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# Fractions - Exercise 6.5 Class 6 Notes | EduRev

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

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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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## Mathematics (Maths) Class 6

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