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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.

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