Fractions - Exercise 6.5 Class 6 Notes | EduRev

Mathematics (Maths) Class 6

Class 6 : Fractions - Exercise 6.5 Class 6 Notes | EduRev

 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 = 79/158 
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