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## Download PDF of RS Aggarwal Solutions for Class 6 Chapter 5 Fractions

### Access answers to Chapter 5 – Fractions

## Exercise 5A PAGE NO: 82

**1. Write the fraction representing the shaded portion:**

** **

**(i)**

**(ii)**

**(iii)**

**(iv)**

**(v)**

**(vi)**

**Solutions **

** (i) **Total parts = 4

Shaded region = 3

Hence, the shaded portion of the region is 3 parts of the whole figure

∴ 3 / 4

(ii) Total parts = 4

Shaded region = 1

Hence, the shaded portion of the region is 1 part of the whole figure

∴ 1 / 4

(iii) Total parts = 3

Shaded region = 2

Hence, the shaded portion of the region is 2 parts of the whole figure

∴ 2 / 3

(iv) Total parts = 10

Shaded region = 3

Hence, the shaded portion of the region is 3 parts of the whole figure

∴ 3 / 10

(v) Total parts = 9

Shaded region = 4

Hence, the shaded portion of the region is 4 parts of the whole figure

∴ 4 / 9

(vi) Total parts = 8

Shaded region = 3

Hence, the shaded portion of the region is 3 parts of the whole figure

∴ 3 / 8

**2. Shade 4/9 on the given figure.**

**Solution**

** **

∴ Above figure represents the shaded region 4 / 9 of the whole figure

**3. In the given figure, if we say that the shaded region is 1/4, then identify the error in it**

** Solution**

** **The shaded region is not equal to 1 / 4 since the above figure does not have equal parts

**4. Write a fraction for each of the following:**

**(i) Three- fourths**

**(ii) Four- sevenths**

**(iii) Two – fifths**

**(iv) Three – tenths**

**(v) One-eighth**

**(vi) Five- sixths**

**(vii) Eight- ninths**

**(viii) Seven-twelfths**

**Solution**

**(i) **The fraction for three – fourths is 3 / 4

(ii) The fraction for four – sevenths is 4 / 7

(iii)The fraction for two – fifths is 2 / 5

(iv) The fraction for three – tenths is 3 / 10

(v) The fraction for one- eighth is 1 / 8

(vi) The fraction for five – sixths is 5 / 6

(vii) The fraction for eight – ninths is 8 / 9

(viii) The fraction for seven – twelfths is 7 / 12

** 5. Write down the numerator and the denominator of each of the fractions given below:**

** (i) 4 / 9 (ii) 6 / 11 (iii) 8 / 15 (iv) 12 / 17 (v) 5 / 1**

** Solutions**

** (i) **4 / 9

Numerator of 4 / 9 is 4

Denominator of 4 / 9 is 9

(ii) 6 / 11

Numerator of 6 / 11 is 6

Denominator of 6 / 11 is 11

(iii) 8 / 15

Numerator of 8 / 15 is 8

Denominator of 8 / 15 is 15

(iv) 12 / 17

Numerator of 12 / 17 is 12

Denominator of 12 / 17 is 17

(v) 5 / 1

Numerator of 5 / 1 is 5

Denominator of 5 / 1 is 1

** 6. Write down the fraction in which **

** (i) numerator = 3, denominator = 8**

** (ii) numerator = 5, denominator = 12**

** (iii) numerator = 7, denominator = 16**

** (iv) numerator = 8, denominator = 15**

** Solutions**

(i) Fraction of numerator = 3, denominator = 8 is 3 / 8

(ii) Fraction of numerator = 5, denominator = 12 is 5 / 12

(iii) Fraction of numerator = 7, denominator = 16 is 7 / 16

(iv) Fraction of numerator = 8, denominator = 15 is 8 / 15

## Exercise 5B PAGE NO: 85

**1. Which of the following are proper fractions?**

** 1 / 2, 3 / 5, 10 / 7, 7 / 4, 2, 15 / 8, 16 / 16, 10 / 11, 23 / 10**

** Solution**

** ** A fraction whose numerator is less than its denominator is called a proper fraction

Here,

1 / 2, 3 / 5 and 10 / 11 are proper fractions

**2**. **Which of the following are** **improper fractions?**

** 3 / 2, 5 / 6, 9 / 4, 8 / 8, 3, 27 / 16, 23 / 31, 19 / 18, 10 / 13, 26 / 26**

** Solution**

** **A fraction whose numerator is greater than or equal to its denominator is called an improper fraction

Here,

3 / 2, 9 / 4, 8 / 8, 3, 27 / 16, 19 / 18 and 26 / 26 are improper fractions.

**3. Write six improper fractions with denominator 5**

** Solution**

6 / 5, 7 / 5, 8 / 5, 9 / 5, 11 / 5, 12 / 5 are improper fractions with denominator 5

**4**. **Write six improper fractions with numerator 13**

** Solution**

13 / 2, 13 / 3 13 / 4, 13 / 5, 13 / 6, 13 / 7 are improper fractions with numerator 13

## Exercise 5C PAGE NO: 89

** 1. Write five fractions equivalent to each of the following:**

**(i) 2 / 3 **

**(ii) 4 / 5**

**(iii) 5 /8**

**(iv) 7 / 10**

**(v) 3 / 7**

**(vi) 6 / 11**

**(vii) 7 / 9**

**(viii) 5 / 12**

**Solution**

** (i) **2 / 3

2 / 3 = (2 / 3 × 2 / 2) = (2 / 3 × 3 / 3) = (2 / 3 × 4 / 4) = (2 / 3 × 5 / 5) = (2 / 3 × 6 / 6)

∴ 2 / 3 = 4 / 6 = 6 / 9 = 8 / 12 = 10 / 15 = 12 / 18

The fractions are 4 / 6, 6 / 9, 8 / 12, 10 / 15 and 12 / 18

Hence, the five fractions equivalent to 2 / 3 are 4 / 6, 6 / 9, 8 / 12, 10 / 15 and 12 / 18

**(ii)** 4 / 5

4 / 5 = (4 / 5 × 2 / 2) = (4 / 5 × 3 / 3) = (4 / 5 × 4 / 4) = (4 / 5 × 5 / 5) = (4 / 5 × 6 / 6)

∴ 4 / 5 = 8 / 10 = 12 / 15 = 16 / 20 = 20 / 25 = 24 / 30

The five fractions are 8 / 10, 12 / 15, 16 / 20, 20 / 25 and 24 / 30

Hence, the five fractions equivalent to 4 / 5 are 8 / 10, 12 / 15, 16 / 20, 20 / 25 and 24 / 30

**(iii)** 5/8

5 / 8 = (5 / 8 × 2 / 2) = (5 / 8 × 3 / 3) = (5 / 8 × 4 / 4) = (5 / 8 × 5 / 5) = (5 / 8 × 6 / 6)

∴ 5 / 8 = 10 / 16 = 15 / 24 = 20 / 32 = 25 / 40 = 30 / 48

The five fractions are 10 / 16, 15 / 24, 20 / 32, 25 / 40 and 30 / 48

Hence, the five fractions equivalent to 5 / 8 are 10 / 16, 15 / 24, 20 / 32, 25 / 40 and 30 / 48

**(iv)** 7/10

7/10 = (7/10 × 2 / 2) = (7 / 10 × 3 / 3) = (7 / 10 × 4 / 4) = (7 / 10 × 5 / 5) = (7 / 10 × 6 / 6)

∴ 7 / 10 = 14 / 20 = 21 / 30 = 28 / 40 = 35/ 50 = 42 / 60

The five fractions are 14 / 20, 21 / 30, 28 / 40, 35 / 50 and 42 / 60

Hence, the five fractions equivalent to 7 / 10 are 14 / 20, 21 / 30, 28 / 40, 35 / 50 and 42 / 60

**(v)** 3 / 7

3 / 7 = (3 / 7 × 2 / 2) = (3 / 7 × 3 / 3) = (3 / 7 × 4 / 4) = (3 / 7 × 5 / 5) = (3 / 7 × 6 / 6)

∴ 3 / 7 = 6 / 14 = 9 / 21 = 12 / 28 = 15 / 35 = 18 / 42

The five fractions are 6 / 14, 9 / 12, 12 / 28, 15 / 35 and 18 / 42

Hence, the five fractions equivalent to 3 / 7 are 6 / 14, 9 / 21, 12 / 28, 15 / 35 and 18 / 42

**(vi)** 6 / 11

6 / 11 = (6 / 11 × 2 / 2) = (6 / 11 × 3 / 3) = (6 / 11 × 4 / 4) = (6 / 11 × 5 / 5) = (6 / 11 × 6 / 6)

∴6 / 11 = 12 / 22 = 18 / 33 = 24 / 44 = 30 / 55 = 36 / 66

The five fractions are 12 / 22, 18 / 33, 24 / 44, 30 / 55 and 36 / 66

Hence, the five fractions equivalent to 6 / 11 are 12 / 22, 18 / 33, 24 / 44, 30 / 55 and 36 / 66

**(vii)** 7/ 9

7/ 9 = (7 / 9 × 2 / 2) = (7 / 9 × 3 / 3) = (7 / 9 × 4 / 4) = (7 / 9 × 5 / 5) = (7 / 9 × 6 / 6)

∴ 6 / 11 = 14 / 18 = 21 / 27 = 28 / 36 = 35 / 45 = 42 / 54

The five fractions are 14 / 18, 21 / 27, 28 / 36, 35 / 45 and 42 / 54

Hence, the five fractions equivalent to 7 / 9 are 14 / 18, 21 / 27, 28 / 36, 35 / 45 and 42 / 54

**(viii)** 5 / 12

5 / 12 = (5 / 12 × 2 / 2) = (5 / 12 × 3 / 3) = (5 / 12 × 4 / 4) = (5 / 12 × 5 / 5) = (5 / 12 × 6 / 6)

∴ 5 / 12 = 10 / 24 = 15 / 36 = 20 / 48 = 25 / 60 = 30 / 72

The five fractions equivalent to 5 / 12 are 10 / 24, 15 / 36, 20 / 48, 25 / 60 and 30 / 72

** 2. Which of the following are the pairs of equivalent fractions?**

** (i) 5 / 6 and 20 / 24**

** (ii) 3 / 8 and 15 / 40**

** (iii) 4 / 7 and 16 / 21**

** (iv) 2 / 9 and 14 / 63**

** (v) 1 / 3 and 9 / 24**

** (vi) 2 / 3 and 33 / 22**

** Solutions **

** (i) **5 / 6 and 20 / 24

Given fractions are 5 / 6 and 20 / 24

By cross multiplication we get

(5 × 24) = 120

(6 × 20) = 120

Now (5 × 24) = (6 × 20) = 120

Hence, 5 / 6 and 20 / 24 are the pairs of equivalent fractions

**(ii)** 3 / 8 and 15 / 40

Given fractions are 3 / 8 and 15 / 40

By cross multiplication we get

(3 × 40) = 120

(8 × 15) = 120

Now (3 × 40) = (8 × 15) = 120

Hence, 3 / 8 and 15 / 40 are the pairs of equivalent fractions

**(iii)** 4 / 7 and 16 / 21

Given fractions are 4 / 7 and 16 / 21

By cross multiplication we get

(4 × 21) = 84

(7 × 16) = 112

Now (4 × 21) ≠ (7 × 16)

Hence, 4 / 7 and 16 / 21 are not the pairs of equivalent fractions

**(iv)** 2 / 9 and 14 / 63

Given fractions are 2 / 9 and 14 / 63

By cross multiplication we get

(2 × 63) = 126

(9 × 14) = 126

Now (2 × 63) = (9 × 14) = 126

Hence, 2 / 9 and 14 / 63 are the pairs of equivalent fractions

**(v)** 1 / 3 and 9 / 24

Given fractions are 1 / 3 and 9 / 24

By cross multiplication we get

(1 × 24) = 24

(3 × 9) = 27

Now (1 × 24) ≠ (3 × 9)

Hence,1 / 3 and 9 / 24 are not the pairs of equivalent fractions

**(vi)** 2 / 3 and 33 / 22

Given fractions are 2 / 3 and 33 / 22

By cross multiplication we get

(2 × 22) = 44

(3 × 33) = 99

Now (2 × 22) ≠ (3 × 33)

Hence, 2 / 3 and 33 / 22 are not the pairs of equivalent fractions

**3. Find the equivalent fraction of 3 / 5 having **

** (i) denominator 30 (ii) numerator 24**

**Solution**

(i) Let 3 / 5 = ☐ / 30

Clearly shows 30 = (5 × 6)

Now multiply the numerator by 6 also

∴ 3 / 5 = (3 × 6) / (5 × 6) = 18 /30

Hence, 18 / 30 is the equivalent fraction of 3 / 5 having denominator 30

(ii) Let 3 / 5 = 24 / ☐

Clearly shows 24 = (3 × 8)

Now multiply the denominator by 8 also

∴ 3 / 5 = (3 × 8) / (5 × 8) = 24 / 40

Hence, 24 / 40 is the equivalent fraction of 3 / 5 having numerator 24

**4**. **Find the equivalent fraction of 5 / 9 having **

** (i) denominator 54 (ii) numerator 35**

**Solution**

** (i) **Let 5 / 9 = ☐ / 54

Clearly shows 54 = (9 × 6)

Now multiply the numerator by 6 also

∴ 5 / 9 = (5 × 6) / (9 × 6) = 30 / 54

Hence, 30 / 54 is the equivalent fraction of 5 / 9 having denominator 54

(ii) Let 5 / 9 = 35 / ☐

Clearly shows 35 = (5 × 7)

Now multiply the denominator by 7 also

∴ 5 / 9 = (5 × 7) / (9 × 7) = 35 / 63

Hence, 35 / 63 is the equivalent fraction of 5 / 9 having numerator 35

**5**. **Find the equivalent fraction of 6 / 11 having **

** (i) denominator 77 (ii) numerator 60**

**Solution**

(i) Let 6 / 11 = ☐ / 77

Clearly shows 77 = (11 × 7)

Now multiply the numerator by 7 also

∴ 6 / 11 = (6 × 7) / (11 × 7) = 42 / 77

Hence, 42 / 77 is the equivalent fraction of 6 / 11 having denominator 77

(ii) Let 6 / 11 = 60 / ☐

Clearly shows 60 = (6 × 10)

Now multiply the denominator by 10 also

∴ 6 / 11 = (6 × 10) / (11 × 10) = 60 / 110

Hence, 60 / 110 is the equivalent fraction of 6 / 11 having numerator 60

## Exercise 5D PAGE NO: 93

** 1. Define like and unlike fractions and give five examples of each.**

** Solution**

Like fractions

Fractions having the same denominator are called ‘Like fractions’

The five examples of like fractions are

2 / 7, 3 / 7, 4 / 7, 5 / 7 and 6 / 7

Unlike fractions

Fractions having different denominators are called ‘Unlike fractions’

The five examples of unlike fractions are

2 / 6, 4 / 7, 5 / 9, 6 / 8, 9 / 6

**2. Convert 3 / 5, 7 / 10, 8 / 15 and 11 / 30 into like fractions**

** Solution**

** **Given fractions are 3 / 5, 7 / 10, 8 / 15 and 11 / 30

LCM of 5, 10, 15 30 = (5 × 3 × 2) = 30

Converting each of the given fractions into an equivalent fraction with denominator as 30

We get

(3 × 6) / (5 × 6) = 18 / 30 (7 × 3) / (10 × 3) = 21 / 30

(8 × 2) / (15 × 2) = 16 / 30 (11 × 1) / (30 × 1) = 11 / 30

∴ 18 / 30, 21 / 30, 16 / 30 and 11 / 30 are the required like fractions

** 3**. **Convert 1 / 4, 5 / 8, 7 / 12 and 13 / 24 into like fractions **

** Solution**

Given fractions are 1 / 4, 5 / 8, 7 / 12 and 13 / 24

LCM of 4, 8, 12, 24 = (2 × 2 × 2 × 3) = 24

Converting each of the given fractions into an equivalent fraction with denominator as 24

We get

(1 × 6) / (4 × 6) = 6 / 24 (5 × 3) / (8 × 3) = 15 / 24

(7 × 2) / (12 × 2) = 14 / 24 (13 × 1) / (24 × 1) = 13 / 24

∴ 6 / 24, 15 / 24, 14 / 24 and 13 / 24 are the required like fractions

**4**. **Fill in the place holders with the correct symbol > or <:**

** (i) 8 / 9 ☐ 5 / 9**

** (ii) 9 / 10 ☐ 7 / 10**

** (iii) 3 / 7 ☐ 6 / 7**

** (iv) 11 / 15 ☐ 8 / 15**

** (v) 6 / 11 ☐ 5 / 11**

** (vi) 11 / 20 ☐ 17 / 20**

** Solutions**

(i) Since among the two fractions with the same denominator, the one with the greater

numerator is the greater of the two

Hence, 8 / 9 > 5 / 9

(ii) Since among the two fractions with the same denominator, the one with the greater

numerator is the greater of the two

Hence, 9 / 10 > 7 / 10

(iii) Since among the two fractions with the same denominator, the one with the greater

numerator is the greater of the two

Hence, 3 / 7 < 6 / 7

(iv)Since among the two fractions with the same denominator, the one with the greater

numerator is the greater of the two

Hence, 11 / 15 > 8 / 15

(v) Since among the two fractions with the same denominator, the one with the greater

numerator is the greater of the two

Hence, 6 / 11 > 5 / 11

(vi)Since among the two fractions with the same denominator, the one with the greater

numerator is the greater of the two

Hence, 11 / 20 < 17 / 20

**5**.** Fill in the place holders with the correct symbol > or <:**

** (i) 3 / 4 ☐ 3 / 5**

** (ii) 7 / 8 ☐ 7 / 10**

** (iii) 4 / 11 ☐ 4 / 9**

** (iv) 8 / 11 ☐ 8 / 13**

** (v) 5 / 12 ☐ 5 / 8**

** (vi) 11 / 4 ☐ 11 / 15**

** Solutions**

(i) Since among two fractions with same numerator, the one with the smaller denominator is the

greater of the two

Hence 3 / 4 > 3 / 5

(ii) Since among two fractions with same numerator, the one with the smaller denominator is the

greater of the two

Hence, 7 / 8 > 7 / 10

(iii) Since among two fractions with same numerator, the one with the smaller denominator is the

greater of the two

Hence, 4 / 11 < 4 / 9

(iv) Since among two fractions with same numerator, the one with the smaller denominator is the

greater of the two

Hence, 8 / 11 > 8 / 13

(v) Since among two fractions with same numerator, the one with the smaller denominator is the

greater of the two

Hence, 5 / 12 < 5 / 8

(vi) Since among two fractions with same numerator, the one with the smaller denominator is the

greater of the two

Hence, 11 / 4 > 11 / 15

** Compare the fractions given below:**

** 6. 4 / 5, 5 / 7**

** Solution**

Given fractions are 4 / 5 and 5 / 7

LCM of 5 and 7 = (5 × 7) = 35

Now convert each one of 4 / 5 and 5 / 7 into an equivalent fraction having 35 as denominator

4 / 5 = (4 × 7) / (5 × 7) = 28 / 35

5 / 7 = (5 × 5) / (7× 5) = 25 / 35

Clearly it shows 28 / 35 > 25 / 35

Hence, 4 / 5 > 5 / 7

**7. 3 / 8, 5 / 6**

** Solution**

** **Given fractions are** **3 / 8 and 5 / 6

** **

** **

** **

** ** LCM of 8 and 6 = (2 × 2 × 2 × 3) = 24

Now convert each one of 3 / 8 and 5 / 6 into an equivalent fraction having 24 as denominator

3 / 8 = (3 × 3) / (8 × 3) = 9 / 24

5 / 6 = (5 × 4) / (6 × 4) = 20 / 24

Clearly it shows 9 / 24 < 20 / 24

Hence, 3 / 8 < 5 / 6

** 8. 7 / 11, 6 / 7**

** Solution**

** **Given fractions are 7 / 11 and 6 / 7

LCM of 11 and 7 = (11 × 7) = 77

Now convert each one of 7/11 and 6/7 into an equivalent fraction having 77 as denominator

7 / 11 = (7 × 7) / (11 × 7) = 49 / 77

6 / 7 = (6 × 11) / (7 × 11) = 66 / 77

Clearly it shows 49 / 77 < 66 / 77

Hence, 7 / 11 < 6 / 7

** 9. 5 / 6, 9 / 11**

** Solution**

** **Given fractions are 5 / 6 and 9 / 11

LCM of 11 and 6 = (11 × 6) = 66

Now convert each one of 5 / 6 and 9 / 11 into an equivalent fraction having 66 as

denominator

5 / 6 = (5 × 11) / (6 × 11) = 55 / 66

9 / 11 = (9 × 6) / (11 × 6) = 54 / 66

Clearly it shows 55 / 66 > 54 / 66

Hence, 5 / 6 > 9 / 11

**10. 2 / 3, 4 / 9**

** Solution**

** **Given fractions are 2 / 3 and 4 / 9

LCM of 3 and 9 = (3 × 3) = 9

Now convert each one of 2 / 3 and 4 / 9 into an equivalent fraction having 9 as

denominator

2 / 3 = (2 × 3) / (3 × 3) = 6 / 9

4 / 9 = (4 ×1) / (9 × 1) = 4 / 9

Clearly it shows 6 / 9 > 4 / 9

Hence, 2 / 3 > 4 / 9

**11. 6 / 13, 3 / 4**

** Solution**

Given fractions are 6 / 13 and 3 / 4

LCM of 13 and 4 = (2 × 2 × 13) = 52

Now convert each one of 6/13 and 3/4 into an equivalent fraction having 52 as denominator

6 / 13 = (6 × 4) / (13 × 4) = 24 / 52

3 / 4 = (3 × 13) / (4 × 13) = 39 / 52

Clearly it shows 24/52 < 39/52

Hence, 6 / 13 < 3 / 4

** 12. 3 / 4, 5 / 6**

** Solution**

Given fractions are 3 / 4 and 5 / 6

LCM of 4 and 6 = (2 × 2 × 3) = 12

Now convert each of 3 / 4 and 5 / 6 into an equivalent fraction having 12 as

denominator

3 / 4 = (3 × 3) / (4× 3) = 9 / 12

5 / 6 = (5 × 2) / (6 × 2) = 10 / 12

Clearly it shows 9 / 12 < 10 / 12

Hence, 3 / 4 < 5 / 6

** 13. 5 / 8, 7 / 12**

** Solution**

** **Given fractions are 5 / 8 and 7 / 12

LCM of 8 and 12 = 24

Now convert each of 5 / 8 and 7 / 12 into an equivalent fraction having 24 as

denominator

5 / 8 = (5 × 3) / (8 × 3) = 15 / 24

7 / 12 = (7 × 2) / (12 × 2) = 14 / 24

Clearly it shows 15 / 24 > 14 / 24

Hence, 5 / 8 > 7 / 12

**14. 4 / 9, 5 / 6**

** Solution**

** **Given fractions are 4 / 9 and 5 / 6

** **

LCM of 9 and 6 = (3 × 3 × 2) = 18

Now convert each of 4 / 9 and 5 / 6 into an equivalent fraction having 18 as

denominator

4 / 9 = (4 × 2) / (9 × 2) = 8 / 18

5 / 6 = (5 × 3) / (6 × 3) = 15 / 18

Clearly it shows 8 / 18 < 15 / 18

Hence, 4 / 9 < 5 / 6

**15. 4 / 5, 7 / 10**

** Solution**

Given fractions are 4 / 5 and 7 / 10

LCM of 5 and 10 = (5 × 2) = 10

Now convert each of 4 / 5 and 7 / 10 into an equivalent fraction having 10 as

denominator

4 / 5 = (4 × 2) / (5 × 2) = 8 / 10

7 / 10 = (7× 1) / (10 ×1) = 7 / 10

Clearly it shows 8 / 10 > 7 / 10

Hence, 4 / 5 > 7 / 10

## Exercise 5E PAGE NO: 96

** Find the sum:**

** 1. 5 / 8 + 1 / 8 **

** Solution**

Given 5 / 8 + 1 / 8

5 / 8 + 1 / 8 = (5 + 1) / 8

= 6 / 8

= 3 / 4

∴ Sum of 5 / 8 + 1 / 8 = 3 / 4

** 2. 4 / 9 + 8 / 9**

** Solution**

** **Given 4 / 9 + 8 / 9

4 / 9 + 8 / 9 = (4 + 8) / 9

= 12 / 9

= 4 / 3

∴ Sum of 4 / 9 + 8 / 9 = 4 / 3

=

** 3. **

** **

Solution

** 4. 2 / 9 + 5 / 6**

** Solution**

**5. 7 / 12 + 9 / 16**

** Solution**

** **

** **

** **

** 6. 4 / 15 + 17 / 20**

** Solution**

** **

** **

** **

** **

** **

** **

## Exercise 5F PAGE NO: 99

** Find the difference:**

** 1. 5 / 8 – 1 / 8**

** Solution**

** **We have

5 / 8 – 1 / 8

5 / 8 – 1 / 8 = (5-1) / 8

= 4 / 8

= 2 / 4

= 1 / 2

Hence, 5 / 8 – 1 / 8 = 1 / 2

** 2. 7 / 12 – 5 / 12**

** Solution**

** **We have

7 / 12 – 5 / 12

7 / 12 – 5 / 12 = (7 – 5) / 12

= 2 / 12

= 1 / 6

Hence, 7 /12 – 5 / 12 = 1 / 6

** 4. 5 / 6 – 4 / 9**

** Solution**

** **Given

5 / 6 – 4 / 9

LCM of 6 and 9 = (3 × 3 × 2) = 18

Now, 5 / 6 = (5 × 3) / (6 × 3) = 15 / 18

4 / 9 = (4 × 2) / (9 × 2) = 8 / 18

∴ 5 / 6 – 4 / 9 = 15 / 18 – 8 /18

= (15 – 8) / 18

= 7 / 18

Hence, 5 / 6 – 4 / 9 = 7 / 18

** 5. 1 / 2 – 3 / 8**

** Solution**

Given

1 / 2 – 3 / 8

LCM of 2 and 8 = (2 × 2 × 2) = 8

Now, 1 / 2 = (1 × 4) / (2 ×4) = 4 / 8

3 / 8 = (3 × 1) / (8 × 1) = 3 / 8

∴ 1 / 2 – 3 / 8 = 4 /8 -3 / 8

= (4 – 3) / 8

= 1 / 8

Hence, 1 / 2 – 3 / 8 = 1 / 8

** **

** 6. 5 / 8 – 7 / 12**

** Solution**

** **Given

5 / 8 – 7 / 12

LCM of 8 and 12 = (2 × 2 × 2 ×3) = 24

Now, 5 / 8 = (5 × 3) / (8 × 3) = 15 / 24

7 / 12 = (7 × 2) / (12 × 2) = 14 / 24

∴5 / 8 – 7 / 12 = 15 / 24 – 14 / 24

= (15 – 14) / 24

= 1 / 24

Hence, 5 / 8 – 7 / 12 = 1 / 24

** **

**14. 5 / 8 + 3 / 4 – 7 / 12**

** Solution**

** **Given

5 / 8 + 3 /4 – 7 / 12

LCM of 4, 8 and 12 = (2 × 2 × 2 × 3) = 24

5 / 8 = (5 × 3) / (8 ×3) = 15 / 24 (by dividing 24 / 8 =3)

3 / 4 = (3 × 6) / (4 × 6) = 9 / 12 (by dividing 24 / 4 = 6)

7 / 12 = (7 × 2) / (12 × 2) = 14 / 24 (by dividing 24 / 12 = 2)

Now, 5 / 8 + 3 / 4 – 7 / 12 = (15 + 18 – 14) / 24

= (33 – 14) / 24

= 19 / 24

Hence, 5 / 8 + 3 / 4 – 7 / 12 = 19 / 24

**15. 2 +** **11 / 15 – 5 / 9**

** Solution**

## Exercise 5G PAGE NO: 99

**1. A fraction equivalent to 3 / 5 is**

** (a) 3 + 2 / 5 + 2 (b) 3 – 2 / 5 – 2 (c) 3 × 2 / 5 × 2 (d) none of these**

** Solution**

Since two or more fractions representing the same part of a whole are called equivalent fraction

Thus 3 × 2 / 5 × 2 is equivalent fraction to 3 / 5

**2. A fraction equivalent to 8 / 12 is **

** (a) 8 + 4 / 12 + 4 (b) 8 – 4 / 12 – 4 (c) 8 ÷ 4 / 12 ÷ 4 (d) none of these**

** Solution**

** ** Since two or more fractions representing the same part of a whole are called equivalent fraction

Thus 8 ÷ 4 / 12 ÷ 4 is equivalent fraction to 8 / 12

**3. A fraction equivalent to 24 / 36 is**

** (a) 3 / 4 (b) 2 / 3 (c) 8 / 9 (d) none of these**

** Solution**

** **1, 2, 3, 4, 6, 8, 12, 24 are the factors of 24

1, 2, 3, 4, 6, 9, 12, 18, 36 are the factors of 36

Common factors of 24 and 36 are 1, 2, 3, 4, 6 and12

HCF = 12

Now dividing both numerator and denominator by 12

= 24 ÷ 12/36 ÷ 12

= 2 / 3

Thus 2 / 3 is the equivalent factor to 24 / 36

** 4. If 3 / 4 is equivalent to x / 20 then the value of x is**

** (a) 15 (b) 18 (c) 12 (d) none of these**

** Solution**

** **Since 3 / 4 = x / 20

= 20 × 3 / 4x

4x = 60

= 60 / 4

x = 30 / 2

x = 15

Hence, the value of x = 15

Option (a) is the correct answer

** 5. If 45 / 60 is equivalent to 3 / x then the value of x is **

** (a) 4 (b) 5 (c) 6 (d) 20**

** Solution**

Since 45 / 60 = 3 / x

45x = 60 × 3

45x = 180

x = 180 / 45

x = 36 / 9

x = 4

Hence, the value of x = 4

Option (a) is the correct answer

**6. Which of the following are like fractions?**

** (a) 2 / 5, 2 / 7, 2 / 9, 2 / 11 (b) 2 / 3, 3 / 4, 4 / 5, 5 / 6**

** (c) 1 / 8, 3 / 8, 5 / 8, 7 / 8 (d) none of these**

** Solution**

Fractions having the same denominator are called like fractions

Hence 1 / 8, 3 / 8, 5 / 8 and 7 / 8 are like fractions

Option (c) is the correct answer

** 7. Which of the following is a proper fraction?**

** (a) 5 / 3 (b) 5 (c) **

** (d) none of these**

** Solution**

** **If the numerator is less than the denominator then the fraction is called as proper fraction

Hence none of these are proper fractions

** 8. Which of the following is a proper fraction?**

** (a) 7 / 8 (b) **

** (c) 8 / 7 (d) none of these**

** Solution**

** **

** **If the numerator is less than the denominator then the fraction is called as proper fraction

Hence, 7 / 8 is a proper fraction

** 9. Which of the following statements is correct?**

** (a) 3 / 4 < 3 / 5 (b) 3 / 4 > 3 / 5 (c) 3 / 4 and 3 / 5 cannot be compared**

** Solution**

Between the two fractions having the same numerator, the one with the smaller denominator is the greater factor

Hence, 3 / 4 > 3 / 5

Option (b) is the correct answer

** 10. The smallest of the fractions 3 / 5, 2 / 3, 5 / 6, 7 / 10 is**

** (a) 2 / 3 (b) 7 / 10 (c) 3 / 5 (d) 5 / 6**

** Solutions**

** **

** **LCM of 5, 3, 6 and 10 = (2 × 3 × 5) = 30

Now, 2 / 3 = (2 × 10) / (3 × 10) = 20 / 30 (by dividing 30 / 3 = 10)

7/10 = (7 × 3) / (10 × 3) = 21 / 30 (by dividing 30 / 10 = 3)

3 / 5 = (3 × 6) / (5 × 6) = 18 / 30 (by dividing 30 / 5 = 6)

5 / 6 = (5 × 5) / (6 × 5) = 25/30 (by dividing 30 / 6 = 5)

∴ 18 / 30 is the smallest fraction

Hence, 3 / 5 is the smallest fraction

Option (c) is the correct answer

### RS Aggarwal Solutions for Class 6 Chapter 5 Fractions

Chapter 5 – Fractions consists of 7 exercises. RS Aggarwal Solutions have been solved in detail for each question in every exercise. Let’s have a look at the topics which are included in this chapter

- Fractions and Fractional Numbers
- Proper, Improper and Mixed Fractions
- Equivalent Fractions
- Like and Unlike Fractions
- Addition of Fractions
- Subtraction of Fractions

Also, access RS Aggarwal Solutions for Class 6 Chapter 5 Exercises

### Chapter Brief of RS Aggarwal Solutions for Class 6 Maths Chapter 5 Fractions

Fractions represent a part of the whole, for example, one-half, one quarter, two-thirds. There are three types of fractions, namely proper, improper and mixed fractions. A fraction whose numerator is less than its denominator is called a proper fraction. A fraction whose numerator is greater than or equal to its denominator is called an improper fraction. A combination of a whole number and a proper fraction is called a mixed fraction. Fractions are used in telling the time, shopping for groceries.