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Class 7 Maths Chapter 8 Working with Fractions Worksheet with Answers Pdf
Working with Fractions Class 7 Maths Worksheet
Class 7 Maths Chapter 8 Worksheet with Answers – Class 7 Working with Fractions Worksheet
Multiple Choice Questions
Choose the correct option.
Question 1.
Product of fractions \(\frac{2}{7}\) and \(\frac{5}{9}\) is
(a) \(\frac{2 \times 5}{7+9}\)
(b) \(\frac{2+5}{7+9}\)
(c) \(\frac{2 \times 9}{5 \times 7}\)
(d) \(\frac{2 \times 5}{7 \times 9}\)
Answer:
(d) \(\frac{2 \times 5}{7 \times 9}\)
Question 2.
The reciprocal of fraction \(\frac{2}{7}\) is
(a) 2
(b) 7
(c) 3\(\frac{1}{2}\)
(d) \(\frac{1}{7}\)
Answer:
(c) 3\(\frac{1}{2}\)
Question 3.
A tortotse can walk 1 km in 1 hour. How much distance wilt ¡t cover in 5 hours?
(a) 1 km
(b) 4 km
(c) \(\frac{4}{5}\) km
(d) 1\(\frac{1}{4}\) km
Answer:
(d) 1\(\frac{1}{4}\) km
Question 4.
The product of \(\frac{1}{2}\) =
(a) \(\frac{3}{10}\)
(b) \(\frac{3}{5}\)
(c) \(\frac{5}{3}\)
(d) \(\frac{40}{12}\)
Answer:
(a) \(\frac{3}{10}\)
Question 5.
The area of a rectangular field of sides 2\(\frac{3}{4}\) m and 4\(\frac{2}{3}\) m, is _______ sq. m
(a) 10\(\frac{5}{6}\)
(b) 12\(\frac{5}{6}\)
(c) 11\(\frac{5}{6}\)
(d) 12\(\frac{1}{6}\)
Answer:
(b) 12\(\frac{5}{6}\)
Question 6.
On dividing 7 by the result is
(a) \(\frac{2}{5}\)
(b) \(\frac{14}{2}\)
(c) \(\frac{14}{5}\)
(d) \(\frac{35}{2}\)
Answer:
(d) \(\frac{35}{2}\)
Assertion and Reason-based Questions.
Directions. In the following questions, a statement of Assertion (A) is followed by a statement of Reason (R). Choose the correct option:
(a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
(c) Assertion (A) is true but Reason (R) is false.
(d) Assertion (A) is false but Reason (R) is true.
Question 1.
Assertion (A): \(\frac{3}{5}\) is the reciprocal of \(\frac{5}{3}\) as \(\frac{3}{5} \times \frac{5}{3}\) = 1.
Reason (R): Two fractions are reciprocal of each other if their product is 1.
Answer:
(a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
Question 2.
Assertion (A): \(\frac{2}{5} \div \frac{4}{7}=\frac{2}{5} \times \frac{7}{4}=\frac{14}{20}\)
Reason (R): Division of one fraction by another fraction is equivalent to multiplication of the first fraction and the second fraction.
Answer:
(c) Assertion (A) is true but Reason (R) is false.
Fill In the blanks.
1. The lowest form of the product 2\(\frac{3}{7} \times \frac{7}{9}\) is _______
Answer:
1\(\frac{8}{2}\)
2. The two non-zero fractions whose product is 1, are called the _______ of each other.
Answer:
reciprocal
3. \(\frac{2}{3} \div \frac{4}{9}\) = __
Answer:
3
4. \(\frac{1}{3}+\frac{1}{3}+\frac{1}{3}+\frac{1}{3}=\frac{1}{3}\) x _______ = \(\frac{4}{3}\)
Answer:
4
5. The product of two proper fractions is always _______ than each of the two fractions.
Answer:
Less
Match the Following.
Question 1.
| Column 1 | Column II. |
| 1. \(\frac{2}{3} \div \frac{1}{2}\) | (a) \(\frac{1}{3}\) |
| 2. \(\frac{2}{3} \div \frac{2}{1}\) | (b) 45 |
| 3. 6 × \(\frac{1}{4}\) | (c) \(\frac{4}{3}\) |
| 4. \(\frac{3}{2}\) × 8 \(\frac{1}{2}\) | (d) \(\frac{3}{2}\) |
| 5. 15 ÷ \(\frac{1}{3}\) | (e) \(\frac{51}{4}\) |
Answer:
| Column 1 | Column II. |
| 1. \(\frac{2}{3} \div \frac{1}{2}\) | (c) \(\frac{4}{3}\) |
| 2. \(\frac{2}{3} \div \frac{2}{1}\) | (a) \(\frac{1}{3}\) |
| 3. 6 × \(\frac{1}{4}\) | (d) \(\frac{3}{2}\) |
| 4. \(\frac{3}{2}\) × 8 \(\frac{1}{2}\) | (e) \(\frac{51}{4}\) |
| 5. 15 ÷ \(\frac{1}{3}\) | (b) 45 |
Answer the following.
Question 1.
A water tank can hold 1000 litres of water. Due to an electricity breakdown, the tank could fill only \(\frac{3}{5}\) of its capacity. How many litres of water are filled in the tank?
Answer:
600 litres
Question 2.
Provide the number in the box, such that \(\frac{4}{7}\) × __ = \(\frac{36}{35}\). Out of all three fractions, which one is greatest?
Answer:
\(\frac{9}{5}\), \(\frac{9}{5}\)
Question 3.
Rita has bought a carpet of size 4m × 6 \(\frac{2}{3}\) m. But her room size is 3\(\frac{1}{3}\) m × 5 \(\frac{2}{3}\) m. What area of carpet should be cut off to fit a wall-to-wall carpet into the room?
Answer:
7\(\frac{7}{9}\)sq.m
Question 4.
The weight of an object on the Moon is \(\frac{1}{6}\) times its weight on the Earth. If an object weighs 36\(\frac{1}{5}\) kg on the Earth, how much would it weigh on the Moon?
Answer:
6\(\frac{1}{30}\)kg
Question 5.
Anuradha can do a piece of work in 6 hours. What part of the work can she do in 1 hour, in 5 hours, in 6 hours?
Answer:
\(\frac{1}{6}\), \(\frac{5}{6}\), 1
MULTIPLICATION OF FRACTIONS
Varun and Arun, two friends, want to participate in a marathon, ‘Run For Pride’. For the marathon, they practice every morning in a park.
During practice, Varun runs 12 km in 1 hour.
Question 1.
How far can Varun go in 3 hours? Fill in the blanks to find the answer.
Distance covered by Varun in 1 hour = _______ km.
Therefore, the distance covered by Varun in 3 hours = _______km + _______km + _______km = _______km
OR
= _______ × _______ = _______ km
Answer:
12 km; 12 km + 12 km + 12 km = 36 km; 3 × 12 km = 36 km
Question 2.
Arun is slower than Varun. He could cover only a third of the distance covered by Varun in 1 hour.
(a) Observe the picture given below and fill in the blanks.
Answer:
\(\frac{1}{3}\), 12
(b) What part of distance will Arun cover in 2 hours?
Distance covered by Arun in 1 hour = \(\frac{1}{3}\) part of distance covered by Varun.
Distance covered by Arun in 2 hours =
part of distance covered by Varun.
Answer:
\(\frac{1}{3}+\frac{1}{3}=\frac{2}{3} ; \frac{1}{3}\) × 2 = \(\frac{2}{3}\)
(c) How much distance will Arun cover in 2 hours?
Thus, Arun will cover _______ km in 2 hours.
Answer:
12 km × \(\frac{2}{3}\) = 8 km; 8 km
Question 3.
Payal is also participating in the marathon. She can run 5 km in 1 hour. Can you find out how far she can run in \(\frac{1}{6}\) hour.
(a) Fill in the blanks to find the answer.
Distance covered in 1 hour = 5 km.
In \(\frac{1}{6}\) hour, distance covered by Payal = _______ × 5 km = _______ km.
Answer:
\(\frac{1}{6} ; \frac{5}{6} ; \frac{5}{6}\)
(b) How far can Payal run in \(\frac{5}{6}\) hours. Also, draw a line diagram as done in part (a).
Answer:
\(\frac{25}{6}\)
To multiply a fraction by a whole number, we divide the whole number by the denominator of the given fraction and then multiply the result by the numerator of the fraction to get the final result.
Question 4.
Multiply the following. Convert the product Into a mixed fraction, If required.
(a) 4 × \(\frac{2}{9}\)
Answer:
\(\frac{8}{9}\)
(b) 7 × \(\frac{3}{4}\)
Answer:
5\(\frac{1}{4}\)
(c) \(\frac{2}{5}\) × 4
Answer:
1\(\frac{3}{5}\)
(d) \(\frac{7}{11}\) × 8
Answer:
5\(\frac{1}{11}\)
(e) 9 × \(\frac{5}{7}\)
Answer:
6\(\frac{3}{7}\)
(f) 1\(\frac{1}{3}\) × 2
Answer:
2\(\frac{2}{3}\)
Question 5.
Ramdiri, a farmer, has 3 sons and 1 daughter. He distrtbuted \(\frac{3}{7}\) bigha of Land to each. How much Land ¡n all did he give to his children?
Answer:
1\(\frac{5}{7}\) bigha
Question 6.
Sathvik eats 3\(\frac{2}{8}\) chapatis in a day. How many chapatis will he eat in a week?
Answer:
22\(\frac{3}{4}\) chapatis
Question 7.
Rashmi makes \(\frac{1}{7}\) part of a painting in a day. What part of the painting will she make in
(a) 5 days and
(b) 7 days?
Answer:
(a) \(\frac{5}{7}\)
(b) 1 whole painting
Multiplying Two Fractions
When a fraction is multiplied by another fraction, we follow the method similar to the one we used multiplying a fraction by a whole number. As,
Thus, \(\frac{3}{4} \times \frac{2}{5}=\frac{6}{20}\)
Question 8.
Find the product of the following. Convert the product into mixed fractions, if required.
(a) \(\frac{2}{3} \times \frac{1}{4}\)
Answer:
\(\frac{1}{6}\)
(b) \(\frac{3}{7} \times \frac{4}{5}\)
Answer:
\(\frac{12}{35}\)
(c) \(\frac{1}{2} \times \frac{3}{5}\)
Answer:
\(\frac{3}{10}\)
(d) \(\frac{11}{12} \times \frac{7}{8}\)
Answer:
\(\frac{77}{96}\)
(e) \(\frac{5}{9} \times \frac{8}{11}\)
Answer:
\(\frac{40}{2}\)
(f) \(\frac{7}{12} \times \frac{13}{15}\)
Answer:
\(\frac{91}{180}\)
Question 9.
A caterpillar can walk \(\frac{1}{8}\) km in 1 hour. How far can it walk in \(\frac{1}{4}\) hour?
Answer:
\(\frac{1}{32}\) km
Question 10.
Susharit reads \(\frac{1}{3}\) part of a book in 1 hour. What part of the book wilL he read in 2\(\frac{1}{5}\) hours?
Answer:
\(\frac{11}{15}\) parts
Question 11.
A car runs 16 km using 1 litre of petrol. How much distance will it cover using \(\frac{3}{4}\) litre of petrol?
Answer:
12 km
Question 12.
Rohan used \(\frac{2}{3}\) bag of soil for his garden. He is digging another garden that will need \(\frac{1}{5}\) as much How much soil will he use in total?
Answer:
\(\frac{4}{5}\) bags
Think and Answer
Think and write the number in the box, such that \(\frac{4}{5}\) × __ = \(\frac{12}{35}\). Out of all three fractions, which one is greatest?
Answer:
\(\frac{3}{7} ; \frac{4}{5}\)
Connection, between the Area of a Rectangle and Fraction Multiplication
Rabid made a square of unit length on A-4 sheet, and she divided the square vertically into two equal parts and then horizontally in four equal parts. By doing this, she divided the unit square into eight small rectangles.
She shades one rectangle out of eight as shown in the figure.
Now, she asks Imran to find the area of a small rectangle formed after dividing the unit square.
Question 13.
Imran tries to find the area of the small shaded rectangle. Help him by filling in the boxes.
Length of shaded rectangle = __, Breadth oj shaded rectangle = __
We have, area of a rectangle = length × breadth
Therefore, area of the shaded rectangle = _______ × __ = __ sq.unit.
Answer:
\(\frac{1}{2}\) units, \(\frac{1}{4}\) units; \(\frac{1}{2} \times \frac{1}{4}=\frac{1}{8}\)
Question 14.
Find the following products. Use a unit square as a whole/or representing the fractions:
(a) \(\frac{1}{2} \times \frac{1}{4}\)
(b) \(\frac{1}{3} \times \frac{1}{5}\)
(c) \(\frac{1}{8} \times \frac{1}{10}\)
Answer:
(a) \(\frac{1}{8}\)
(b) \(\frac{1}{15}\)
(c) \(\frac{1}{80}\)
Multiplying Numerators and Denominators
If \(\frac{a}{b}\) and \(\frac{c}{d}\) are two fractions, then \(\frac{a}{b} \times \frac{c}{d}=\frac{a \times c}{b \times d}\). Thus, we can say that:
The Product of two fractions = \(\frac{\text { Product of numerators }}{\text { Product of denominators }}\)
Question 15.
Fill in the blanks.
Answer:
(a) \(\frac{3}{2} \times \frac{4}{5}=\frac{3 \times 4}{2 \times 5}=\frac{12}{10}\)
(b) \(\frac{4}{7} \times \frac{2}{3}=\frac{4 \times 2}{7 \times 3}=\frac{8}{21}\)
(c) \(\frac{4}{7} \times \frac{5}{4}=\frac{4 \times 5}{7 \times 4}=\frac{20}{28}\)
Multiplication of Fractions-Simplifying to Lowest Form
When multiplying fractions, we can first divide the numerator and denominator by their common factors before multiplying the numerators and denominators. This is called cancelling the common factors.
Question 16.
Multiply the following fractions and express the product to their lowest form.
(a) \(\frac{12}{18} \times \frac{8}{18}\)
(b) \(\frac{15}{36} \times \frac{45}{30}\)
(c) \(\frac{1}{2} \times \frac{26}{55}\)
Answer:
(a) \(\frac{8}{27}\)
(b) \(\frac{5}{8}\)
(c) \(\frac{13}{55}\)
Is the Product Always Greater than the Numbers Multiplied?
- The product of two proper fractions is always less than each of the two fractions.
- The product of two improper fractions is always greater than each of the two fractions.
Question 17.
Find the product of the following. Is the product always greater than the numbers multiplied?
(a) 3 × \(\frac{4}{7}\)
(b) \(\frac{11}{10} \times \frac{8}{12}\)
(c) \(\frac{4}{5} \times \frac{8}{7}\)
Answer:
(a) \(\frac{12}{7}\)
(b) \(\frac{11}{15}\)
(c) \(\frac{32}{35}\)
Order of Multiplication
Question 18.
Is \(\frac{5}{10} \times \frac{4}{9}\) equal to \(\frac{4}{9} \times \frac{5}{10}\)? What do you observe from the multiplication of fractions?
Answer:
Yes
Question 19.
Verify whether the products of both sides are same.
(a) \(\frac{2}{3} \times \frac{5}{6}=\frac{5}{6} \times \frac{2}{3}\)
(b) \(\frac{7}{10} \times \frac{5}{6}=\frac{5}{6} \times \frac{7}{10}\)
(c) \(\frac{7}{9} \times \frac{11}{13}=\frac{11}{13} \times \frac{7}{9}\)
Answer:
Do it yourself
DIVISION OF FRACTIONS
To divide two fractions:
- Find the reciprocal of the divisor.
- Multiply this by the dividend to get the quotient.
In general, if \(\frac{a}{b}\) and \(\frac{c}{d}\) are two fractions, then \(\frac{a}{b} \div \frac{c}{d}=\frac{a}{b}\) × (Reciprocal of \(\frac{c}{d}\)) = \(\frac{a}{b} \times \frac{d}{c}\)
The reciprocal of the divisor is also called the multiplicative inverse of the divisor fraction. Two numbers or fractions are said to be reciprocals of each other if their product is 1.
For example, the reciprocal of \(\frac{4}{7}\) is \(\frac{7}{4}\) i.e., \(\frac{4}{7} \times \frac{7}{4}=\frac{4 \times 7}{7 \times 4}\) = 1
Question 20.
Write the reciprocal of the following:
(a) 4
(b) \(\frac{1}{8}\)
(c) \(\frac{4}{5}\)
(d) 1\(\frac{3}{7}\)
Answer:
(a) \(\frac{1}{4}\)
(b) 8
(c) \(\frac{5}{4}\)
(d) \(\frac{7}{10}\)
Question 21.
(a) \(\frac{3}{4}\) ÷ 6
(b) 11 ÷ \(\frac{6}{7}\)
(c) \(\frac{5}{10} \div \frac{3}{4}\)
Answer:
(a) \(\frac{1}{8}\)
(b) \(\frac{77}{6}\)
(c) \(\frac{2}{3}\)
Question 22.
Rani has a 10 m long rope. She wants to cut it into peces of equal Length for her project. If the Length of each piece is \(\frac{5}{8}\)m, how many pieces wilL she make from the rope?
Answer:
16 pieces
Question 23.
How many \(\frac{5}{6}\) hour periods are there in 7\(\frac{1}{2}\) hours?
Answer:
9 periods
SOME PROBLEMS INVOLVING FRACTIONS
Question 24.
Lakshmi. and her family Love fitter coffee, so she made 5 cups of filter coffee. She used \(\frac{1}{2}\) Litre of milk for this. How much milk is there in each cup of coffee? Also, complete the given diagram.
Answer:
\(\frac{1}{2}\) litres; \(\frac{1}{2}\)litres of 5 cups of coffee
Question 25.
A road roller can repair \(\frac{11}{5}\) km of road la a day. How many days will it take to repair 26\(\frac{2}{5}\) km long road?
Answer:
12 days
Question 26.
Rajan has to cover the floor of the courtyard, having a area of 21\(\frac{3}{5}\) square metres, with square bricks each of whose sides is \(\frac{1}{10}\) m. How maay bricks are required to cover the centire area?
Answer:
2160 bricks
Question 27.
CKoose the o ptlon(s) describing the result oj
(a) \(\frac{729}{676} \times \frac{576}{444}\)
(i) >\(\frac{729}{676}\)
(ii) <\(\frac{729}{676}\)
(iii) <\(\frac{576}{444}\)
(iv) >\(\frac{576}{444}\)
(v) >1
(vi) <1
Answer:
(i), (iv), (v)
(b) \(\frac{425}{520} \div \frac{600}{324}\)
(i) <1
(ii) >1
(iii) >\(\frac{425}{520}\)
(iv) <\(\frac{425}{520}\)
(v) >\(\frac{600}{324}\)
(vi) <\(\frac{600}{324}\)
Answer:
(i), (iv), (vi)
Fractional Relations
Question 28.
In each of the figures given below, find the fraction of the big square that the skaded region occupies.
Answer:
(a) \(\frac{1}{32}\)
(b) \(\frac{1}{24}\)
Coinage of India
Rajat’s dada ji tells Kim about ancient times, noting that in the 12th century, several types of coins were in use across different kingdoms of the Indian subcontinent. Dinars/Gadyanas and Hunas were gold coins, with high value, used for large transactions and for storing wealth. Drammas/Tankas were silver coins, more commonly used in everyday transactions; Kasus/Panas and Mashakas were copper coins, with lower value, used in smaller transactions; and cowrie shells, which represented the lowest denomination, were used for very small transactions and as change.
He also tells Rajat that the exact conversion rates between these coins varied depending on the region, time period, economic conditions, weights of the coins and their purity.
Question 29.
Assume that: 1 Gold dinar = 12 Silver drammas/Tankas,
- 1 Silver dramma = 4 Copper panas/Kasus
- 1 Copper pana = 30 Cowrie shells
- 1 Copper pana = 6 Mashakas
Now, fill in the blanks.
(a) If 1 copper pana = \(\frac{1}{48}\) gold dinar, then the value of 4 copper panas = _______ gold dinar.
(b) If 1 cowrie shell = \(\frac{1}{30}\) copper pana, then the value of 10 cowrie shell = _______ copper
pana = __ silver drama.
(c) 1 mashaka = \(\frac{1}{6}\) copper pana and 1 copper pana = \(\frac{1}{4}\) silver dramma and 1 silver dramma = \(\frac{1}{12}\) gold dinar, then 1 mashaka = _______ silver drama.
Answer:
(a) \(\frac{1}{12}\)
(b) \(\frac{1}{3}, \frac{1}{12}\)
(c) \(\frac{1}{288}\)
The post Working with Fractions Class 7 Worksheet with Answers Maths Chapter 8 appeared first on Learn CBSE.
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