 3/13. (iv) 40/72 We know that Factors of 40 are 1, 2, 4, 5, 8, 10, 20 and 40 Factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36 and 72 So the common factors are 1, 2, 4 and 8 We get HCF = 8 By dividing numerator and denominator by 8 40/72 ÷ 8/8 = 5/9 Hence, the simplest form of 40/72 is 5/9. (v) 80/24 We know that Factors of 80 are 1, 2, 4, 5, 8, 10, 16, 20, 40 and 80 Factors of 24 are 1, 2, 3, 4, 6, 8, 12 and 24 So the common factors are 1, 2, 4 and 8 We get HCF = 8 By dividing numerator and denominator by 8 80/24 ÷ 8/8 = 10/3 Hence, the simplest form of 80/24 is 10/3. (vi) 84/56 We know that Factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42 and 84 Factors of 56 are 1, 2, 4, 7, 8, 14, 28 and 56 So the common factors are 1, 2, 4, 7, 14 and 28 We get HCF = 28 By dividing numerator and denominator by 28 84/56 ÷ 28/28 = 3/2 Hence, the simplest form of 84/56 is 3/2. 2. Simplify each of the following to its lowest term: (i) 75/80 (ii) 52/76 (iii) 84/98 (iv) 68/17 (v) 150/50 (vi) 162/108 Solution: (i) 75/80 We know that Factors of 75 are 1, 3, 5, 15, 25 and 75 Factors of 80 are 1, 2, 4, 5, 8, 10, 12, 16, 20, 40 and 80 So the common factors are 1 and 5 We get HCF = 5 By dividing numerator and denominator by 5 75/80 ÷ 5/5 = 15/16 Hence, the simplest form of 75/80 is 15/16. (ii) 52/76 We know that Factors of 52 are 1, 2, 4, 13, 26 and 52 Factors of 76 are 1, 2, 4, 19, 38 and 76 So the common factors are 1, 2 and 4 We get HCF = 4 By dividing numerator and denominator by 4 52/76 ÷ 4/4 = 13/19 Hence, the simplest form of 52/76 is 13/19. (iii) 84/98 We know that Factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42 and 84 Factors of 98 are 1, 2, 7, 14, 49 and 98 So the common factors are 1, 2, 7 and 14 We get HCF = 14 By dividing numerator and denominator by 14 84/98 ÷ 14/14 = 6/7 Hence, the simplest form of 84/98 is 6/7. (iv) 68/17 We know that Factors of 68 are 1, 2, 4, 17, 34 and 68 Factors of 17 are 1 and 17 So the common factors are 1 and 17 We get HCF = 17 By dividing numerator and denominator by 17 68/17 ÷ 17/17 = 4/1 Hence, the simplest form of 68/17 is 4/1. (v) 150/50 We know that Factors of 150 are 1, 2, 3, 5, 6, 10, 15, 25, 50 and 150 Factors of 50 are 1, 2, 5, 10, 25 and 50 So the common factors are 1, 2, 5, 10, 25 and 50 We get HCF = 50 By dividing numerator and denominator by 50 150/50 ÷ 50/50 = 3/1 Hence, the simplest form of 150/50 is 3/1. (vi) 162/108 We know that Factors of 162 are 1, 2, 3, 6, 9, 18, 27, 54, 81 and 162 Factors of 108 are 1, 2, 3, 4, 6, 9, 12, 18, 27 and 54 So the common factors are 1, 2, 3, 6, 9, 18, 27 and 54 We get HCF = 54 By dividing numerator and denominator by 54 162/108 ÷ 54/54 = 3/2 Hence, the simplest form of 162/108 is 3/2.Read More

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