Class 7 Maths Chapter 8 NCERT Book - Working with Fractions

 Page 1


WORKING WITH 
FRACTIONS
8
8.1 Multiplication of Fractions
Aaron walks 3 kilometres in 1 hour. 
How far can he walk in 5 hours?
This is a simple question. We know 
that to find the distance, we need to 
find the product of 5 and 3, i.e., we 
multiply 5 and 3. 
Distance covered in 1 hour = 3 km.
Therefore, 
Distance covered in 5 hours
= 5 × 3 km
= 3 + 3 + 3 + 3 + 3 km
= 15 km.
Aaron’s pet tortoise walks at a much slower pace. It can walk only 
1
4
   
kilometre in 1 hour. How far can it walk in 3 hours?
Here, the distance covered in an hour is a fraction. This does not 
matter. The total distance covered is calculated in the same way, as 
multiplication.
Distance covered in 1 hour = 
1
4
 km.
Distance in 
1 hour
Distance in 3 hour
1
4
 km
0
Chapter-8.indd   173 Chapter-8.indd   173 4/12/2025   12:41:31 PM 4/12/2025   12:41:31 PM
Page 2


WORKING WITH 
FRACTIONS
8
8.1 Multiplication of Fractions
Aaron walks 3 kilometres in 1 hour. 
How far can he walk in 5 hours?
This is a simple question. We know 
that to find the distance, we need to 
find the product of 5 and 3, i.e., we 
multiply 5 and 3. 
Distance covered in 1 hour = 3 km.
Therefore, 
Distance covered in 5 hours
= 5 × 3 km
= 3 + 3 + 3 + 3 + 3 km
= 15 km.
Aaron’s pet tortoise walks at a much slower pace. It can walk only 
1
4
   
kilometre in 1 hour. How far can it walk in 3 hours?
Here, the distance covered in an hour is a fraction. This does not 
matter. The total distance covered is calculated in the same way, as 
multiplication.
Distance covered in 1 hour = 
1
4
 km.
Distance in 
1 hour
Distance in 3 hour
1
4
 km
0
Chapter-8.indd   173 Chapter-8.indd   173 4/12/2025   12:41:31 PM 4/12/2025   12:41:31 PM
Ganita Prakash | Grade 7
Therefore, distance covered in 3 hours = 3 × 
1
4
 km
= 
1
4
 + 
1
4
 + 
1
4
 km
= 
3
4
 km.
The tortoise can walk 
3
4
 km in 3 hours.
Let us consider a case where the time spent walking is a fraction of 
an hour.
We saw that Aaron can walk 3 kilometres in 1 hour. How far can he 
walk in 
1
5
 hours?
We continue to calculate the total distance covered through 
multiplication.
Distance covered in 
1
5
 hours = 
1
5
  × 3 km.
Finding the product:
Distance covered in 1 hour = 3 km.
In 
1
5
 hours, distance covered is equal to the length we get by dividing 
3 km into 5 equal parts, which is  
3
5
 km.
This tells us that 
1
5
 × 3 = 
3
5
?.
How far can Aaron walk in 
2
5
 hours?
Distance in 1 hour
Distance in 
1
5
 
hour
0 3 km
174
Chapter-8.indd   174 Chapter-8.indd   174 4/12/2025   12:41:31 PM 4/12/2025   12:41:31 PM
Page 3


WORKING WITH 
FRACTIONS
8
8.1 Multiplication of Fractions
Aaron walks 3 kilometres in 1 hour. 
How far can he walk in 5 hours?
This is a simple question. We know 
that to find the distance, we need to 
find the product of 5 and 3, i.e., we 
multiply 5 and 3. 
Distance covered in 1 hour = 3 km.
Therefore, 
Distance covered in 5 hours
= 5 × 3 km
= 3 + 3 + 3 + 3 + 3 km
= 15 km.
Aaron’s pet tortoise walks at a much slower pace. It can walk only 
1
4
   
kilometre in 1 hour. How far can it walk in 3 hours?
Here, the distance covered in an hour is a fraction. This does not 
matter. The total distance covered is calculated in the same way, as 
multiplication.
Distance covered in 1 hour = 
1
4
 km.
Distance in 
1 hour
Distance in 3 hour
1
4
 km
0
Chapter-8.indd   173 Chapter-8.indd   173 4/12/2025   12:41:31 PM 4/12/2025   12:41:31 PM
Ganita Prakash | Grade 7
Therefore, distance covered in 3 hours = 3 × 
1
4
 km
= 
1
4
 + 
1
4
 + 
1
4
 km
= 
3
4
 km.
The tortoise can walk 
3
4
 km in 3 hours.
Let us consider a case where the time spent walking is a fraction of 
an hour.
We saw that Aaron can walk 3 kilometres in 1 hour. How far can he 
walk in 
1
5
 hours?
We continue to calculate the total distance covered through 
multiplication.
Distance covered in 
1
5
 hours = 
1
5
  × 3 km.
Finding the product:
Distance covered in 1 hour = 3 km.
In 
1
5
 hours, distance covered is equal to the length we get by dividing 
3 km into 5 equal parts, which is  
3
5
 km.
This tells us that 
1
5
 × 3 = 
3
5
?.
How far can Aaron walk in 
2
5
 hours?
Distance in 1 hour
Distance in 
1
5
 
hour
0 3 km
174
Chapter-8.indd   174 Chapter-8.indd   174 4/12/2025   12:41:31 PM 4/12/2025   12:41:31 PM
Working with Fractions
Once again, we have?—
Distance covered = 
2
5
 × 3 km.
Finding the product:
1. We can first find the distance covered in 
1
5
 hours.
2. Since, the duration 
2
5
  is twice 
1
5
, we multiply this distance by 2 to 
get the total distance covered.
Here is the calculation.
Distance covered in 1 hour = 3 km.
1. Distance covered in 
1
5
 hour 
 = The length we get by dividing 3 km in 5 equal parts    
=  
3
5
 km.
2. Multiplying this distance by 2, we get 
 2 × 
3
5
 = 
6
5
 km.
From this we can see that
2
5
 × 3 = 
6
5
.
Discussion
We did this multiplication as follows:
•  First, we divided the 
multiplicand, 3 , by the 
denominator of the multiplier, 5, to get 
3
5
.
Distance in 1 hour
Distance in 
1
5
 hour
Distance in 
2
5
 hour
Multiplier Multiplicand
2
5
 × 3
175
Chapter-8.indd   175 Chapter-8.indd   175 4/12/2025   12:41:31 PM 4/12/2025   12:41:31 PM
Page 4


WORKING WITH 
FRACTIONS
8
8.1 Multiplication of Fractions
Aaron walks 3 kilometres in 1 hour. 
How far can he walk in 5 hours?
This is a simple question. We know 
that to find the distance, we need to 
find the product of 5 and 3, i.e., we 
multiply 5 and 3. 
Distance covered in 1 hour = 3 km.
Therefore, 
Distance covered in 5 hours
= 5 × 3 km
= 3 + 3 + 3 + 3 + 3 km
= 15 km.
Aaron’s pet tortoise walks at a much slower pace. It can walk only 
1
4
   
kilometre in 1 hour. How far can it walk in 3 hours?
Here, the distance covered in an hour is a fraction. This does not 
matter. The total distance covered is calculated in the same way, as 
multiplication.
Distance covered in 1 hour = 
1
4
 km.
Distance in 
1 hour
Distance in 3 hour
1
4
 km
0
Chapter-8.indd   173 Chapter-8.indd   173 4/12/2025   12:41:31 PM 4/12/2025   12:41:31 PM
Ganita Prakash | Grade 7
Therefore, distance covered in 3 hours = 3 × 
1
4
 km
= 
1
4
 + 
1
4
 + 
1
4
 km
= 
3
4
 km.
The tortoise can walk 
3
4
 km in 3 hours.
Let us consider a case where the time spent walking is a fraction of 
an hour.
We saw that Aaron can walk 3 kilometres in 1 hour. How far can he 
walk in 
1
5
 hours?
We continue to calculate the total distance covered through 
multiplication.
Distance covered in 
1
5
 hours = 
1
5
  × 3 km.
Finding the product:
Distance covered in 1 hour = 3 km.
In 
1
5
 hours, distance covered is equal to the length we get by dividing 
3 km into 5 equal parts, which is  
3
5
 km.
This tells us that 
1
5
 × 3 = 
3
5
?.
How far can Aaron walk in 
2
5
 hours?
Distance in 1 hour
Distance in 
1
5
 
hour
0 3 km
174
Chapter-8.indd   174 Chapter-8.indd   174 4/12/2025   12:41:31 PM 4/12/2025   12:41:31 PM
Working with Fractions
Once again, we have?—
Distance covered = 
2
5
 × 3 km.
Finding the product:
1. We can first find the distance covered in 
1
5
 hours.
2. Since, the duration 
2
5
  is twice 
1
5
, we multiply this distance by 2 to 
get the total distance covered.
Here is the calculation.
Distance covered in 1 hour = 3 km.
1. Distance covered in 
1
5
 hour 
 = The length we get by dividing 3 km in 5 equal parts    
=  
3
5
 km.
2. Multiplying this distance by 2, we get 
 2 × 
3
5
 = 
6
5
 km.
From this we can see that
2
5
 × 3 = 
6
5
.
Discussion
We did this multiplication as follows:
•  First, we divided the 
multiplicand, 3 , by the 
denominator of the multiplier, 5, to get 
3
5
.
Distance in 1 hour
Distance in 
1
5
 hour
Distance in 
2
5
 hour
Multiplier Multiplicand
2
5
 × 3
175
Chapter-8.indd   175 Chapter-8.indd   175 4/12/2025   12:41:31 PM 4/12/2025   12:41:31 PM
Ganita Prakash | Grade 7
•  W e then multiplied the result by the numerator of the multiplier, 
that is 2, to get 
6
5
. 
Thus, whenever we need to 
multiply a fraction and a whole 
number, we follow the steps above.
Example 1: A farmer had 5 
grandchildren. She distributed 
2
3
 acre 
of land to each of her grandchildren. 
How much land in all did she give to her grandchildren?
5 × 
2
3
 = 
2
3
 + 
2
3
 + 
2
3
 + 
2
3
 + 
2
3
 = 
10
3
.
Example 2: 1 hour of internet time costs ?8. How much will 1 
1
4
 hours 
of internet time cost?
1 
1
4
 hours is 
5
4
 hours (converting from a mixed fraction).
Cost of  
5
4
 hour of internet time = 
5
4
 × 8 
= 5 × 
8
4
 
= 5 × 2
= 10.
It costs ?10 for 1 
1
4
 hours of internet time.
Figure it Out
1. Tenzin drinks 
1
2
 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?
2.  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.
3.  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? 
4.  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
 hour later than 
Multiplier Multiplicand
2
5
 × 3
3 ÷ 5 = 
3
5
2 × 
3
5
 = 
6
5
2
5
2
5
176
Chapter-8.indd   176 Chapter-8.indd   176 4/12/2025   12:41:31 PM 4/12/2025   12:41:31 PM
Page 5


WORKING WITH 
FRACTIONS
8
8.1 Multiplication of Fractions
Aaron walks 3 kilometres in 1 hour. 
How far can he walk in 5 hours?
This is a simple question. We know 
that to find the distance, we need to 
find the product of 5 and 3, i.e., we 
multiply 5 and 3. 
Distance covered in 1 hour = 3 km.
Therefore, 
Distance covered in 5 hours
= 5 × 3 km
= 3 + 3 + 3 + 3 + 3 km
= 15 km.
Aaron’s pet tortoise walks at a much slower pace. It can walk only 
1
4
   
kilometre in 1 hour. How far can it walk in 3 hours?
Here, the distance covered in an hour is a fraction. This does not 
matter. The total distance covered is calculated in the same way, as 
multiplication.
Distance covered in 1 hour = 
1
4
 km.
Distance in 
1 hour
Distance in 3 hour
1
4
 km
0
Chapter-8.indd   173 Chapter-8.indd   173 4/12/2025   12:41:31 PM 4/12/2025   12:41:31 PM
Ganita Prakash | Grade 7
Therefore, distance covered in 3 hours = 3 × 
1
4
 km
= 
1
4
 + 
1
4
 + 
1
4
 km
= 
3
4
 km.
The tortoise can walk 
3
4
 km in 3 hours.
Let us consider a case where the time spent walking is a fraction of 
an hour.
We saw that Aaron can walk 3 kilometres in 1 hour. How far can he 
walk in 
1
5
 hours?
We continue to calculate the total distance covered through 
multiplication.
Distance covered in 
1
5
 hours = 
1
5
  × 3 km.
Finding the product:
Distance covered in 1 hour = 3 km.
In 
1
5
 hours, distance covered is equal to the length we get by dividing 
3 km into 5 equal parts, which is  
3
5
 km.
This tells us that 
1
5
 × 3 = 
3
5
?.
How far can Aaron walk in 
2
5
 hours?
Distance in 1 hour
Distance in 
1
5
 
hour
0 3 km
174
Chapter-8.indd   174 Chapter-8.indd   174 4/12/2025   12:41:31 PM 4/12/2025   12:41:31 PM
Working with Fractions
Once again, we have?—
Distance covered = 
2
5
 × 3 km.
Finding the product:
1. We can first find the distance covered in 
1
5
 hours.
2. Since, the duration 
2
5
  is twice 
1
5
, we multiply this distance by 2 to 
get the total distance covered.
Here is the calculation.
Distance covered in 1 hour = 3 km.
1. Distance covered in 
1
5
 hour 
 = The length we get by dividing 3 km in 5 equal parts    
=  
3
5
 km.
2. Multiplying this distance by 2, we get 
 2 × 
3
5
 = 
6
5
 km.
From this we can see that
2
5
 × 3 = 
6
5
.
Discussion
We did this multiplication as follows:
•  First, we divided the 
multiplicand, 3 , by the 
denominator of the multiplier, 5, to get 
3
5
.
Distance in 1 hour
Distance in 
1
5
 hour
Distance in 
2
5
 hour
Multiplier Multiplicand
2
5
 × 3
175
Chapter-8.indd   175 Chapter-8.indd   175 4/12/2025   12:41:31 PM 4/12/2025   12:41:31 PM
Ganita Prakash | Grade 7
•  W e then multiplied the result by the numerator of the multiplier, 
that is 2, to get 
6
5
. 
Thus, whenever we need to 
multiply a fraction and a whole 
number, we follow the steps above.
Example 1: A farmer had 5 
grandchildren. She distributed 
2
3
 acre 
of land to each of her grandchildren. 
How much land in all did she give to her grandchildren?
5 × 
2
3
 = 
2
3
 + 
2
3
 + 
2
3
 + 
2
3
 + 
2
3
 = 
10
3
.
Example 2: 1 hour of internet time costs ?8. How much will 1 
1
4
 hours 
of internet time cost?
1 
1
4
 hours is 
5
4
 hours (converting from a mixed fraction).
Cost of  
5
4
 hour of internet time = 
5
4
 × 8 
= 5 × 
8
4
 
= 5 × 2
= 10.
It costs ?10 for 1 
1
4
 hours of internet time.
Figure it Out
1. Tenzin drinks 
1
2
 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?
2.  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.
3.  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? 
4.  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
 hour later than 
Multiplier Multiplicand
2
5
 × 3
3 ÷ 5 = 
3
5
2 × 
3
5
 = 
6
5
2
5
2
5
176
Chapter-8.indd   176 Chapter-8.indd   176 4/12/2025   12:41:31 PM 4/12/2025   12:41:31 PM
Working with Fractions
the previous day. How many hours after 10 pm will the moon set 
on Thursday?
5.  Multiply and then convert it into a mixed fraction:
(a)  7 × 
3
5
(b)  4 × 
1
3
(c) 
9
7
 × 6   
(d) 
13
11
 × 6
So far, we have learnt multiplication of a whole number with a 
fraction, and a fraction with a whole number. What happens when 
both numbers in the multiplication are fractions?
Multiplying Two Fractions
We know, that Aaron’s pet tortoise can walk only 
1
4
 km in 1 hour. How 
far can it walk in half an hour?
Following our approach of using 
multiplication to solve such problems, we 
have,
Distance covered in 
1
2
 hour = 
1
2
 × 
1
4
 km.
Finding the product:
Distance covered in 1 hour = 
1
4
 km.
Therefore, the distance covered in 
1
2
 an hour is the length we get by 
dividing 
1
4
 into 2 equal parts.
To find this, it is useful to represent fractions using the unit square 
to stand for a “whole”.
Hour Distance
1
1
4
1
2
?
1
4
Unit square as a “whole” 1
4
 of the whole
177
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