| Exercise 7.1 Exercise 7.2 Exercise 7.3 Exercise 7.4 Exercise 7.5 Exercise 7.6 |
NCERT Answers for Class 6 Maths Chapter 7 Fractions Ex 7.6
Ex 7.6 Class 6 Maths Question 1. Solve
Answer
Taking LCM
[(2 × 7) + (1 × 3)] / 21
= (14 + 3) / 21
= 17 / 21
(b) 3 / 10 + 7 / 15
Taking LCM 30
= [(3 × 3) + (7 × 2)] / 30
= (9 + 14) / 30
= 23 / 30
(c) 4 / 9 + 2/ 7
Taking LCM 63
= [(4 × 7) + (2 × 9)] / 63
= (28 + 18) / 63
= 46 / 63
(d) 5 / 7 + 1 / 3
Taking LCM 21
= [(5 × 3) + (1 × 7)] / 21
= (15 + 7) / 21
= 22 / 21
(e) 2 / 5 + 1 / 6
Taking LCM 30
= [(2 × 6) + (1 × 5)] / 30
= (12 + 5) / 30
= 17 / 30
(f) 4 / 5 + 2 / 3
Taking LCM 15
= [(4 × 3) + (2 × 5)] / 15
= (12 + 10) / 15
= 22 / 15
(g) 3 / 4 – 1 / 3
Taking LCM 12
= [(3 × 3) – (1 × 4)] / 12
= (9 – 4) / 12
= 5 / 12
(h) 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
Taking LCM 12
= [(2 × 4) + (3 × 3) + (1 × 6)] / 12
= (8 + 9 + 6) / 12
= 23 / 12
(j) 1 / 2 + 1 / 3 + 1 / 6
Taking LCM 6
= [(1 × 3) + (1 × 2) + (1 × 1)] / 6
= (3 + 2 + 1) / 6
= 6 / 6
= 1
(k) 
= [(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) 
= [(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
= (16 – 7) / 5
= 9 / 5
(n) 4 /3 – 1 / 2
Taking LCM 6
= [(4 × 2) – (1 × 3)] / 6
= (8 – 3) /6
= 5 / 6
Ex 7.6 Class 6 Maths Question 2. Sarita bought 2/5 metre of ribbon and Lalita 3/4 metre of ribbon. What is the total length of the ribbon they bought?
Answer:
Ribbon length bought by Sarita = 2/5 metre
Ribbon length bought by Lalita = 3/4 metre
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
∴ Total length of the ribbon bought by both Sarita and Lalita is 23/20 metre
Ex 7.6 Class 6 Maths Question 3.
Answer:
Fraction of cake Naina got =
= 3/2
Fraction of cake Najma got =
= 4/3
Total amount of cake given to both of them = 3 / 2 + 4 / 3
= [(3 × 3) + (4 × 2)] / 6
= (9 + 8) / 6
= 17 / 6
= 
Ex 7.6 Class 6 Maths Question 4. Fill in the boxes:
(a) ▯ – 5 / 8 = 1 / 4
(b) ▯ – 1 / 5 = 1 / 2
(c) 1 / 2 – ▯ = 1 / 6
Answer:
(a) ▯ – 5 / 8 = 1 / 4
▯ = 1 / 4 + 5 / 8
▯ = [(1 × 2 + 5)] / 8
▯ = 7 / 8
(b) ▯ – 1 / 5 = 1 / 2
▯ = 1 / 2 + 1 / 5
▯ = [(1 × 5) + (1 × 2)] / 10
▯ = (5 + 2) / 10
▯ = 7 / 10
(c) 1 / 2 – ▯ = 1 / 6
▯ = 1 / 2 – 1 / 6
▯ = [(1 × 3) – (1 × 1)] / 6
▯ = (3 – 1) / 6
▯ = 2 / 6
▯ 1 / 3
Ex 7.6 Class 6 Maths Question 5. Complete the addition and subtraction box.
Answer:
(a) 2 / 3 + 4 / 3
= (2 + 4) / 3
= 6 / 3
= 2
1 / 3 + 2 / 3
= (1 + 2) / 3
= 3 / 3
= 1
2 / 3 – 1 / 3
= (2 – 1) / 3
= 1 / 3
4 / 3 – 2 / 3
= (4 – 2) / 3
= 2 / 3
1 / 3 + 2 / 3
= (1 + 2) / 3
= 3 / 3
= 1
Hence, the complete given box is
(b) 1 / 2 + 1 / 3
= [(1 × 3) + (1 × 2)] / 6
= (3 + 2) / 6
= 5 / 6
1 / 3 + 1 / 4
= [(1 × 4) + (1 × 3)] / 12
= (4 + 3) / 12
= 7 / 12
1 / 2 – 1 / 3
= [(1 × 3) – (1 × 2)] / 6
= (3 – 2) / 6
= 1 / 6
1 / 3 – 1 / 4
= [(1 × 4) – (1 ×3)] / 12
= (4 – 3) / 12
= 1 / 12
1 / 6 + 1 / 12
= [(1 × 2) + 1] / 12
= (2 + 1) / 12
= 3 / 12
= 1 / 4
Hence, the complete given box is
Ex 7.6 Class 6 Maths 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?
Answer:
Total length of wire = 7 / 8 metre
Length of one piece of wire = 1 / 4 metre
Length of 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
Ex 7.6 Class 6 Maths 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?
Answer:
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
Ex 7.6 Class 6 Maths Question 8. Asha and Samuel have bookshelves of the same size partly filled with books. Asha’s shelf is 5/6 th full and Samuel’s shelf is 2/ 5 th full. Whose bookshelf is more full? By what fraction?
Answer:
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
Ex 7.6 Class 6 Maths Question 9.
Answer:
Time taken by Jaidev to walk across the school ground =
= 11 / 5 minutes
Time taken by Rahul to walk across the school ground = 7 / 4 minutes
Convert these fractions into like fractions
11 / 5 = 11 / 5 × 4 / 4
= (11 × 4) / (5 × 4)
= 44 / 20
7 / 4 = 7 / 4 × 5 / 5
= (7 × 5) / (4 × 5)
= 35 / 20
Clearly, 44 / 20 > 35 / 20
11 / 5 > 7 / 4
∴ 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
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