CBSE Important Questions Class 7 Maths Chapter 8 Working with Fractions

CBSE Important Questions Class 7 Maths Chapter 8 – Working with Fractions

Class 7 Maths Chapter 8 Working with Fractions is a chapter of the new NCERT (National Council of Educational Research and Training) textbook Ganita Prakash. It teaches students how to multiply and divide fractions, how to find a fraction of a quantity, how to use reciprocals, and how to change between improper fractions and mixed numbers. These skills are used every day when we share, measure and compare things.

These CBSE important questions for Class 7 Maths Chapter 8 include multiple choice questions, reciprocal and product questions, and word problems on lace, ribbon, flour, money, land, milk, bottles and a robotic cleaner. Every question has a clear step-by-step answer in simple English, so students can practise on their own, parents can check the working, and teachers can use them in class. A free printable PDF of these important questions is also available on this page.

CBSE Important Questions Class 7 Maths Chapter 8 Working with Fractions

Working with Fractions (New NCERT)

Medium

Q.

Construct a triangle with sidelengths 3 cm, 4 cm, and 8 cm.
What is happening? Are you able to construct the triangle?

View Solution

Working with Fractions (New NCERT)

Medium

Q.

Patiganita, a book written by Sridharacharya in the 9th century CE, mentions this problem: "Friend, after thinking, what sum will be obtained by adding together $$\;1 \div \frac{1}{6}, 1 \div \frac{1}{10}, 1 \div \frac{1}{13}, 1 \div \frac{1}{9}\;$$​, and $$\;1 \div \frac{1}{2}{ } ^{\prime \prime}$$​. What should the friend say?

View Solution

Working with Fractions (New NCERT)

Medium

Q.

A colony of ants set out in search of food. As they search, they keep splitting equally at each point (as shown in the figure) 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?

​

View Solution

Working with Fractions (New NCERT)

Medium

Q.

What fraction of the whole square is shaded?

View Solution

Working with Fractions (New NCERT)

Medium

Q.

Choose the option(s) describing the product of $$\;\left(\frac{565}{465} \times \frac{707}{676}\right):$$

(a) >$$\;\frac{565}{465}$$

​​

(b) <$$\;\frac{565}{465}$$​ 

(c ) >$$\;\frac{707}{676}$$

(d) < $$\;\frac{707}{676}$$​

(e) > 1
(f) < 1

View Solution

Working with Fractions (New NCERT)

Medium

Q.

Mariam’s grandmother baked a cake. Mariam and her cousins finished $$\;\frac45\;$$​ of the cake. The remaining cake was shared equally by Mariam’s three friends. How much of the cake did each friend get?

View Solution

Working with Fractions (New NCERT)

Medium

Q.

Amritpal decides on a destination for his vacation. If he takes a train, it will take him 5$$\frac 16 \;$$​hours to get there. If he takes a plane, it will take him$$\;\frac12\;$$​hour. How many hours does the plane save?

View Solution

Working with Fractions (New NCERT)

Medium

Q.

A car runs 16 km using 1 litre of petrol. How far will it go using 2$$\frac34\;$$​litres of petrol?

View Solution

Working with Fractions (New NCERT)

Medium

Q.

Mira is reading a novel that has 400 pages. She read $$\;\frac{1}{5}\;$$​ of the pages yesterday and$$\;\frac{3}{10}\;$$​of the pages today. How many more pages does she need to read to finish the novel?

View Solution

Working with Fractions (New NCERT)

Medium

Q.

​If $$\;\frac14\;$$​ of flour is used to make 12 rotis, how much flour is used to make 6 rotis?​

View Solution

Working with Fractions (New NCERT)

Medium

Q.

​Find the area of a rectangle of sides 3$$\frac{3}{4}\;$$ft and 9$$\frac{3}{5}\;$$​ ft.​

View Solution

Working with Fractions (New NCERT)

Medium

Q.

​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$$\;\frac14\;$$​m for each bag and finished the lace. How many bags did she decorate?

(i)  $$\;8 \times \frac{1}{4}$$

​​

(ii) $$\;\frac{1}{8} \times \frac{1}{4}$$

​​

(iii) $$\;8 \div \frac{1}{4}$$

​​

(iv) $$\;\frac{1}{4} \div 8$$

(b) $$\;\frac{1}{2}\;$$​metre of ribbon is used to make 8 badges. What is the length of the ribbon used for each badge?
(i) $$\;8 \times \frac{1}{2}$$

​​
(ii) $$\;\frac{1}{2} \div \frac{1}{8}$$

​​

(iii) $$\;8 \div \frac{1}{2}$$

​​

(iv) $$\;\frac{1}{2} \div 8$$

​​

(c) A baker needs$$\;\frac{1}{6}\;$$ kg of flour to make one loaf of bread. He has 5 kg of flour. How many loaves of bread can he make?
(i) $$\;5 \times \frac{1}{6}$$

​​

(ii) $$\;\frac{1}{6} \div 5$$

​​

(iii) $$\;5 \div \frac{1}{6}$$

​​

(iv) $$\;5 \times 6$$​​​

View Solution

Working with Fractions (New NCERT)

Medium

Q.

If we assume 1 gold dinar = 12 silver drammas, 1 silver dramma = 4 copper panas, 1 copper pana = 6 mashakas, and 1 pana = 30 cowrie shells,
1 copper pana $$\;=\frac{1}{48}\;$$​ gold dinar $$\;\left(\frac{1}{12} \times \frac{1}{4}\right)\;$$​​
1 cowrie shell =  ________ copper panas
1 cowrie shell =  ________ gold dinar.

View Solution

Working with Fractions (New NCERT)

Medium

Q.

In each of the figures given below, find the fraction of the big square that the shaded region occupies.

​

View Solution

Working with Fractions (New NCERT)

Medium

Q.

This problem was posed by Chaturveda Prithudakasvami (c. 860 CE) in his commentary on Brahmagupta’s book Brahmasphutasiddhanta.
Four fountains fill a cistern. The first fountain can fill the cistern in a day. The second can fill it in half a day. The third can fill it in a quarter of a day. The fourth can fill the cistern in one-fifth of a day. If they all flow together, in how much time will they fill the cistern?
Let us solve this problem step by step.
In a day, the number of times-

he first fountain will fill the cistern in 1 ÷ 1 = 1
The second fountain will fil the cistern is 1 ÷$$\;\frac{1}{2}\;$$​ = _____
The third fountain will fil the cistern is 1 ÷ $$\;\frac{1}{4}\;$$​ = _____
The fourth fountain will fil the cistern is 1 ÷ $$\;\frac{1}{5}\;$$​ = _____
The number of times the four fountains together will fill the cistern in a day is ___ + ____ + ___ + ____ = 12.

View Solution

Working with Fractions (New NCERT)

Medium

Q.

What can you conclude about the relationship between the numbers multiplied and the product? Fill in the blanks:

• When one of the numbers being multiplied is between 0 and 1, the product is ____________ (greater/less) than the other number.
• When one of the numbers being multiplied is greater than 1, the product is ____________ (greater/less) than the other number.

View Solution

Working with Fractions (New NCERT)

Medium

Q.

Which is heavier:$$\;\frac{12}{15}\;$$​of 500 grams or$$\;\frac{3}{20}\;$$​ of 4 kg ?

View Solution

Working with Fractions (New NCERT)

Medium

Q.

Tsewang plants four saplings in a row in his garden. The distance between two saplings is $$\;\frac{3}{4}\;$$​m. Find the distance between the first and last sapling.
[Hint: Draw a rough diagram with four saplings with distance between two saplings as $$\;\frac{3}{4}\;$$​ m]

View Solution

Working with Fractions (New NCERT)

Medium

Q.

​What is 1 – $$\;\frac12$$​?

$$\left(1-\frac{1}{2}\right) \times\left(1-\frac{1}{3}\right) ?$$​​
​$$\left(1-\frac{1}{2}\right) \times\left(1-\frac{1}{3}\right) \times\left(1-\frac{1}{4}\right) \times\left(1-\frac{1}{5}\right) ?$$​​
​$$\left(1-\frac{1}{2}\right) \times\left(1-\frac{1}{3}\right) \times\left(1-\frac{1}{4}\right) \times\left(1-\frac{1}{5}\right) \times\left(1-\frac{1}{6}\right) \times\left(1-\frac{1}{7}\right) \times\left(1-\frac{1}{8}\right) \times\left(1-\frac{1}{9}\right) \times\left(1-\frac{1}{10}\right) ?$$

Make a general statement and explain.​​

View Solution

Q1. 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 m for each bag and finished the lace. How many bags did she decorate?
(i) 8 × 1/4 (ii) 1/8 × 1/4 (iii) 8 ÷ 1/4 (iv) 1/4 ÷ 8
(b) 1/2 metre of ribbon is used to make 8 badges. What is the length of the ribbon used for each badge?
(i) 8 × 1/2 (ii) 1/2 ÷ 1/8 (iii) 8 ÷ 1/2 (iv) 1/2 ÷ 8
(c) A baker needs 1/6 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 (ii) 1/6 ÷ 5 (iii) 5 ÷ 1/6 (iv) 5 × 6

Answer: (a) To find the number of bags, divide the total lace by the lace used for one bag: 8 ÷ 1/4. The correct expression is (iii).
8 ÷ 1/4 = 8 × 4 = 32 bags.
(b) To find the ribbon for one badge, divide the total ribbon by the number of badges: 1/2 ÷ 8. The correct expression is (iv).
1/2 ÷ 8 = 1/2 × 1/8 = 1/16 metre.
(c) To find the number of loaves, divide the total flour by the flour needed for one loaf: 5 ÷ 1/6. The correct expression is (iii).
5 ÷ 1/6 = 5 × 6 = 30 loaves.

Q2. What is the reciprocal of (−1/3) × (−15/6)?
(a) −6/5
(b) 5/18
(c) 6/5
(d) 5/6

Answer: (c) 6/5
First find the product: (−1/3) × (−15/6) = 15/18 (a negative number times a negative number is positive). Simplify: 15/18 = 5/6.
The reciprocal of 5/6 is 6/5.

Q3. Ria had ₹3650 in her bank account. She used half of her money to buy gifts for her sister and 3/4 of the remaining money to buy clothes for herself. How much money is left with her?

Answer: Step 1: Money at the start = ₹3650
Step 2: Money spent on gifts = 1/2 × 3650 = ₹1825. Remaining = 3650 − 1825 = ₹1825
Step 3: Money spent on clothes = 3/4 × 1825 = 5475/4 = ₹1368.75
Money left = 1825 − 1368.75 = ₹456.25 = ₹456 1/4
Ria is left with ₹456 1/4 (₹456.25).

Q4. A farmer uses 2/3 of his land for vegetables. He uses 5/8 of that area for tomatoes. What fraction of his total land is used for tomatoes, in the lowest form?
(a) 5/11
(b) 10/24
(c) 5/12
(d) 15/24

Answer: (c) 5/12
Fraction of land for tomatoes = 5/8 of 2/3 = 5/8 × 2/3 = 10/24 = 5/12 in the lowest form.

Q5. A bamboo grows 5/6 metres in a day. How much does it grow in 9 days, and what is the simplified mixed number form of the answer?
(a) 7 1/2
(b) 1 4/5
(c) 15/7
(d) 2 1/2

Answer: (a) 7 1/2
Growth in 9 days = 9 × 5/6 = 45/6 = 15/2 m.
As a mixed number, 15/2 = 7 1/2 m. So the bamboo grows 7 1/2 metres in 9 days.

Q6. Rohani paints for 2 3/7 hours every day and takes 15 days to paint the entire wall. How many hours did she take to paint the wall?

Answer: Total hours = hours per day × number of days = 2 3/7 × 15
2 3/7 = (2 × 7 + 3)/7 = 17/7
17/7 × 15 = 255/7 = 36 3/7
Rohani took 36 3/7 hours to paint the wall.

Q7. The cost of one litre of milk is ₹16 3/5. What is the cost of 12 1/2 litres of milk?
(a) ₹128 1/2
(b) ₹167 1/2
(c) ₹207 1/2
(d) ₹212 1/2

Answer: (c) ₹207 1/2
Cost of 1 litre = 16 3/5 = 83/5. Quantity = 12 1/2 = 25/2 litres.
Total cost = 83/5 × 25/2 = 83 × 5/2 = 415/2 = ₹207 1/2.

Q8. What is the reciprocal of 1?

Answer: The reciprocal of a number is found by flipping it. 1 can be written as 1/1, and flipping 1/1 gives 1/1 = 1. So the reciprocal of 1 is 1.

Q9. Product of 11/12 × 16/4 × 9/16 is
(a) 2 1/16
(b) 3/4
(c) 1/4
(d) 1 1/2

Answer: (a) 2 1/16
11/12 × 16/4 × 9/16 = (11 × 16 × 9)/(12 × 4 × 16). Cancel 16: (11 × 9)/(12 × 4) = 99/48 = 33/16.
33/16 = 2 1/16.

Q10. The given fractions are 1/2, 4/5, 7/8. If the numbers are arranged in the ascending order or descending order, then the middle number is
(a) 1/2
(b) 7/8
(c) 4/5
(d) 3/5

Answer: (c) 4/5
Convert to decimals: 1/2 = 0.5, 4/5 = 0.8, 7/8 = 0.875. In ascending order: 0.5, 0.8, 0.875. The middle number is 0.8 = 4/5.

Q11. A square has an area of 1 square unit. A small square inside it covers 1/3 of its area. A triangle occupies 3/5 of this small square. Find the fraction of the whole square occupied by the triangle.

Answer: Fraction of the whole square covered by the triangle = 1/3 × 3/5 = 3/15 = 1/5
So 1/5 of the square is occupied by the triangle.

Q12. You are given 3/4 litre of a herbal concentrate. You need to pack it into bottles of 1/8 litre each. If one bottle is dropped and wasted after packing, how many full bottles are left?

Answer: Total bottles filled = 3/4 ÷ 1/8 = 3/4 × 8 = 6 bottles
One bottle is wasted, so 6 − 1 = 5 full bottles are left.

Q13. A robotic cleaner can clean 3/8 of a room in 45 minutes. At the same rate, how much of the room can it clean in 1 hour 15 minutes?

Answer: Time for 3/8 of the room = 45 min
Time for the full room = 45 ÷ 3/8 = 45 × 8/3 = 15 × 8 = 120 minutes
1 hour 15 minutes = 75 minutes
Fraction of the room cleaned in 75 minutes = 75/120 = 5/8

Q14. If 3/4 of a number is 9/10, what is the number?

Answer: Let the number be x. Then 3/4 × x = 9/10
x = 9/10 ÷ 3/4 = 9/10 × 4/3 = 36/30 = 6/5
Hence, the number is 6/5.

Related Study Material on Extramarks

• CBSE Important Questions Class 7 Maths Chapter 1
• CBSE Important Questions Class 7 Maths Chapter 2
• CBSE Important Questions Class 7 Maths Chapter 3
• CBSE Important Questions Class 7 Maths Chapter 4
• CBSE Important Questions Class 7 Maths Chapter 5
• CBSE Important Questions Class 7 Maths Chapter 6
• CBSE Important Questions Class 7 Maths Chapter 7
• CBSE Important Questions Class 7 Maths Chapter 9
• CBSE Important Questions Class 7 Maths Chapter 10
• CBSE Important Questions Class 7 Maths Chapter 11