Working with Fractions Class 7 Extra Questions Maths Chapter 8

During revision, students quickly go through Class 7 Maths Extra Questions Chapter 8 Working with Fractions Class 7 Extra Questions with Answers for clarity.

Class 7 Working with Fractions Extra Questions

Class 7 Maths Chapter 7 Working with Fractions Extra Questions

Class 7 Maths Chapter 8 Extra Questions – Working with Fractions Extra Questions Class 7

Question 1.
Multiply.
(a) \(\frac{5}{19} \times \frac{18}{7}\)
Solution:
\(\frac{5}{19} \times \frac{18}{7}=\frac{5 \times 18}{19 \times 7}\)
= \(\frac{90}{133}\)

(b) \(\frac{15}{16} \times \frac{12}{7} \times \frac{119}{75}\)
Solution:

\(\frac{3 \times 17}{4 \times 5}=\frac{51}{20}=2 \frac{11}{20}\)

Question 2.
Each side of a square iron sheet is 1 \(\frac{3}{8}\) m. Find its area.
Solution:
Area of a square sheet = side x side = 1 \(\frac{3}{8}\) × 1 \(\frac{3}{8}\)
= \(\frac{11}{8} \times \frac{11}{8}=\frac{121}{64}\)
= 1\( sq. m
Hence, the area of the square iron sheet is 1[latex\frac{57}{64}\) sq. m.

Question 3.
The cost of 1 kg of flour is ₹ 21\(\frac{1}{2}\). Find the cost of 6\(\frac{1}{2}\) kg of flour.
Solution:
Cost of 1 kg of flour = ₹ 21 \(\frac{1}{2}\) = ₹ \(\frac{43}{2}\)
So, cost of 6 \(\frac{1}{2}\) kg of flour = ₹ \(\frac{43}{2}\) x 6\(\frac{1}{2}\)
= ₹ \(\frac{43}{2}\) × \(\frac{13}{2}\)
= \(\frac{13}{2}\)
= ₹ 139 \(\frac{3}{4}\)
Therefore, the cost of 6 \(\frac{1}{2}\) kg flour is ₹ 139 \(\frac{3}{4}\).

Question 4.
Divide
(a) 4 \(\frac{5}{6}\) ÷ 29
Solution:
4 \(\frac{5}{6}\) ÷ 29
= \(\frac{29}{6} \div \frac{29}{1}\)
= \(\frac{29}{6} \times \frac{1}{29}\)
= \(\frac{1}{6}\)

(b) 3\(\frac{5}{7}\) ÷ \(\frac{14}{15}\)
Solution:

(c) 20 + \(\frac{8}{11}\)
Solution:

Question 5.
Divide the sum of \(\frac{4}{7}\) and \(\frac{1}{7}\) by \(\frac{9}{7}\).
Solution:
\(\left(\frac{4}{7}+\frac{1}{7}\right) \div \frac{9}{7}=\frac{5}{7} \div \frac{9}{7}\)
= \(\frac{5}{7} \times \frac{7}{9}=\frac{5}{9}\)
= \(\frac{1}{2}\)

Question 6.
Reduce the following fractions into their simplest form.
(a) \(\frac{132}{148}\)
Solution:

[∵ 2 × 2 is the common factor of 132 and 148]
Thus, \(\frac{33}{37}\) is the simplest form of \(\frac{132}{148}\).

(b) \(\frac{145}{200}\)
Solution:

[∵ 5 is the common factor of 145 and 200]
Thus, \(\frac{29}{40}\) is the simplest form of .

Question 7.
Insert a number in ____ so that \(\frac{3}{4} \times \frac{2}{7}\) = ____. Out of all three fractions, which one is greatest?
Solution:

Out of the three fractions, \(\frac{3}{4}\) is the greatest.

Question 8.
A machine can print \(\frac{13}{4}\) pages in one minute. How many minutes will it take to print \(\frac{104}{4}\) pages?
Solution:
Number of minutes required to print \(\frac{104}{2}\) pages
= \(\frac{\frac{104}{4}}{\frac{13}{4}}\)
= \(\frac{104}{4} \times \frac{4}{13}\)
= 8

Very Short Answer Type Questions

Question 1.
Find the following products.
(i) \(\frac{3}{7}\) × 4
(ii) 6 × \(\frac{11}{18}\)
(iii) 9 × \(\frac{13}{21}\)
(iv) 2 × 4 \(\frac{1}{5}\)
(v) 2 × 2 \(\frac{2}{3}\)
(vi) \(\frac{1}{9}\) × 2 \(\frac{3}{7}\)
Answer:

Question 2.
Find the value of the following fractions of numbers.
(i) \(\frac{1}{3}\) of 15
(ii) \(\frac{1}{4} \)of 20
Answer:

Question 3.
Find the value of the following division of fractions.
(i) 2+\(\frac{8}{9}\)
(ii) 1 \(\frac{3}{5}\) + \(\frac{1}{2}\)
(iii) 2 \(\frac{1}{2}\) + 2 \(\frac{3}{5}\)
Answer:

Short Answer Type Questions

Question 1.
What is the product of \(\frac{7}{197}\) and its reciprocal?
Answer:
Product of \(\frac{7}{197}\) and its reciprocal = \(\frac{7}{197}\) × \(\frac{197}{7}\) = 1

Question 2.
Amit has one piece of chocolate cake. Sumit has one piece of strawberry cake. Amit slices his cake into 8 equal pieces. Sumit slices his cake into 16 equal pieces. Amit wants to exchange a portion of his cake for an equal portion of Sumit’s cake. If he gives 4 pieces of his cake to Sumit, how many pieces of cake should Sumit give to Amit?
Answer:
Given, Amit divides cake into 8 equal pieces.
So, each piece = \(\frac{1}{8}\) of chocolate cake
Sumit divides cake into 16 equal pieces.
So, each piece = \(\frac{1}{16}\) of strawberry cake
Now, 8 × \(\frac{1}{16}\) = 4 × \(\frac{1}{8}\) [∵ Amit gives 4 pieces to Sumit ]
Hence, Sumit should give 8 pieces of cake to Amit.

Question 3.
Raj travels 360 km on three fifth of his petrol tank. How far would he travel at the same rate with a full tank of petrol?
Answer:
Given, Raj travels 360 km on three-fifth of his petrol tank
∴ Total distance travelled = Reciprocal of \(\frac{3}{5}\) × 360km
= \(\frac{5}{3}[latex] × 360 = [latex]\frac{1800}{3}\) = 600 km
Hence, the total distance travelled by Raj with full tank of petrol is 600 km.

Question 4.
A picture hall has seats for 820 persons. At a recent film show, user Mr. X guessed it was \(\frac{3}{4}\) full, another user Mr. Y guessed that it was \(\frac{2}{3}\) full. The ticket office reported 648 sales. Which user ( X or Y) made the better guess? What value depict here?
Answer:
Given, picture hall seats = 820
One user Mr. X guesses \(\frac{3}{4}\) full.

648 tickets are sold that is nearly to 615 .
So, Mr. X guess was better.
The value depicted here is, in many situations, we solve our problems by approximation or guessing.

Question 5.
Mukesh cut a cake into 4 equal pieces. If he wanted to divide each of them into 3 equal pieces, what fraction of the whole cake would each small piece be?
Answer:
Given, the number of pieces = 4
Since, Mukesh wants to divide each piece of cake in 3 equal pieces.

Question 6.
Ramu finished \(\frac{1}{3}\) part of a work in 1 h . How much part of the work will be finished in 2 \(\frac{1}{5}\) h ?
Answer:
Given, the part of the work finished by Ramu in 1 h = \(\frac{1}{3}\) So, the part of the work finished by Ramu in 2 \(\frac{1}{5}\) h

Hence, Ramu will finish \(\frac{11}{15}\) part of the work in 2 \(\frac{1}{5}\) h.

Question 7.
If Radhika takes 2 \(\frac{1}{3}\) m of cloth to make a shirt. How many shirts can Radhika make from a piece of cloth 9 \(\frac{1}{3}\) m long?
Answer:
Given, Radhika takes 2 \(\frac{1}{3}\) m of cloth to make a shirt

Hence, Radhika makes 4 shirts from available pièce of cloth.

Question 8.
Ravi can walk 3 \(\frac{1}{3}\) km in one hour. How long will it take him to walk to his office which is 10 km from his home?
Answer:
Given, Ravi can walk 3 \(\frac{1}{3}\) km in 1 h.

Hence, Ravi reaches office in 3 h.

Question 9.
Rohan is dividing 1 \(\frac{3}{4}\) kg of sweets equally among his seven friends. How much does each friend receive?
Answer:
Total quantity of sweets = 1 \(\frac{3}{4}\) kg

Hence, each friend receive \(\frac{1}{4}\) kg sweets.

Question 10.
How many \(\frac{2}{3}\) kg pieces can be cut from a cake of weight 4 kg ?
Answer:
Given, weight of each piece = \(\frac{2}{3}\) kg and weight of cake that is to be cut in small pieces = 4 kg So, 4 + \(\frac{2}{3}\)=\(\frac{4}{1}\) × \(\frac{3}{2}\) = \(\frac{12}{2}\) = 6
Hence, 6 pieces can be cut from given cake.

Question 11.
Rama has 6 \(\frac{1}{4}\) kg of cotton wool for making pillows. If one pillow takes 1 \(\frac{1}{4}\) kg, how many pillows can she make?
Answer:
Given, Rama has 6 \(\frac{1}{4}\) kg of cotton for making pillows

Hence, Rama can make 5 pillows.

Question 12.
The weight of an object on Moon is \(\frac{1}{6}\) of its weight on Earth. If an object weights 5 \(\frac{3}{5}\) kg on Earth, how much would it weight on the Moon?
Answer:
Given, weight of an object on Moon is \(\frac{1}{6}\) of its weight on Earth.

Hence, the object will weight \(\frac{14}{15}\) kg on Moon.

Long Answer Type Questions

Question 1.
Lalita reads a book for 2 \(\frac{4}{8}\) h everyday. She reads the entire book in 64 days. How many hours in all were required by her to the read the entire book?
Answer:
Given, Lalita reads the book for 2 \(\frac{4}{8}\) h everyday. If she reads the entire book in 64 days, then the total number of reading hours = 64 × Reading hours per day

Hence, Lalita reads the entire book in 160 h.

Question 2.
Rita has bought a carpet of size 4m × 6 \(\frac{2}{3}\) m. But her room size is 3 \(\frac{1}{3}\) m × 5 \(\frac{1}{3}\) m. What fraction of area should be cut-off to fit carpet into the room?
Answer:

Question 3.
A hill 101 \(\frac{1}{3}\) m in height, has \(\frac{1}{4}\) th of its height under water. What is the height of the hill visible above the water?
Answer:

Hence, 76 m of hill is visible.

Skill Based Questions

Question 1.
State whether the answer is greater than 1 or less than 1 . Put a ‘✓’ mark in appropriate box.

Direction In questions 2 and 3 , replace ‘?’ with appropriate fraction.
Answer:
Do yourself

Question 2.

Answer:
\(\frac{7}{648}\)

Question 3.

Answer:
\(\frac{3}{2}\)

Question 4.
A student multiplied two mixed fractions in the following manner:
2 \(\frac{4}{7}\) × 3 \(\frac{1}{4}\) = 6 \(\frac{1}{7}\)
What error the student has done?
Answer:
Do yourself

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