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**Joy of Mathematics Class 6 Solutions Chapter 5 Fractions**

Welcome to NCTB Solution. Here with this post we are going to help 6th class students for the Solutions of Joy of Mathematics Class 6 Book, Chapter 5 Fractions. Here students can easily find step by step solutions of all the problems for Fractions. Exercise wise proper solutions for every problems. All the problem are solved with easily understandable methods so that all the students can understand easily. Students will get chapter 5 solutions. Here students will find exercise wise solutions for chapter 5 Exercise 5.1, 5.2, 5.3 and 5.4

**Fractions Exercise 5.1 Solution :**

**Question no – (1)**

**Solution :**

**(a)** 1/4

**(b)** 3/9

**(c)** 3/8

**(d)** 3/8

**Question no – (2) **

**Solution :**

= 8/24 = 1/3

**Question no – (3) **

**Solution :**

= Fraction is = 5/24

**Question no – (5) **

**Solution :**

**(a)** 2/3

= – 4/6, 6/9, 8/12, 10/15,12/18

**(b)** 1/5

= 2/10, 3/15, 4/20, 5/25, 6/30

**(c)** 2/9

= 4/18, 6/27, 8/36, 10/45, 12/54

**(d)** 2/7

= 4/14, 6/21, 828, 10/35, 12/42

**Question no – (6) **

**Solution :**

**(a)** 36/60 = 9/15

**(b)** 36/60= 9/15

**(c)** 36/60 = 72/120

**(d)** 36/60 = 18/30

**Question no – (7) **

**Solution :**

**(a)** 4/19 =16/76

**(b)** 6/49 = 36/294

**(c)** 13/165 = 117/135

**Question no – (8) **

**Solution :**

Proper – 8/15, 10/11, 7/8, 9/25

Improper – 20/17, 15/8, 8/7, 11/7

Mixed – 1 5/8, 2 1/15, 3 1/7

**Question no – (9)**

**Solution :**

**(a)** 18/5 = 3 3/5

**(b)** 12/5 = 2 2/5

**(c)** 16/7 = 2 2/7

**(d)** 11/3 = 3 2/3

**(e)** 28/5 = 5 3/5

**(f)** 35/6 = 5 5/6

**Question no – (10) **

**Solution :**

**(a)** 36/60

= 6/1

= 3/5

**(b) 18/24**

= 3/4

**(c) 13/39**

=1/3

**(d) 35/105**

= 1/3

**(e) 180/220**

= 18/122

= 9/11

**(f) 112/144**

= 56/72

= 14/18

= 7/9

**Question no – (11) **

**Solutions : **

**(a) 5/7**

**(b) 4/6**

**(c) 2 5/8**

**Question no – (12) **

**Solutions :**

**(a)** 4 6/7 = 34/7

**(b)** 2 3/5 = 13/5

**(c)** 6 8/9 = 62/9

**(d)** 79/11 = 86/11

**Question no – (13)**

**Solution** :

**(a)** Like fractions

**(b)** Unlike fractions

**(c)** Like fractions

**(d)** Unlike fraction

**(e)** Unlike fractions

**(f)** Like fractions

**Question no – (14)**

**Solutions :**

**(a)** 2/9, 3/9, 4/9

**(b)** 1/11, 2/11, 3/11

**(c)** 6/15, 7/15, 8/15

**Question no – (15) **

**Solution :**

= 5/9 14/3, 6/19, 2/7, 14/15, 21/28

LCM of 9, 3, 19, 7, 15, 28 is = 23940

Now, 5/9 = 5 × 92660/9 × 2660

= 13300/23940

= 14/3 = 14 × 7980/3 × 7980

= 111720/23940

= 6/19 = 6 × 1260/19 × 1260

= 6840/23940

= 2/7 = 2 × 3420/7 × 3420

= 6840/23940

= 14/15 = 14 × 1596/15 × 1596

= 22344/23940

= 21/28 = 21 × 855/28 × 855

= 17955/23940

**Fractions Exercise 5.2 Solution :**

**Question no – (1) **

**Solution :**

In ascending order,

**(a) 1/9, 3/9, 4/9, 5/9, 7/9**

In ascending order,

**(b) 1/8, 3/8, 5/8, 7/8**

In ascending order,

**(c) 2/11, 4/11, 6/11, 7/11, 8/11,**

In ascending order,

**(d) 2/25, 7/25, 9/25, 11/25, 14/25**

In ascending order,

**(e) 1/4, 5/12, 5/6, 3/8**

LCM of 4, 12, 6, 8, = 24

**∴ **1/4 = 6/24

= 5/12 = 10/24

= 5/6 = 20/24

= 3/8 = 9/24

In Ascending order,

= 1/4, 3/8, 5/12, 5/6

**(f) 3/4, 5/11, 9/22, 1/2**

LCM, is = 44

**∴** 3/4 = 33/44

= 5/4 = 20/44

= 9/22 = 18/44

= 1/2 = 22/44

**∴** Ascending, 9/22, 5/11, 1/2, 3/4

**Question no – (2) **

**Solution :**

**(a) 3/4, 4/5, 7/8, 10/11**

L.C.M is = 440

= 3/4 = 330/440

= 4/5 = 332/440

= 7/8 = 385/440

= 10/11 = 400/440

Ascending order, 3/4, 4/5, 7/8, 10/10

Descending order, 10/11, 7/8, 4/, 3/4

**(b) 7/8, 5/8, 1/8, 3/5**

In ascending order, 7/8, 5/8, 3/8, 1/5

**(e) 1/4, 3/8, 11/16, 1/3**

L.C.M is = 48

= 1/4 = 12/48

= 3/8 = 18/48

= 11/16 = 33/48

= 1/3 = 16/48

Descending order, 11/16, 3/8, 1/3, 1/4

**Question no – (3) **

**Solution :**

**(a) 4/11 + 2/11 + 1/11**

= 7/11

**(b) 1/15 + 4/15 + 9/15**

= 14/15

**(c) 3/8 + 1/8 + 7/8**

= 11/8

= 1 3/8

**(d) 1/3 + 2/5 + 5/6**

= 10 + 12 + 25/30

= 47/30

**(e) 3/8 + 5/12 + 7/16**

= 18 + 20 + 21/48

= 59/48

= 1 11/48

**(f) 1/2 + 2/3 + 3/4**

= 6 + 8 + 9/12

= 23/12

= 1 11/12

**Question no – (4) **

**Solution :**

**(a) 7/12 – 1/8**

= 14 – 3/24

= 11/24

**(b) 5/12 – 2/9**

= 15 – 8/36

= 7/36

**(c) 2/5 – 4/1**

= 22 – 20/53

= 2/55

**Question no – (5) **

**Solution :**

**(a) 3/11 + 9/22 – 5/44**

= 24 + 36 – 10/88

= 50/88

**(b) 5 1/2 + 1/3 + 2 1/4**

= 11/2 + 1/3 + 9/4

= 66 + 4 + 27/12

= 97/12

= 8 1/12

**(c) 4 3/5 + 5 1/7 – 7/35**

= 23/5 + 36/7 – 248/35

= 161 + 180 – 248/35

= 93/35

= 2 23/35

**Question no – (6)**

**Solution :**

No should be added

= 9 3/7 – 5 2/3

= 66/7 – 17/3

= 19 – 119/21

= 3 16/21

**Question no – (7)**

**Solution :**

Sum of = (2 1/5 + 14 5/16)

= 11/5 + 229/16

= 176 + 1145/80

= 1321/80

And, (6 1/9 + 3 2/5 + 1/16)

= (55/9 + 17/5 + 65/16)

= 4400 + 2449 + 2925/720

= 9774/720

Subtract = (1321/80 – 9774/720)

= 11889 – 9774/720

= 2 135/144

**Fractions Exercise 5.3 Solution :**

**Question no – (1)**

**Solution :**

**(a) 5/6 of 50**

= 250/6

**(b) 5/6 × 180**

= 150

**(c) 1/4 × 64**

= 16

**(d) 2/9 × 81**

= 2/9 × 81

= 18

**(e) 1/5 × 60**

= 12

**(f) 5/6 × 90**

= 75

**(g) 3/15 × 56**

= 63/2m

**(h) (11/81 × 1000) ml**

= 11000/9 ml

**Question no – (2)**

**Solution :**

**(a) 2/3 × 3/5**

= 2/5

**(b) 3/5 × 7/9**

=7/15

**(c) 7 × 2 3/7**

= 7 × 17/7

= 17

**(d) 2 1/3 × 4 5/7**

= 19/8 × 24/19

**(f) 1 1/4 × 4/5**

= 5/4 × 4/5

= 1

**Question no – (3) **

**Solution :**

**(a)** 5

**(b)** 7/2

**(c)** 2/7

**(d)** 1/11

**(e)** 5/13

**(f)** 1

**Question no – (4) **

**Solution :**

**(a) 8 ÷ 4/9**

= 8 × 9/4

= 18

**(b) 5 1/7 ÷ 4 1/2**

= 36/7 × 2/9

= 8/7

**(c) 3 3/5 ÷ 1 1/5**

= 18/5 ÷ 6/5

= 18/5 × 5/6

= 3

**(d) 3 3/7 ÷ 2 1/7**

= 24/7 ÷ 15/7

= 24/7 × 7/15

= 8/5

**Question no – (5)**

**Solution :**

**(a)** Sum = (5 1/12 + 3/23

= (61/12 + 11/3)

= 61 + 44/12

= 105/12

= 8 9/12

Difference = (5 1/12 – 3 2/3)

= 61/12 – 11/3

= 61 – 44/12

= 17/12

∴ 8 9/12 ÷ 17/12

= 105/12 × 12/17

= 6 3/17

**(c)** Other fraction = 11/27 ÷ 4/9

= 28/27 ÷ 4/9

= 28/27 × 9/4

= 7/3

= 2 1/3

**Question no – (6) **

**Solution :**

**(a) 5 1/2 of (2/3 – 3/5) + 1/2 ÷ 3/11**

= 11/2 of (10 – 9 /15) + 1/2 × 1/3

= 11/2 of 1/15 + 11/6

= 11/2 × 1/15 + 11/6

= 11/30 + 11/6

= 11 + 5/30

= 66/30

= 11/5

= 2 1/5

**(b) 5 1/7 + [5 2/3 + {3 3/10 ÷ (2 (4/5 – 7/10)}]**

= 36/7 + [17/3 + {33/10 + (14/5 – 710)}]

= 36/7 [17 + {33/10 ÷ (28 – 7/10)}]

= 36/7+ [17 + {33/10 × 10/21}

= 36/7 + [17/3 + 11/7]

= 36/7 + 152/21

= 108 + 152/21

= 260/21

= 12 8/21

**(d) 3/10 of 91/3 + 7/12) ÷ (5/6 – 2/5)**

= 3/10 of (4 + 7/12) ÷ (25 – 12/30)

= 3/10 of (11/12 ÷ 13/30)

= 3/10 of (11/12 ÷ 30/13)

= 3/10 of 55/26

= 3/10 of 55/26

= 33/52

**(e) (1/2 – 1/3) of (2/3 – 3/5) × (4/5 – 7/15)**

= 93 – 2/6) of (10 – 9/15) × (12 – 7/15)

= 1/6 of 1/15 × 5/15

= 1/6 × 1/45

= 1/270

**(f) (3/5 – 2/15) ÷ (9/25 ÷ 1/5) + (7/10 – 1/5)**

= (9 – 2/15) ÷ (9 – 5/25) + (7 – 2/10)

= 7/15 ÷ 4/25 + 5/10

= 7/15 × 25/4 + 5/10

= 35/12 + 5/10

= 175 + 30/60

= 205/60

= 41/12

**(g) 9 1/2 – [7 1/2 + {4 – (5 – 2)}]**

= 19/2 – [15/2 + {4 – 95 – 2)}]

= 19/2 – 15/2 + 1

= 19/2 – [15/2 + 1

= 19/2 – [15 + 2/2]

= 19/2 – 17/2

= 19 – 17/2

= 2/2

= 1

**(h) (2/5 + 1/7) ÷ (1/5 – 1/8) – 5/21**

= (14 + 5/35) ÷ (98 – 5/40) – 5/21

= 19/35 ÷ 3/40- 5/21

= 152/21 – 5/21

= 152 – 5/21

= 147/21

= 7

**Fractions Exercise 5.4 Solution :**

**Question no – (1)**

**Solution :**

Measure of one side = 16 1/2 ÷ 4

= 33/2 × 1/4

= 33/8

= 4 1/8 m

**Question no – (2)**

**Solution :**

Cost of 1 kg rice = 150 ÷ 3 3/4

= 150 ÷ 15/4

= 150 × 4/5

= 40 Rs

**Question no – (3)**

**Solution :**

Packets = (10 kg ÷ 1 1/4)

= (10 ÷ 5/4)

= (10 × 4/5)

= 8 packets

**Question no – (4)**

**Solution :**

Total pieces = (15 ÷ 3/4)

= 15 × 4/3

= 20 pieces

**Question no – (5)**

**Solution :**

Number, be x

= 1/5 × x = 132

= x = 132 × 5

= 660

**Question no – (6)**

**Solution :**

Girls = (40 × 3/5)

= 24

Boys = (1 – 3/5)

= 5 – 3/5

= 2/5

**Question no – (7)**

**Solution :**

= 2/13 pairs copper

Gold = (1 – 2/13) parts

= (13 – 2/13)

= 11/13 parts

∴ Weight of gold = (65 × 11/13)

= 53 gm

**Question no – (8)**

**Solution :**

Son + Daughter = (1/3 + 1/5)

= 5 + 3/15

= 8/15

Rest = (1 – 8/15)

= 7/15

**Question no – (9)**

**Solution : **

Total travel by bus and scooter,

= (5/16 + 7/20)

= 25 + 28/80

= 53/80

Running, = (1 – 53/80)

= 80 – 53/80

= 27/80

**∴** 27/80 = 540

= 27 = 540 × 80/27

= 1600 m

Therefore, altogether he will go 1600 m.

**Question no – (10)**

**Solution :**

Let, the capacity = x

= 3/4x – 12 = 5/12x

= 3/4x – 5/12x = 12

= 9x – 5x/12 = 12

= 4x = 12 × 12

= x = 12 × 12/4

= x = 36 litre

Therefore, the capacity of the can will be 36 litre.

**Question no – (11)**

**Solution :**

Broken eggs = (52 × 6/13)

= 24 eggs.

Left = (52 – 24)

= 28 eggs

Thus, there are 24 eggs are left.

**Question no – (12)**

**Solution :**

Bharat covered = ( 1 – 2/5)

= 5 – 2/5

= 3/5th

Let, total length = 1

**∴** 3/5th journey = 210

= 3 = 210 × 5

= 1 = 210 × 5/3

= 350 km

Therefore, the total length of Bharat journey was 350 km.

**Next Chapter Solution :**

👉 Chapter 6 👈