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07
NCERT Solutions · Maths Ch 7
Fractions
49 questions · 6 exercises
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Ex 7.1
Ex 7.2
Ex 7.3
Ex 7.4
Ex 7.5
Ex 7.6
NCERT answers with full exam-style working, step by step. Tap a question to open its solution.
1
EXERCISE 7.1 · 5 QUESTIONS
Fractional Units
Q1
Fill in the blanks with fractions: (1) Three guavas together weigh 1 kg. If they are roughly of the same size, each guava will weigh roughly ___ kg. (2) A wholesale merchant packed 1 kg of rice in four packets of equal weight. The weight of each packet is ___ kg. (3) Four friends ordered 3 glasses of sugarcane juice and shared it equally. Each one drank ___ glass.
(2 marks)
Q2
The big fish weighs 1/2 kg. The small one weighs 1/4 kg. Together they weigh ___ kg.
(2 marks)
Q3
Arrange these fraction words in order of size from the smallest to the biggest: One and a half, three quarters, one and a quarter, half, quarter, two and a half.
(3 marks)
Q4
A whole chikki is cut into 6 equal pieces in different ways. Are the 1/6 pieces of different shapes the same size?
(1 mark)
Q5
The figures show different fractional units of a whole chikki (pieces a to h). How much of a whole chikki is each piece?
(5 marks)
2
EXERCISE 7.2 · 11 QUESTIONS
Measuring and the Number Line
Q1
Continue the table for 1/2 for 2 more steps (1/2 = 1 time half; 1/2 + 1/2 = 2 times half; ... up to 5 times half).
(2 marks)
Q2
Can you create a similar table for 1/4?
(2 marks)
Q3
Make 1/3 using a paper strip. Can you use this to also make 1/6?
(2 marks)
Q4
Draw a picture and write an addition statement to show: (a) 5 times 1/4 of a roti (b) 9 times 1/4 of a roti.
(2 marks)
Q5
Match each fractional unit (1/3, 1/5, 1/8, 1/6) with the correct picture.
(2 marks)
Q6
On the number line, a unit is divided into 3 equal parts and the blue line reaches the second mark. Write the length of the blue line.
(2 marks)
Q7
On a number line a unit is divided into 5 equal parts. Write the fractions for the blue lines (reaching the 2nd and 4th marks), and then for a unit divided into 8 equal parts.
(1 mark)
Q8
On a number line, draw lines of lengths 1/10, 3/10 and 4/5.
(2 marks)
Q9
Write five more fractions of your choice and mark them on the number line.
(2 marks)
Q10
How many fractions lie between 0 and 1?
(1 mark)
Q11
The distance 0 to 1 is divided into two equal parts. The blue line is 1/2 unit long. Write the fraction for the black line which is longer (it reaches the 3rd mark). Also write the fractions for black lines on a number line with 5 parts per unit that reach the 6th, 7th, 8th and 9th marks.
(2 marks)
3
EXERCISE 7.3 · 5 QUESTIONS
Mixed Fractions
Q1
How many whole units are there in 7/2? And in 4/3 and in 7/3?
(2 marks)
Q2
Figure out the number of whole units in each of the following fractions: (a) 8/3 (b) 11/5 (c) 9/4
(2 marks)
Q3
Can all fractions greater than 1 be written as mixed numbers (a whole part plus a fractional part less than 1)?
(2 marks)
Q4
Write the following fractions as mixed fractions: (a) 9/2 (b) 9/5 (c) 21/19 (d) 47/9 (e) 12/11 (f) 19/6
(3 marks)
Q5
Write the following mixed numbers as fractions: (a) 3 1/4 (b) 7 2/3 (c) 9 4/9 (d) 3 1/6 (e) 2 3/11 (f) 3 9/10
(3 marks)
4
EXERCISE 7.4 · 13 QUESTIONS
Equivalent Fractions
Q1
Are the lengths 1/2 and 3/6 equal? Are 2/3 and 4/6 equivalent fractions? Why? How many pieces of length 1/6 make a length of 1/2? And of 1/3?
(2 marks)
Q2
Are 3/6, 4/8 and 5/10 equivalent fractions? Why?
(3 marks)
Q3
Write two equivalent fractions for 2/6. And write as many fractions as you can that are equal to 4/6.
(5 marks)
Q4
Three rotis are shared equally by four children. How much does each child get? Write the division fact, addition fact and multiplication fact.
(2 marks)
Q5
Draw a picture to show how much each child gets when 2 rotis are shared equally by 4 children. Write the division, addition and multiplication facts.
(3 marks)
Q6
Anil was in a group where 2 cakes were divided equally among 5 children. How much cake would Anil get? If another group has 10 children, how many cakes are needed so that each gets the same?
(2 marks)
Q7
Find the missing numbers: (a) 5 glasses of juice shared equally among 4 friends is the same as ___ glasses shared among 8 friends. (b) 4 kg of potatoes divided equally in 3 bags is the same as 12 kg divided equally in ___ bags. (c) 7 rotis divided among 5 children is the same as ___ rotis divided among ___ children.
(3 marks)
Q8
In which group will each child get more chikki: 1 chikki divided between 2 children or 5 chikkis divided among 8 children?
(2 marks)
Q9
In which group will each child get more: 1 chikki divided between 2 children or 4 chikkis divided among 7 children?
(2 marks)
Q10
Suppose the number of children is kept the same, but the number of units shared is increased. What happens to each child's share? Explain 1/5 (2 marks)
Q11
Decide in which group each child gets a larger share: (1) Group 1: 3 glasses among 4 children; Group 2: 7 glasses among 10 children. (2) Group 1: 4 glasses among 7 children; Group 2: 5 glasses among 7 children. Which was easier to compare?
(3 marks)
Q12
Find equivalent fractions with the same fractional unit (denominator) for the pairs: (a) 7/2 and 3/5 (b) 8/3 and 5/6 (c) 3/4 and 3/5 (d) 6/7 and 8/5 (e) 9/4 and 5/2 (f) 1/10 and 2/9 (g) 8/3 and 11/4 (h) 13/6 and 1/9
(3 marks)
Q13
Express the following fractions in lowest terms: (a) 17/51 (b) 64/144 (c) 126/147 (d) 525/112
(3 marks)
5
EXERCISE 7.5 · 3 QUESTIONS
Comparing Fractions
Q1
Compare the following fractions and justify your answers: (a) 8/3, 5/2 (b) 4/9, 3/7 (c) 7/10, 9/14 (d) 12/5, 8/5 (e) 9/4, 5/2
(3 marks)
Q2
Write the following fractions in ascending order: (a) 7/10, 11/15, 2/5 (b) 19/24, 5/6, 7/12
(3 marks)
Q3
Write the following fractions in descending order: (a) 25/16, 7/8, 13/4, 17/32 (b) 3/4, 12/5, 7/12, 5/4
(3 marks)
6
EXERCISE 7.6 · 12 QUESTIONS
Addition and Subtraction of Fractions
Q1
Add 4/7 and 6/7 using a number line.
(2 marks)
Q2
Add the following fractions using Brahmagupta's method: (a) 2/7 + 5/7 + 6/7 (b) 3/4 + 1/3 (c) 2/3 + 5/6 (d) 2/3 + 2/7 (e) 3/4 + 1/3 + 1/5
(3 marks)
Q3
Add: (f) 2/3 + 4/5 (g) 4/5 + 2/3 (h) 3/5 + 5/8 (i) 9/2 + 5/4 (j) 8/3 + 2/7
(3 marks)
Q4
Add: (k) 3/4 + 1/3 + 1/5 (l) 2/3 + 4/5 + 3/7 (m) 9/2 + 5/4 + 7/6
(3 marks)
Q5
Rahim mixes 2/3 litre of yellow paint with 3/4 litre of blue paint to make green paint. What is the volume of green paint he has made?
(2 marks)
Q6
Geeta bought 2/5 metre of lace and Shamim bought 3/4 metre of the same lace to put a complete border on a table cloth whose perimeter is 1 metre. Find the total length of lace they bought. Will it be sufficient?
(2 marks)
Q7
Subtract: (1) 5/8 − 3/8 (2) 7/9 − 5/9 (3) 10/27 − 1/27
(3 marks)
Q8
Carry out the following subtractions using Brahmagupta's method: (a) 8/15 − 3/15 (b) 2/5 − 4/15 (c) 5/6 − 4/9 (d) 2/3 − 1/2
(3 marks)
Q9
Subtract as indicated: (a) 13/4 from 10/3 (b) 18/5 from 23/3 (c) 29/7 from 45/7
(3 marks)
Q10
Jaya's school is 7/10 km from her home. She takes an auto for 1/2 km and then walks the remaining distance. How much does she walk daily?
(2 marks)
Q11
Jeevika takes 10/3 minutes to take a complete round of the park and her friend Namit takes 13/4 minutes. Who takes less time and by how much?
(2 marks)
Q12
Puzzle: can you find three different fractional units (with numerator 1) that add up to 1? And four different fractional units?
(3 marks)