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# Fractions - Exercise 6.6 Class 6 Notes | EduRev

## Class 6 : Fractions - Exercise 6.6 Class 6 Notes | EduRev

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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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## Mathematics (Maths) Class 6

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