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NCERT Solutions
Fractions
50 Solutions
Exercise:
All Exercises
Section 7.1 Figure it Out
Section 7.2 Figure it Out
Section 7.3 Figure it Out
Section 7.4 Figure it Out
Section 7.5 Figure it Out
Section 7.6 Answer the following questions
Section 7.6 Comparison Problems
Section 7.6 Figure it Out
Section 7.6 Figure it Out (Lowest Terms)
Section 7.6 Find equivalent fractions
Section 7.7 Figure it Out
Section 7.8 Figure it Out
Section 7.9 Puzzle!
Q1
Section 7.1 Figure it Out
Three guavas together weigh 1 kg . If they are roughly of the same size, each guava will roughly weigh ______ kg.
Q2
Section 7.1 Figure it Out
A wholesale merchant packed 1 kg of rice in four packets of equal weight. The weight of each packet is ______ kg.
Q3
Section 7.1 Figure it Out
Four friends ordered 3 glasses of sugarcane juice and shared it equally among themselves. Each one drank ______ glass of sugarcane juice.
Q4
Section 7.1 Figure it Out
The big fish weighs
1
2
\frac{1}{2}
2
1
kg. The small one weighs
1
4
\frac{1}{4}
4
1
kg. Together they weigh ______ kg.
Q5
Section 7.1 Figure it Out
Arrange these fraction words in order of size from the smallest to the biggest in the empty box below: One and a half, three quarters, one and a quarter, half, quarter, two and a half.
Q1
Section 7.2 Figure it Out
The figures below show different fractional units of a whole chikki. How much of a whole chikki is each piece? a. A rectangular chikki is shown divided into 12 small equal squares. One square is highlighted. b. A rectangular chikki is shown divided into 4 equal vertical bars. One bar is highlighted. c. A rectangular chikki is shown divided into 8 small equal squares. One square is highlighted. d. A rectangular chikki is shown divided into 6 equal vertical bars. One bar is highlighted. e. A rectangular chikki is shown divided into 8 equal triangles. One triangle is highlighted. f. A rectangular chikki is shown divided into 6 equal horizontal bars. One bar is highlighted. g. A rectangular chikki is shown divided into 24 small equal squares. One square is highlighted. h. A rectangular chikki is shown divided into 24 small equal triangles. One triangle is highlighted.
Q1
Section 7.3 Figure it Out
Continue this table of
1
2
\frac{1}{2}
2
1
for 2 more steps.
Q2
Section 7.3 Figure it Out
Can you create a similar table for
1
4
\frac{1}{4}
4
1
?
Q3
Section 7.3 Figure it Out
Make
1
3
\frac{1}{3}
3
1
using a paper strip. Can you use this to also make
1
6
\frac{1}{6}
6
1
?
Q4
Section 7.3 Figure it Out
Draw a picture and write an addition statement as above to show: a. 5 times
1
4
\frac{1}{4}
4
1
of a roti b. 9 times
1
4
\frac{1}{4}
4
1
of a roti
Q5
Section 7.3 Figure it Out
Match each fractional unit with the correct picture: Fractions:
1
3
,
1
5
,
1
8
,
1
6
\frac{1}{3}, \frac{1}{5}, \frac{1}{8}, \frac{1}{6}
3
1
,
5
1
,
8
1
,
6
1
Pictures: A circle divided into 5 equal sectors, with one shaded. A circle divided into 6 equal sectors, with one shaded. A circle divided into 3 equal sectors, with one shaded. A circle divided into 8 equal sectors, with one shaded.
Q1
Section 7.4 Figure it Out
On a number line, draw lines of lengths
1
10
,
3
10
\frac{1}{10}, \frac{3}{10}
10
1
,
10
3
, and
4
5
\frac{4}{5}
5
4
.
Q2
Section 7.4 Figure it Out
Write five more fractions of your choice and mark them on the number line.
Q3
Section 7.4 Figure it Out
How many fractions lie between 0 and 1? Think, discuss with your classmates, and write your answer.
Q4
Section 7.4 Figure it Out
What is the length of the blue line and black line shown below? The distance between 0 and 1 is 1 unit long, and it is divided into two equal parts. The length of each part is
1
2
\frac{1}{2}
2
1
. So the blue line is
1
2
\frac{1}{2}
2
1
units long. Write the fraction that gives the length of the black line in the box.
Q5
Section 7.4 Figure it Out
Write the fraction that gives the lengths of the black lines in the respective boxes.
Q1
Section 7.5 Figure it Out
How many whole units are there in
7
2
\frac{7}{2}
2
7
?
Q2
Section 7.5 Figure it Out
How many whole units are there in
4
3
\frac{4}{3}
3
4
and in
7
3
\frac{7}{3}
3
7
?
Q3
Section 7.5 Figure it Out
Figure out the number of whole units in each of the following fractions: a.
8
3
\frac{8}{3}
3
8
b.
11
5
\frac{11}{5}
5
11
c.
9
4
\frac{9}{4}
4
9
Q4
Section 7.5 Figure it Out
Can all fractions greater than 1 be written as such mixed numbers?
Q5
Section 7.5 Figure it Out
Write the following fractions as mixed fractions (e.g.,
9
2
=
4
1
2
\frac{9}{2}=4\frac{1}{2}
2
9
=
4
2
1
): a.
9
2
\frac{9}{2}
2
9
b.
9
5
\frac{9}{5}
5
9
c.
21
19
\frac{21}{19}
19
21
d.
47
9
\frac{47}{9}
9
47
e.
12
11
\frac{12}{11}
11
12
f.
19
6
\frac{19}{6}
6
19
Q6
Section 7.5 Figure it Out
Write the following mixed numbers as fractions: a.
3
1
4
3\frac{1}{4}
3
4
1
b.
7
2
3
7\frac{2}{3}
7
3
2
c.
9
4
9
9\frac{4}{9}
9
9
4
d.
3
1
6
3\frac{1}{6}
3
6
1
e.
2
3
11
2\frac{3}{11}
2
11
3
f.
3
9
10
3\frac{9}{10}
3
10
9
Q1
Section 7.6 Answer the following questions
Are the lengths
1
2
\frac{1}{2}
2
1
and
3
6
\frac{3}{6}
6
3
equal?
Q2
Section 7.6 Answer the following questions
Are
2
3
\frac{2}{3}
3
2
and
4
6
\frac{4}{6}
6
4
equivalent fractions? Why?
Q3
Section 7.6 Answer the following questions
How many pieces of length
1
6
\frac{1}{6}
6
1
will make a length of
1
2
\frac{1}{2}
2
1
?
Q4
Section 7.6 Answer the following questions
How many pieces of length
1
6
\frac{1}{6}
6
1
will make a length of
1
3
\frac{1}{3}
3
1
?
Q1
Section 7.6 Comparison Problems
In which group will each child get more chikki? 1 chikki divided between 2 children or 5 chikkis divided among 8 children.
Q2
Section 7.6 Comparison Problems
What about the following groups? In which group will each child get more? 1 chikki divided between 2 children or 4 chikkis divided among 7 children.
Q3
Section 7.6 Comparison Problems
Now, decide in which of the two groups will each child get a larger share:
Group 1: 3 glasses of sugarcane juice divided equally among 4 children. Group 2: 7 glasses of sugarcane juice divided equally among 10 children.
Group 1: 4 glasses of sugarcane juice divided equally among 7 children. Group 2: 5 glasses of sugarcane juice divided equally among 7 children. Which groups were easier to compare? Why?
Q1
Section 7.6 Figure it Out
Are
3
6
,
4
8
,
5
10
\frac{3}{6}, \frac{4}{8}, \frac{5}{10}
6
3
,
8
4
,
10
5
equivalent fractions? Why?
Q2
Section 7.6 Figure it Out
Write two equivalent fractions for
2
6
\frac{2}{6}
6
2
.
Q3
Section 7.6 Figure it Out
4
6
=
□
=
□
=
□
=
…
…
…
\frac{4}{6} = \square = \square = \square = \ldots\ldots\ldots
6
4
=
□
=
□
=
□
=
………
(Write as many as you can)
Q4
Section 7.6 Figure it Out
Three rotis are shared equally by four children. Show the division in the picture and write a fraction for how much each child gets. Also, write the corresponding division facts, addition facts, and, multiplication facts.
Q5
Section 7.6 Figure it Out
Draw a picture to show how much each child gets when 2 rotis are shared equally by 4 children. Also, write the corresponding division facts, addition facts, and multiplication facts.
Q6
Section 7.6 Figure it Out
Anil was in a group where 2 cakes were divided equally among 5 children. How much cake would Anil get?
Q7
Section 7.6 Figure it Out
Find the missing numbers: a. 5 glasses of juice shared equally among 4 friends is the same as ______ glasses of juice shared equally among 8 friends. So,
5
4
=
□
8
\frac{5}{4} = \frac{\square}{8}
4
5
=
8
□
. b. 4 kg of potatoes divided equally in 3 bags is the same as 12 kgs of potatoes divided equally in ______ bags. So,
4
3
=
12
□
\frac{4}{3} = \frac{12}{\square}
3
4
=
□
12
. c. 7 rotis divided among 5 children is the same as ______ rotis divided among ______ children. So,
7
5
=
□
□
\frac{7}{5} = \frac{\square}{\square}
5
7
=
□
□
.
Q1
Section 7.6 Figure it Out (Lowest Terms)
Express the following fractions in lowest terms: a.
17
51
\frac{17}{51}
51
17
b.
64
144
\frac{64}{144}
144
64
c.
126
147
\frac{126}{147}
147
126
d.
525
112
\frac{525}{112}
112
525
Q1
Section 7.6 Find equivalent fractions
Find equivalent fractions for the given pairs of fractions such that the fractional units are the same. a.
7
2
\frac{7}{2}
2
7
and
3
5
\frac{3}{5}
5
3
b.
8
3
\frac{8}{3}
3
8
and
5
6
\frac{5}{6}
6
5
c.
3
4
\frac{3}{4}
4
3
and
3
5
\frac{3}{5}
5
3
d.
6
7
\frac{6}{7}
7
6
and
8
5
\frac{8}{5}
5
8
e.
9
4
\frac{9}{4}
4
9
and
5
2
\frac{5}{2}
2
5
f.
1
10
\frac{1}{10}
10
1
and
2
9
\frac{2}{9}
9
2
g.
8
3
\frac{8}{3}
3
8
and
11
4
\frac{11}{4}
4
11
h.
13
6
\frac{13}{6}
6
13
and
1
9
\frac{1}{9}
9
1
Q1
Section 7.7 Figure it Out
Compare the following fractions and justify your answers: a.
8
3
,
5
2
\frac{8}{3}, \frac{5}{2}
3
8
,
2
5
b.
4
9
,
3
7
\frac{4}{9}, \frac{3}{7}
9
4
,
7
3
c.
7
10
,
9
14
\frac{7}{10}, \frac{9}{14}
10
7
,
14
9
d.
12
5
,
8
5
\frac{12}{5}, \frac{8}{5}
5
12
,
5
8
e.
9
4
,
5
2
\frac{9}{4}, \frac{5}{2}
4
9
,
2
5
Q2
Section 7.7 Figure it Out
Write the following fractions in ascending order. a.
7
10
,
11
15
,
2
5
\frac{7}{10}, \frac{11}{15}, \frac{2}{5}
10
7
,
15
11
,
5
2
b.
19
24
,
5
6
,
7
12
\frac{19}{24}, \frac{5}{6}, \frac{7}{12}
24
19
,
6
5
,
12
7
Q3
Section 7.7 Figure it Out
Write the following fractions in descending order. a.
25
16
,
7
8
,
13
4
,
17
32
\frac{25}{16}, \frac{7}{8}, \frac{13}{4}, \frac{17}{32}
16
25
,
8
7
,
4
13
,
32
17
b.
3
4
,
12
5
,
7
12
,
5
4
\frac{3}{4}, \frac{12}{5}, \frac{7}{12}, \frac{5}{4}
4
3
,
5
12
,
12
7
,
4
5
Q1
Section 7.8 Figure it Out
Add the following fractions using Brahmagupta's method: a.
2
7
+
5
7
+
6
7
\frac{2}{7}+\frac{5}{7}+\frac{6}{7}
7
2
+
7
5
+
7
6
b.
3
4
+
1
3
\frac{3}{4}+\frac{1}{3}
4
3
+
3
1
c.
2
3
+
5
6
\frac{2}{3}+\frac{5}{6}
3
2
+
6
5
d.
2
3
+
2
7
\frac{2}{3}+\frac{2}{7}
3
2
+
7
2
e.
3
4
+
1
3
+
1
5
\frac{3}{4}+\frac{1}{3}+\frac{1}{5}
4
3
+
3
1
+
5
1
f.
2
3
+
4
5
\frac{2}{3}+\frac{4}{5}
3
2
+
5
4
g.
4
5
+
2
3
\frac{4}{5}+\frac{2}{3}
5
4
+
3
2
h.
3
5
+
5
8
\frac{3}{5}+\frac{5}{8}
5
3
+
8
5
i.
9
2
+
5
4
\frac{9}{2}+\frac{5}{4}
2
9
+
4
5
j.
8
3
+
2
7
\frac{8}{3}+\frac{2}{7}
3
8
+
7
2
k.
3
4
+
1
3
+
1
5
\frac{3}{4}+\frac{1}{3}+\frac{1}{5}
4
3
+
3
1
+
5
1
l.
2
3
+
4
5
+
3
7
\frac{2}{3}+\frac{4}{5}+\frac{3}{7}
3
2
+
5
4
+
7
3
m.
9
2
+
5
4
+
7
6
\frac{9}{2}+\frac{5}{4}+\frac{7}{6}
2
9
+
4
5
+
6
7
Q2
Section 7.8 Figure it Out
Rahim mixes
2
3
\frac{2}{3}
3
2
litres of yellow paint with
3
4
\frac{3}{4}
4
3
litres of blue paint to make green paint. What is the volume of green paint he has made?
Q3
Section 7.8 Figure it Out
Geeta bought
2
5
\frac{2}{5}
5
2
meter of lace and Shamim bought
3
4
\frac{3}{4}
4
3
meter of the same lace to put a complete border on a table cloth whose perimeter is 1 meter long. Find the total length of the lace they both have bought. Will the lace be sufficient to cover the whole border?
Q4
Section 7.8 Figure it Out
Subtract:
5
8
−
3
8
\frac{5}{8}-\frac{3}{8}
8
5
−
8
3
7
9
−
5
9
\frac{7}{9}-\frac{5}{9}
9
7
−
9
5
10
27
−
1
27
\frac{10}{27}-\frac{1}{27}
27
10
−
27
1
Q5
Section 7.8 Figure it Out
Carry out the following subtractions using Brahmagupta's method: a.
8
15
−
3
15
\frac{8}{15}-\frac{3}{15}
15
8
−
15
3
b.
2
5
−
4
15
\frac{2}{5}-\frac{4}{15}
5
2
−
15
4
c.
5
6
−
4
9
\frac{5}{6}-\frac{4}{9}
6
5
−
9
4
d.
2
3
−
1
2
\frac{2}{3}-\frac{1}{2}
3
2
−
2
1
Q6
Section 7.8 Figure it Out
Subtract as indicated: a.
13
4
\frac{13}{4}
4
13
from
10
3
\frac{10}{3}
3
10
b.
18
5
\frac{18}{5}
5
18
from
23
3
\frac{23}{3}
3
23
c.
29
7
\frac{29}{7}
7
29
from
45
7
\frac{45}{7}
7
45
Q7
Section 7.8 Figure it Out
Solve the following problems: a. Jaya's school is
7
10
\frac{7}{10}
10
7
km from her home. She takes an auto for
1
2
\frac{1}{2}
2
1
km from her home daily, and then walks the remaining distance to reach her school. How much does she walk daily to reach the school? b. Jeevika takes
10
3
\frac{10}{3}
3
10
minutes to take a complete round of the park and her friend Namit takes
13
4
\frac{13}{4}
4
13
minutes to do the same. Who takes less time and by how much?
Q1
Section 7.9 Puzzle!
Can you find three different fractional units that add up to 1?
Q2
Section 7.9 Puzzle!
Can you find four different fractional units that add up to 1?
More from this chapter
Chapter overview
Important Points
Practice Questions
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