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Working with Fractions
NCERT Solutions
NCERT Solutions
Working with Fractions
48 Solutions
Exercise:
All Exercises
Figure it Out (Applications of Fraction Multiplication)
Figure it Out (Division and Mixed Problems)
Figure it Out (Multiplication of Fractions and Whole Numbers)
Figure it Out (Multiplication of Two Fractions)
Figure it Out 1
Figure it Out 2
Figure it Out 3
Figure it Out 4
Q1
Figure it Out (Applications of Fraction Multiplication)
A water tank is filled from a tap. If the tap is open for 1 hour,
7
10
\frac{7}{10}
10
7
of the tank gets filled. How much of the tank is filled if the tap is open for
(a)
1
3
\frac{1}{3}
3
1
hour _____
(b)
2
3
\frac{2}{3}
3
2
hour _____
(c)
3
4
\frac{3}{4}
4
3
hour _____
(d)
7
10
\frac{7}{10}
10
7
hour _____
(e) For the tank to be full, how long should the tap be running?
Q2
Figure it Out (Applications of Fraction Multiplication)
The government has taken
1
6
\frac{1}{6}
6
1
of Somu's land to build a road. What part of the land remains with Somu now? She gives half of the remaining part of the land to her daughter Krishna and
1
3
\frac{1}{3}
3
1
of it to her son Bora. After giving them their shares, she keeps the remaining land for herself.
(a)
What part of the original land did Krishna get?
(b)
What part of the original land did Bora get?
(c)
What part of the original land did Somu keep for herself?
Q3
Figure it Out (Applications of Fraction Multiplication)
Find the area of a rectangle of sides
3
3
4
ft
3\frac{3}{4} \text{ ft}
3
4
3
ft
and
9
3
5
ft
9\frac{3}{5} \text{ ft}
9
5
3
ft
.
Q4
Figure it Out (Applications of Fraction Multiplication)
Tsewang plants four saplings in a row in his garden. The distance between two saplings is
3
4
m
\frac{3}{4} \text{ m}
4
3
m
. Find the distance between the first and last sapling.
Q5
Figure it Out (Applications of Fraction Multiplication)
Which is heavier:
12
15
\frac{12}{15}
15
12
of 500 grams or
3
20
\frac{3}{20}
20
3
of 4 kg ?
Q1
Figure it Out (Division and Mixed Problems)
Evaluate the following:
3
÷
7
9
3 \div \frac{7}{9}
3
÷
9
7
14
4
÷
2
\frac{14}{4} \div 2
4
14
÷
2
2
3
÷
2
3
\frac{2}{3} \div \frac{2}{3}
3
2
÷
3
2
14
6
÷
7
3
\frac{14}{6} \div \frac{7}{3}
6
14
÷
3
7
4
3
÷
3
4
\frac{4}{3} \div \frac{3}{4}
3
4
÷
4
3
7
4
÷
1
7
\frac{7}{4} \div \frac{1}{7}
4
7
÷
7
1
8
2
÷
4
15
\frac{8}{2} \div \frac{4}{15}
2
8
÷
15
4
1
5
÷
1
9
\frac{1}{5} \div \frac{1}{9}
5
1
÷
9
1
1
6
÷
11
12
\frac{1}{6} \div \frac{11}{12}
6
1
÷
12
11
3
2
3
÷
1
3
8
3\frac{2}{3} \div 1\frac{3}{8}
3
3
2
÷
1
8
3
Q2
Figure it Out (Division and Mixed Problems)
For each of the questions below, choose the expression that describes the solution. Then simplify it. (a) Maria bought 8 m of lace to decorate the bags she made for school. She used
1
4
\frac{1}{4}
4
1
m for each bag and finished the lace. How many bags did she decorate?
(i)
8
×
1
4
8 \times \frac{1}{4}
8
×
4
1
(ii)
1
8
×
1
4
\frac{1}{8} \times \frac{1}{4}
8
1
×
4
1
(iii)
8
÷
1
4
8 \div \frac{1}{4}
8
÷
4
1
(iv)
1
4
÷
8
\frac{1}{4} \div 8
4
1
÷
8
(b)
1
2
\frac{1}{2}
2
1
meter of ribbon is used to make 8 badges. What is the length of the ribbon used for each badge?
(i)
8
×
1
2
8 \times \frac{1}{2}
8
×
2
1
(ii)
1
2
÷
1
8
\frac{1}{2} \div \frac{1}{8}
2
1
÷
8
1
(iii)
8
÷
1
2
8 \div \frac{1}{2}
8
÷
2
1
(iv)
1
2
÷
8
\frac{1}{2} \div 8
2
1
÷
8
(c)
A baker needs
1
6
\frac{1}{6}
6
1
kg of flour to make one loaf of bread. He has 5 kg of flour. How many loaves of bread can he make?
(i)
5
×
1
6
5 \times \frac{1}{6}
5
×
6
1
(ii)
1
6
÷
5
\frac{1}{6} \div 5
6
1
÷
5
(iii)
5
÷
1
6
5 \div \frac{1}{6}
5
÷
6
1
(iv)
5
×
6
5 \times 6
5
×
6
Q3
Figure it Out (Division and Mixed Problems)
If
1
4
\frac{1}{4}
4
1
kg of flour is used to make 12 rotis, how much flour is used to make 6 rotis?
Q4
Figure it Out (Division and Mixed Problems)
Pāṭīganita, a book written by Sridharacharya in the 9th century CE, mentions this problem: "Friend, after thinking, what sum will be obtained by adding together
1
÷
1
6
,
1
÷
1
10
,
1
÷
1
13
,
1
÷
1
9
1 \div \frac{1}{6}, 1 \div \frac{1}{10}, 1 \div \frac{1}{13}, 1 \div \frac{1}{9}
1
÷
6
1
,
1
÷
10
1
,
1
÷
13
1
,
1
÷
9
1
, and
1
÷
1
2
1 \div \frac{1}{2}
1
÷
2
1
. What should the friend say?
Q5
Figure it Out (Division and Mixed Problems)
Mira is reading a novel that has 400 pages. She read
1
5
\frac{1}{5}
5
1
of the pages yesterday and
3
10
\frac{3}{10}
10
3
of the pages today. How many more pages does she need to read to finish the novel?
Q6
Figure it Out (Division and Mixed Problems)
A car runs 16 km using 1 litre of petrol. How far will it go using
2
3
4
2\frac{3}{4}
2
4
3
litres of petrol?
Q7
Figure it Out (Division and Mixed Problems)
Amritpal decides on a destination for his vacation. If he takes a train, it will take him
5
1
6
5\frac{1}{6}
5
6
1
hours to get there. If he takes a plane, it will take him
1
2
\frac{1}{2}
2
1
hour. How many hours does the plane save?
Q8
Figure it Out (Division and Mixed Problems)
Mariam's grandmother baked a cake. Mariam and her cousins finished
4
5
\frac{4}{5}
5
4
of the cake. The remaining cake was shared equally by Mariam's three friends. How much of the cake did each friend get?
Q9
Figure it Out (Division and Mixed Problems)
Choose the option(s) describing the product of
(
565
465
×
707
676
)
(\frac{565}{465} \times \frac{707}{676})
(
465
565
×
676
707
)
:
(a)
>
565
465
> \frac{565}{465}
>
465
565
(b)
<
565
465
< \frac{565}{465}
<
465
565
(c)
>
707
676
> \frac{707}{676}
>
676
707
(d)
<
707
676
< \frac{707}{676}
<
676
707
(e)
>
1
> 1
>
1
(f)
<
1
< 1
<
1
Q10
Figure it Out (Division and Mixed Problems)
What fraction of the whole square is shaded?
Q11
Figure it Out (Division and Mixed Problems)
A colony of ants set out in search of food. As they search, they keep splitting equally at each point (as shown in the Fig. 8.7) and reach two food sources, one near a mango tree and another near a sugarcane field. What fraction of the original group reached each food source?
Q12
Figure it Out (Division and Mixed Problems)
What is
1
−
1
2
1-\frac{1}{2}
1
−
2
1
?
(
1
−
1
2
)
×
(
1
−
1
3
)
(1-\frac{1}{2}) \times (1-\frac{1}{3})
(
1
−
2
1
)
×
(
1
−
3
1
)
?
(
1
−
1
2
)
×
(
1
−
1
3
)
×
(
1
−
1
4
)
×
(
1
−
1
5
)
(1-\frac{1}{2}) \times (1-\frac{1}{3}) \times (1-\frac{1}{4}) \times (1-\frac{1}{5})
(
1
−
2
1
)
×
(
1
−
3
1
)
×
(
1
−
4
1
)
×
(
1
−
5
1
)
?
(
1
−
1
2
)
×
(
1
−
1
3
)
×
(
1
−
1
4
)
×
(
1
−
1
5
)
×
(
1
−
1
6
)
×
(
1
−
1
7
)
×
(
1
−
1
8
)
×
(
1
−
1
9
)
×
(
1
−
1
10
)
(1-\frac{1}{2}) \times (1-\frac{1}{3}) \times (1-\frac{1}{4}) \times (1-\frac{1}{5}) \times (1-\frac{1}{6}) \times (1-\frac{1}{7}) \times (1-\frac{1}{8}) \times (1-\frac{1}{9}) \times (1-\frac{1}{10})
(
1
−
2
1
)
×
(
1
−
3
1
)
×
(
1
−
4
1
)
×
(
1
−
5
1
)
×
(
1
−
6
1
)
×
(
1
−
7
1
)
×
(
1
−
8
1
)
×
(
1
−
9
1
)
×
(
1
−
10
1
)
? Make a general statement and explain.
Q1
Figure it Out (Multiplication of Fractions and Whole Numbers)
Tenzin drinks
1
2
\frac{1}{2}
2
1
glass of milk every day. How many glasses of milk does he drink in a week? How many glasses of milk did he drink in the month of January?
Q2
Figure it Out (Multiplication of Fractions and Whole Numbers)
A team of workers can make 1 km of a water canal in 8 days. So, in one day, the team can make ______ km of the water canal. If they work 5 days a week, they can make ______ km of the water canal in a week.
Q3
Figure it Out (Multiplication of Fractions and Whole Numbers)
Manju and two of her neighbours buy 5 litres of oil every week and share it equally among the 3 families. How much oil does each family get in a week? How much oil will one family get in 4 weeks?
Q4
Figure it Out (Multiplication of Fractions and Whole Numbers)
Safia saw the Moon setting on Monday at 10 pm. Her mother, who is a scientist, told her that every day the Moon sets
5
6
\frac{5}{6}
6
5
hour later than the previous day. How many hours after 10 pm will the moon set on Thursday?
Q5
Figure it Out (Multiplication of Fractions and Whole Numbers)
Multiply and then convert it into a mixed fraction:
(a)
7
×
3
5
7 \times \frac{3}{5}
7
×
5
3
(b)
4
×
1
3
4 \times \frac{1}{3}
4
×
3
1
(c)
9
7
×
6
\frac{9}{7} \times 6
7
9
×
6
(d)
13
11
×
6
\frac{13}{11} \times 6
11
13
×
6
Q1
Figure it Out (Multiplication of Two Fractions)
Find the following products. Use a unit square as a whole for representing the fractions:
(a)
1
3
×
1
5
\frac{1}{3} \times \frac{1}{5}
3
1
×
5
1
(b)
1
4
×
1
3
\frac{1}{4} \times \frac{1}{3}
4
1
×
3
1
(c)
1
5
×
1
2
\frac{1}{5} \times \frac{1}{2}
5
1
×
2
1
(d)
1
6
×
1
5
\frac{1}{6} \times \frac{1}{5}
6
1
×
5
1
Now, find
1
12
×
1
18
\frac{1}{12} \times \frac{1}{18}
12
1
×
18
1
.
Q2
Figure it Out (Multiplication of Two Fractions)
Find the following products. Use a unit square as a whole for representing the fractions and carrying out the operations.
(a)
2
3
×
4
5
\frac{2}{3} \times \frac{4}{5}
3
2
×
5
4
(b)
1
4
×
2
3
\frac{1}{4} \times \frac{2}{3}
4
1
×
3
2
(c)
3
5
×
1
2
\frac{3}{5} \times \frac{1}{2}
5
3
×
2
1
(d)
4
6
×
3
5
\frac{4}{6} \times \frac{3}{5}
6
4
×
5
3
Q1
Figure it Out 1
Tenzin drinks
1
2
\frac{1}{2}
2
1
glass of milk every day. How many glasses of milk does he drink in a week? How many glasses of milk did he drink in the month of January?
Q2
Figure it Out 1
A team of workers can make 1 km of a water canal in 8 days. So, in one day, the team can make ______ km of the water canal. If they work 5 days a week, they can make ______ km of the water canal in a week.
Q3
Figure it Out 1
Manju and two of her neighbours buy 5 litres of oil every week and share it equally among the 3 families. How much oil does each family get in a week? How much oil will one family get in 4 weeks?
Q4
Figure it Out 1
Safia saw the Moon setting on Monday at 10 pm. Her mother, who is a scientist, told her that every day the Moon sets
5
6
\frac{5}{6}
6
5
hour later than the previous day. How many hours after 10 pm will the moon set on Thursday?
Q5
Figure it Out 1
Multiply and then convert it into a mixed fraction:
(a)
7
×
3
5
7 \times \frac{3}{5}
7
×
5
3
(b)
4
×
1
3
4 \times \frac{1}{3}
4
×
3
1
(c)
9
7
×
6
\frac{9}{7} \times 6
7
9
×
6
(d)
13
11
×
6
\frac{13}{11} \times 6
11
13
×
6
Q1
Figure it Out 2
Find the following products. Use a unit square as a whole for representing the fractions:
(a)
1
3
×
1
5
\frac{1}{3} \times \frac{1}{5}
3
1
×
5
1
(b)
1
4
×
1
3
\frac{1}{4} \times \frac{1}{3}
4
1
×
3
1
(c)
1
5
×
1
2
\frac{1}{5} \times \frac{1}{2}
5
1
×
2
1
(d)
1
6
×
1
5
\frac{1}{6} \times \frac{1}{5}
6
1
×
5
1
Now, find
1
12
×
1
18
\frac{1}{12} \times \frac{1}{18}
12
1
×
18
1
.
Q2
Figure it Out 2
Find the following products. Use a unit square as a whole for representing the fractions and carrying out the operations.
(a)
2
3
×
4
5
\frac{2}{3} \times \frac{4}{5}
3
2
×
5
4
(b)
1
4
×
2
3
\frac{1}{4} \times \frac{2}{3}
4
1
×
3
2
(c)
3
5
×
1
2
\frac{3}{5} \times \frac{1}{2}
5
3
×
2
1
(d)
4
6
×
3
5
\frac{4}{6} \times \frac{3}{5}
6
4
×
5
3
Q1
Figure it Out 3
A water tank is filled from a tap. If the tap is open for 1 hour,
7
10
\frac{7}{10}
10
7
of the tank gets filled. How much of the tank is filled if the tap is open for
(a)
1
3
\frac{1}{3}
3
1
hour _____
(b)
2
3
\frac{2}{3}
3
2
hour _____
(c)
3
4
\frac{3}{4}
4
3
hour _____
(d)
7
10
\frac{7}{10}
10
7
hour _____
(e) For the tank to be full, how long should the tap be running?
Q2
Figure it Out 3
The government has taken
1
6
\frac{1}{6}
6
1
of Somu's land to build a road. What part of the land remains with Somu now? She gives half of the remaining part of the land to her daughter Krishna and
1
3
\frac{1}{3}
3
1
of it to her son Bora. After giving them their shares, she keeps the remaining land for herself.
(a)
What part of the original land did Krishna get?
(b)
What part of the original land did Bora get?
(c)
What part of the original land did Somu keep for herself?
Q3
Figure it Out 3
Find the area of a rectangle of sides
3
3
4
3\frac{3}{4}
3
4
3
ft and
9
3
5
9\frac{3}{5}
9
5
3
ft.
Q4
Figure it Out 3
Tsewang plants four saplings in a row in his garden. The distance between two saplings is
3
4
\frac{3}{4}
4
3
m. Find the distance between the first and last sapling.
Q5
Figure it Out 3
Which is heavier:
12
15
\frac{12}{15}
15
12
of 500 grams or
3
20
\frac{3}{20}
20
3
of 4 kg ?
Q1
Figure it Out 4
Evaluate the following:
3
÷
7
9
3 \div \frac{7}{9}
3
÷
9
7
14
4
÷
2
\frac{14}{4} \div 2
4
14
÷
2
2
3
÷
2
3
\frac{2}{3} \div \frac{2}{3}
3
2
÷
3
2
14
6
÷
7
3
\frac{14}{6} \div \frac{7}{3}
6
14
÷
3
7
4
3
÷
3
4
\frac{4}{3} \div \frac{3}{4}
3
4
÷
4
3
7
4
÷
1
7
\frac{7}{4} \div \frac{1}{7}
4
7
÷
7
1
8
2
÷
4
15
\frac{8}{2} \div \frac{4}{15}
2
8
÷
15
4
1
5
÷
1
9
\frac{1}{5} \div \frac{1}{9}
5
1
÷
9
1
1
6
÷
11
12
\frac{1}{6} \div \frac{11}{12}
6
1
÷
12
11
3
2
3
÷
1
3
8
3\frac{2}{3} \div 1\frac{3}{8}
3
3
2
÷
1
8
3
Q2
Figure it Out 4
For each of the questions below, choose the expression that describes the solution. Then simplify it. (a) Maria bought 8 m of lace to decorate the bags she made for school. She used
1
4
\frac{1}{4}
4
1
m for each bag and finished the lace. How many bags did she decorate?
(i)
8
×
1
4
8 \times \frac{1}{4}
8
×
4
1
(ii)
1
8
×
1
4
\frac{1}{8} \times \frac{1}{4}
8
1
×
4
1
(iii)
8
÷
1
4
8 \div \frac{1}{4}
8
÷
4
1
(iv)
1
4
÷
8
\frac{1}{4} \div 8
4
1
÷
8
(b)
1
2
\frac{1}{2}
2
1
meter of ribbon is used to make 8 badges. What is the length of the ribbon used for each badge?
(i)
8
×
1
2
8 \times \frac{1}{2}
8
×
2
1
(ii)
1
2
÷
1
8
\frac{1}{2} \div \frac{1}{8}
2
1
÷
8
1
(iii)
8
÷
1
2
8 \div \frac{1}{2}
8
÷
2
1
(iv)
1
2
÷
8
\frac{1}{2} \div 8
2
1
÷
8
(c)
A baker needs
1
6
\frac{1}{6}
6
1
kg of flour to make one loaf of bread. He has 5 kg of flour. How many loaves of bread can he make?
(i)
5
×
1
6
5 \times \frac{1}{6}
5
×
6
1
(ii)
1
6
÷
5
\frac{1}{6} \div 5
6
1
÷
5
(iii)
5
÷
1
6
5 \div \frac{1}{6}
5
÷
6
1
(iv)
5
×
6
5 \times 6
5
×
6
Q3
Figure it Out 4
If
1
4
\frac{1}{4}
4
1
kg of flour is used to make 12 rotis, how much flour is used to make 6 rotis?
Q4
Figure it Out 4
Pāțīganita, a book written by Sridharacharya in the 9th century CE, mentions this problem: "Friend, after thinking, what sum will be obtained by adding together
1
÷
1
6
,
1
÷
1
10
,
1
÷
1
13
,
1
÷
1
9
1 \div \frac{1}{6}, 1 \div \frac{1}{10}, 1 \div \frac{1}{13}, 1 \div \frac{1}{9}
1
÷
6
1
,
1
÷
10
1
,
1
÷
13
1
,
1
÷
9
1
, and
1
÷
1
2
1 \div \frac{1}{2}
1
÷
2
1
. What should the friend say?
Q5
Figure it Out 4
Mira is reading a novel that has 400 pages. She read
1
5
\frac{1}{5}
5
1
of the pages yesterday and
3
10
\frac{3}{10}
10
3
of the pages today. How many more pages does she need to read to finish the novel?
Q6
Figure it Out 4
A car runs 16 km using 1 litre of petrol. How far will it go using
2
3
4
2\frac{3}{4}
2
4
3
litres of petrol?
Q7
Figure it Out 4
Amritpal decides on a destination for his vacation. If he takes a train, it will take him
5
1
6
5\frac{1}{6}
5
6
1
hours to get there. If he takes a plane, it will take him
1
2
\frac{1}{2}
2
1
hour. How many hours does the plane save?
Q8
Figure it Out 4
Mariam's grandmother baked a cake. Mariam and her cousins finished
4
5
\frac{4}{5}
5
4
of the cake. The remaining cake was shared equally by Mariam's three friends. How much of the cake did each friend get?
Q9
Figure it Out 4
Choose the option(s) describing the product of
(
565
465
×
707
676
)
(\frac{565}{465} \times \frac{707}{676})
(
465
565
×
676
707
)
:
(a)
>
565
465
> \frac{565}{465}
>
465
565
(b)
<
565
465
< \frac{565}{465}
<
465
565
(c)
>
707
676
> \frac{707}{676}
>
676
707
(d)
<
707
676
< \frac{707}{676}
<
676
707
(e)
>
1
> 1
>
1
(f)
<
1
< 1
<
1
Q10
Figure it Out 4
What fraction of the whole square is shaded?
Q11
Figure it Out 4
A colony of ants set out in search of food. As they search, they keep splitting equally at each point (as shown in the Fig. 8.7) and reach two food sources, one near a mango tree and another near a sugarcane field. What fraction of the original group reached each food source?
Q12
Figure it Out 4
What is
1
−
1
2
1-\frac{1}{2}
1
−
2
1
?
(
1
−
1
2
)
×
(
1
−
1
3
)
(1-\frac{1}{2}) \times (1-\frac{1}{3})
(
1
−
2
1
)
×
(
1
−
3
1
)
?
(
1
−
1
2
)
×
(
1
−
1
3
)
×
(
1
−
1
4
)
×
(
1
−
1
5
)
(1-\frac{1}{2}) \times (1-\frac{1}{3}) \times (1-\frac{1}{4}) \times (1-\frac{1}{5})
(
1
−
2
1
)
×
(
1
−
3
1
)
×
(
1
−
4
1
)
×
(
1
−
5
1
)
?
(
1
−
1
2
)
×
(
1
−
1
3
)
×
(
1
−
1
4
)
×
(
1
−
1
5
)
×
(
1
−
1
6
)
×
(
1
−
1
7
)
×
(
1
−
1
8
)
×
(
1
−
1
9
)
×
(
1
−
1
10
)
(1-\frac{1}{2}) \times (1-\frac{1}{3}) \times (1-\frac{1}{4}) \times (1-\frac{1}{5}) \times (1-\frac{1}{6}) \times (1-\frac{1}{7}) \times (1-\frac{1}{8}) \times (1-\frac{1}{9}) \times (1-\frac{1}{10})
(
1
−
2
1
)
×
(
1
−
3
1
)
×
(
1
−
4
1
)
×
(
1
−
5
1
)
×
(
1
−
6
1
)
×
(
1
−
7
1
)
×
(
1
−
8
1
)
×
(
1
−
9
1
)
×
(
1
−
10
1
)
?
Make a general statement and explain.
More from this chapter
Chapter overview
Important Points
Practice Questions
Flashcards