NCERT Solutions Class 6th Maths Chapter – 7 Fractions Exercise – 7.6

Question 1. Solve-

(a) 2/3 + 1/7

Solution –

2/3 + 1/7
Taking LCM
[(2 × 7) + (1 × 3)] /21
= (14 + 3) /21
= 17/21

(b) 3/10 + 7/15

Solution –

3/10 + 7/15
Taking LCM 30,
= [(3 × 3) + (7 × 2)] /30
= (9 + 14) /30
= 23/30

(c) 4/9 + 2/7

Solution –

4/9 + 2/7
Taking LCM 63,
= [(4 × 7) + (2 × 9)] /63
= (28 + 18) /63
= 46/63

(d) 5/7 + 1/3

Solution –

5 /7 + 1/3
Taking LCM 21,
= [(5 × 3) + (1 × 7)] /21
= (15 + 7) /21
= 22/21

(e) 2/5 + 1/6

Solution –

2/5 + 1/6
Taking LCM 30,
= [(2 × 6) + (1 × 5)] /30
= (12 + 5) /30
= 17/30

(f) 4/5 + 2/3

Solution –

4/5 + 2/3
Taking LCM 15,
= [(4 × 3) + (2 × 5)] /15
= (12 + 10) /15
= 22/15

(g) 3/4 – 1/3

Solution –

3/4 – 1/3
Taking LCM 12,
= [(3 × 3) – (1 × 4)] /12
= (9 – 4) /12
= 5/12

(h) 5/6 – 1/3

Solution –

5/6 – 1/3
Taking LCM 6,
= [(5 × 1) – (1 × 2)] /6
= (5 – 2) /6
= 3/6
= 1/2

(i) 2/3 + 3/4 + 1/2

Solution –

2/3 + 3/4 + 1/2
Taking LCM 12,
= [(2 × 4) + (3 × 3) + (1 × 6)] /12
= (8 + 9 + 6) /12
= 23/12

(j) 1/2 + 1/3 + 1/6

Solution – 

1/2 + 1/3 + 1/6
Taking LCM 6,
= [(1 × 3) + (1 × 2) + (1 × 1)] /6
= (3 + 2 + 1) /6
= 6/6
= 1

(k) 1 1/3 + 3 2/3

Solution –

= [(3 × 1) + 1] / 3 + [(3 × 3) + 2] /3
= (3 + 1) /3 + (9 + 2) /3
= 4/3 + 11/3
= (4 + 11) /3
= 15/3
= 5

(l) 4 2/3 + 3 1/4

Solution – 

= [(3 × 4) + 2] /3 + [(3 × 4) + 1] /4
= 14/3 + 13/4
= [(14 × 4) + (13 × 3)] /12
= (56 + 39) /12
= 95/12

(m) 16/5 – 7/5

Solution –

16/5 – 7/5
= (16 – 7) /5
= 9/5

(n) 4/3 – 1/2

Solution –

4/3 – 1/2
Taking LCM 6,
= [(4 × 2) – (1 × 3)] /6
= (8 – 3) /6
= 5/6

Question 2. Sarita bought 25 metres of ribbon and Lalita 34 metres of ribbon. What is the total length of the ribbon they bought?

Solution –

Ribbon length bought by Sarita = 2/5 metre
Ribbon length bought by Lalita = 3/4 metre

The total length of the ribbon bought by both of them = 2/5 + 3/4
Taking LCM 20,
= [(2 × 4) + (3 × 5)] / 20
= (8 + 15) / 20
= 23/20 metre
∴ The total length of the ribbon bought by both Sarita and Lalita is 23/20 metre.

Question 3. Naina was given 1 1/2 piece of cake and Najma was given 1 1/3 piece of cake. Find the total amount of cake given to both of them.

Solution –

Piece of the cake given to Naina = 11/12
Piece of the cake given to Najma = 11/13
Piece of the cake given to Naina and Najma

= 1 1/2 + 1 1/3 = 1 + 1/2 + 1 + 1/3 = 1 + 1 = 1/2 + 1/3
= 2 + 1 × 3/2 × 3 + 1 × 2/3 × 2 = 2 + 3/6 + 2/6 = 2 + 5/6
= 2 5/6

Hence the total amount of pieces given to both 

Question 4. Fill in the boxes.

(a) ▯ – 5/8 = 1/4

Solutions – 

▯ – 5/8 = 1/4
▯ = 1/4 + 5/8
▯ = [(1 × 2 + 5)] /8
▯ = 7/8

(b) ▯ – 1/5 = 1/2

Solutions – 

▯ – 1/5 = 1/2
▯ = 1/2 + 1/5
▯ = [(1 × 5) + (1 × 2)] /10
▯ = (5 + 2) /10
▯ = 7/10

(c) 1/2 – ▯ = 1/6

Solutions – 

1/2 – ▯ = 1/6
▯ = 1/2 – 1/6
▯ = [(1 × 3) – (1 × 1)] /6
▯ = (3 – 1) /6
▯ = 2/6
▯ = 1/3

Question 5. Complete the addition-subtraction box.

Solution – 

(a) Addition- I Row 2/3 + 4/3 = 6/3 = 2
II Row 1/3 + 2/3 = 3/3 = 1
Subtraction- I Column – 2/3 – 1/3 = 1/3
II Column – 4/3 – 2/3 = 2/3

Thus the box may be completed as follows-

(b) Addition- I Row – 1/2 + 1/3 = 1 × 3 + 1 × 2/6 = 3 + 2/6 = 5/6
II Row – 1/3 + 1/4 = 1 × 4 + 1 × 3/12 = 4 + 3/12 = 7/12
Subtraction- I Column – 1/2 – 1/3 = 1 × 3 – 1 × 2/6 = 3 – 2/6 = 1/6
II Column – 1/3 – 1/4 = 1 × 4 – 1 × 3/12 = 4 – 3/12 = 1/12

Thus, the box may be completed as follows-

Question 6. A piece of wire 7/8 metre long broke into two pieces. One-piece was 1/4 metre long. How long is the other piece?

Solution –

Total length of wire = 7/8 metre
Length of one piece of wire = 1/4 metre
Length of the other piece of wire = Length of the original wire and this one piece of wire
= 7 / 8 – 1/4
= [(7 × 1) – (1 × 2)] / 8
= (7 – 2) / 8
= 5/8
∴ Length of the other piece of wire = 5/8 metre.

Question 7. Nandini’s house is 9/10 km from her school. She walked some distance and then took a bus for 1/2 km to reach the school. How far did she walk?

Solution –

Distance of the school from house = 9/10 km
Distance she travelled by bus = 1/2 km
Distance walked by Nandini = Total distance of the school – Distance she travelled by bus
= 9 / 10 – 1/2
= [(9 × 1) – (1 × 5)] / 10
= (9 – 5) / 10
= 4/10
= 2/5 km
∴ Distance walked by Nandini is 2/5 km.

Question 8. Asha and Samuel have bookshelves of the same size partly filled with books. Asha’s shelf is 5/6 the full and Samuel’s shelf is 2/5 th full. Whose bookshelf is more full? By what fraction?

Solution –

Fraction of Asha’s bookshelf = 5 / 6
Fraction of Samuel’s bookshelf = 2 / 5

Convert these fractions into like fractions.
5 / 6 = 5 / 6 × 5 / 5
= (5 × 5) / (6 × 5)
= 25 / 30
2 / 5 = 2 / 5 × 6 / 6
= (2 × 6) / (5 × 6)
= 12 / 30
25 / 30 > 12 / 30
5 / 6 > 2 / 5

∴ Asha’s bookshelf is more full than Samuel’s bookshelf.
Difference = 5 / 6 – 2 / 5
= 25 / 30 – 12 / 30
= 13 / 30

Question 9. Jaidev takes 2 1/5 minutes to walk across the school ground. Rahul takes 7/4 minutes to do the same. Who takes less time and by what fraction?

Solution – 

Jaidev takes 2 1/5 minutes 5
Rahul takes 2 7/4 minutes
Comparing 2 1/5 minutes and 7/4 minutes
2 1/5 = 2 + 1/5 = 2/1 + 1/5 = 2 × 5/1 × 5 = 10/5 + 1/5
= 10 + 1/5 = 11/5

Now, the given fractions are 11/5 and 7/4
11/5 × 4/4 = 44/20 and 7/4 × 5/5 = 35/20
Here, 35 < 44 ∴ 7/4 < 11/5.

∴ Rahul takes less time than Jaidev to walk across the school ground.
Difference = 11 / 5 – 7 / 4
= 44 / 20 – 35 / 20
= 9 / 20
Hence, Rahul walks across the school ground by 9 / 20 minutes.