Working with Fractions Class 7 Maths Worksheet with Answers Chapter 8

Ganita Prakash Part-I, Grade 7, Textbook of Mathematics – Chapter 8 is called “Working with Fractions”. You know how to add and subtract fractions from earlier chapters. This chapter is the next step to that – multiplying and dividing them. The lesson start with simple stories, like how far a slow tortoise walks in an hour, and grow into full rules you can use anywhere. The worksheet below tests every skill from the chapter. The main topics are:

• Multiplying a fraction by a whole number
• Multiplying two fractions
• Fraction multiplication and the area of a rectangle
• Cancelling common factors before multiplying
• Reciprocals and division of fractions
• Comparing the product or quotient with the original numbers
• Word problems on fractions

These are the formulas you must know before starting:

• Multiply fractions: a/b × c/d = (a × c) / (b × d)
• Reciprocal of a/b is b/a, and a fraction times its reciprocal equals 1
• Divide fractions: a/b ÷ c/d = a/b × d/c = (a × d) / (b × c) – flip the divisor, then multiply
• Multiplying by a number between 0 and 1 makes the answer smaller than the other number; multiplying by a number bigger than 1 makes it bigger
• Dividing by a number between 0 and 1 makes the answer bigger than the dividend; dividing by a number bigger than 1 makes it smaller

Always simplify by cancelling common factors before you multiply. And remember, “of” means multiply – “1/4 of 500 grams” is just 1/4 × 500. Work through the problems from easy to hard. The worksheet is split into four levels – Basic, Standard, Advanced, and HOTS. A complete answer key given at the end of the page.

Class 7 Maths Worksheet – Chapter 8: Working with Fractions

Basic

1. Multiply and convert the answers into mixed fractions:
   • 7 × 3/5
   • 5 × 7/8
   • 9 × 4/7
2. Find the products in simplest form:
   • 3/4 × 2/3
   • 5/6 × 9/10
   • 7/8 × 4/21
3. Multiply:
   • 1 1/2 × 2/3
   • 2 1/4 × 4/9
   • 3 1/5 × 5/8
4. Write the reciprocal of each number:
   • 3/7
   • 11/4
   • 2 1/2
   • 1
5. Verify that a fraction multiplied by its reciprocal gives 1:
   • 5/9
   • 7/3
   • 1 1/4
6. Divide:
   • 3/4 ÷ 1/2
   • 5/6 ÷ 5/12
   • 7/8 ÷ 14/3
7. Choose the correct operation and solve:
   • How many 1/4 m pieces can be cut from 6 m ribbon?
   • What is the length of one piece if 3/4 m ribbon is shared equally among 3 children?
8. State whether the quotient is greater than or less than the dividend:
   • 5/6 ÷ 1/3
   • 5/6 ÷ 2
   • 3 ÷ 3/4

Standard

1. Tenzin drinks 1/2 glass of milk every day. Find the number of glasses of milk he drinks:
   • In one week
   • In January, which has 31 days
2. Three families buy 5 litres of oil and divide it equally. How much oil does each family get?
   How much oil will one family get in 4 weeks?
3. Every day, the Moon sets 5/6 hour later than on the previous day. If it sets at 10 p.m. on Monday,
   how many hours after 10 p.m. will it set on Thursday? At what time will it set?
4. Internet time costs ₹8 per hour. Find the cost of using the internet for:
   • 1 1/4 hours
   • 2 3/4 hours
5. A rectangular sheet is 5 1/2 cm long and 2 2/3 cm wide. Find its area.
6. A baker needs 1/6 kg of flour for one loaf of bread. How many loaves can be made using 5 kg of flour?
7. A car runs 16 km using 1 litre of petrol. How far will it travel using 2 3/4 litres of petrol?
8. A cake has 4/5 of it remaining. This remaining cake is shared equally among 3 friends.
   What fraction of the whole cake does each friend get?

Advance

1. Evaluate:
   • 4 2/3 × 3/7
   • 5 1/4 × 2 2/5
   • 3 3/8 × 8/9
2. Divide and simplify:
   • 4/5 ÷ 2/3
   • 7/12 ÷ 14/9
   • 2 1/4 ÷ 3/8
3. A 4 m wooden block is cut into pieces, each of length 5/8 m.
   How many pieces can be made?
4. A 3 litre jug of watermelon juice is shared equally among 8 friends.
   How much juice does each friend receive in:
   • Litres
   • Millilitres
5. Mira is reading a novel with 400 pages. She read 1/5 of the book yesterday and 3/10 today.
   How many pages are left to read?
6. A tailor has 7 1/2 m of cloth. Each school uniform requires 1 1/4 m of cloth.
   How many complete uniforms can be stitched?
7. A colony of ants splits equally into two groups, and then each group splits equally into three groups.
   What fraction of the original colony reaches each final group?
8. A farmer gives 2/3 acre of land to each of her 5 grandchildren.
   How much land does she give away altogether? Express the answer as a mixed fraction.

HOTS

1. Without multiplying completely, compare the product
   
   (565/465) × (707/676)
   
   with each of the following:
   • 565/465
   • 707/676
   • 1
2. Find the value of:
   • (1 − 1/2) × (1 − 1/3)
   • (1 − 1/2) × (1 − 1/3) × (1 − 1/4)
   • (1 − 1/2) × (1 − 1/3) × (1 − 1/4) × … × (1 − 1/10)
3. A number is multiplied by 3/5 and the answer is 18.
   Find the original number.
4. A water tank is 3/4 full. After using 2/5 of the water currently in the tank,
   what fraction of the full tank remains?
5. Riya says, “Dividing a fraction by a fraction always makes it smaller.”
   Is she correct? Give one example where the quotient is greater than the dividend and one where it is less.
6. A shop has 12 m of ribbon. It is used to make bows, each requiring 3/8 m of ribbon.
   After making 25 bows, how much ribbon remains?
7. A recipe requires 3/4 cup of flour for 1 batch of cookies.
   How much flour is needed for 2 2/3 batches? If 3 cups of flour are available, how much flour remains?
8. A school has 240 students. On Monday, 3/8 of the students participate in a cleanliness drive.
   On Tuesday, 2/5 of the remaining students participate.
   How many students have not participated on either day?

Answer Key

Basic – Answers

1. • 7 × 3/5 = 21/5 = 4 1/5
   • 5 × 7/8 = 35/8 = 4 3/8
   • 9 × 4/7 = 36/7 = 5 1/7
2. • 3/4 × 2/3 = 1/2
   • 5/6 × 9/10 = 3/4
   • 7/8 × 4/21 = 1/6

   Hint: Cancel common factors before multiplying.

3. • 1 1/2 × 2/3 = 3/2 × 2/3 = 1
   • 2 1/4 × 4/9 = 9/4 × 4/9 = 1
   • 3 1/5 × 5/8 = 16/5 × 5/8 = 2
4. • Reciprocal of 3/7 = 7/3
   • Reciprocal of 11/4 = 4/11
   • Reciprocal of 2 1/2 = 5/2, so reciprocal = 2/5
   • Reciprocal of 1 = 1
5. • 5/9 × 9/5 = 1
   • 7/3 × 3/7 = 1
   • 1 1/4 × 4/5 = 5/4 × 4/5 = 1
6. • 3/4 ÷ 1/2 = 3/4 × 2/1 = 3/2 = 1 1/2
   • 5/6 ÷ 5/12 = 5/6 × 12/5 = 2
   • 7/8 ÷ 14/3 = 7/8 × 3/14 = 3/16
7. • 6 ÷ 1/4 = 24 pieces
   • 3/4 ÷ 3 = 1/4 m
8. • 5/6 ÷ 1/3: Quotient is greater than the dividend.
   • 5/6 ÷ 2: Quotient is less than the dividend.
   • 3 ÷ 3/4: Quotient is greater than the dividend.

Standard – Answers

1. • In one week = 7 × 1/2 = 7/2 = 3 1/2 glasses
   • In January = 31 × 1/2 = 31/2 = 15 1/2 glasses
2. Oil per family per week = 5 ÷ 3 = 5/3 = 1 2/3 L
   Oil in 4 weeks = 4 × 5/3 = 20/3 = 6 2/3 L
3. Time after 10 p.m. = 3 × 5/6 = 15/6 = 2 1/2 hours
   The Moon will set at 12:30 a.m. on Thursday night.
4. • 1 1/4 × 8 = 5/4 × 8 = ₹10
   • 2 3/4 × 8 = 11/4 × 8 = ₹22
5. Area = 5 1/2 × 2 2/3
   = 11/2 × 8/3 = 44/3 = 14 2/3 sq cm
6. 5 ÷ 1/6 = 5 × 6 = 30 loaves
7. 16 × 2 3/4 = 16 × 11/4 = 44 km
8. 4/5 ÷ 3 = 4/5 × 1/3 = 4/15
   Each friend gets 4/15 of the whole cake.

Advance – Answers

1. • 4 2/3 × 3/7 = 14/3 × 3/7 = 2
   • 5 1/4 × 2 2/5 = 21/4 × 12/5 = 63/5 = 12 3/5
   • 3 3/8 × 8/9 = 27/8 × 8/9 = 3
2. • 4/5 ÷ 2/3 = 4/5 × 3/2 = 6/5 = 1 1/5
   • 7/12 ÷ 14/9 = 7/12 × 9/14 = 3/8
   • 2 1/4 ÷ 3/8 = 9/4 × 8/3 = 6
3. 4 ÷ 5/8 = 4 × 8/5 = 32/5 = 6 2/5
   So, 6 complete pieces can be made.
4. Each friend receives 3 ÷ 8 = 3/8 L
   3/8 L = 375 mL
5. Pages read = 1/5 + 3/10 = 2/10 + 3/10 = 1/2
   Pages left = 1/2 × 400 = 200 pages
6. 7 1/2 ÷ 1 1/4 = 15/2 ÷ 5/4 = 15/2 × 4/5 = 6
   6 complete uniforms can be stitched.
7. Each final group receives 1/2 × 1/3 = 1/6 of the original colony.
8. 5 × 2/3 = 10/3 = 3 1/3 acres

HOTS – Answers

1. The product is greater than 565/465, greater than 707/676, and greater than 1.
   • Hint: Both 565/465 and 707/676 are greater than 1. Multiplying two positive fractions greater than 1 gives a product greater than each factor.
2. • (1 − 1/2) × (1 − 1/3) = 1/2 × 2/3 = 1/3
   • (1 − 1/2) × (1 − 1/3) × (1 − 1/4) = 1/2 × 2/3 × 3/4 = 1/4
   • (1 − 1/2) × (1 − 1/3) × … × (1 − 1/10) = 1/10
3. Original number = 18 ÷ 3/5 = 18 × 5/3 = 30
4. Water used = 2/5 of 3/4 = 2/5 × 3/4 = 3/10
   Water remaining = 3/4 − 3/10 = 15/20 − 6/20 = 9/20
5. Riya is incorrect.
   • Greater example: 3/4 ÷ 1/2 = 1 1/2, which is greater than 3/4.
   • Smaller example: 3/4 ÷ 2 = 3/8, which is less than 3/4.
6. Ribbon used for 25 bows = 25 × 3/8 = 75/8 = 9 3/8 m
   Ribbon remaining = 12 − 9 3/8 = 2 5/8 m
7. Flour needed = 3/4 × 2 2/3 = 3/4 × 8/3 = 2 cups
   Flour remaining = 3 − 2 = 1 cup
8. Students participating on Monday = 3/8 × 240 = 90
   Students remaining = 240 − 90 = 150
   Students participating on Tuesday = 2/5 × 150 = 60
   Students not participating = 150 − 60 = 90

Other Class 7 Maths worksheet

Ganita Prakash Part-I, Grade 7

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• Arithmetic Expressions Class 7 Maths Worksheet
• A Peek Beyond the Point Class 7 Maths Worksheet
• Number Play Class 7 Maths Worksheet
• Working with Fractions Class 7 Maths Worksheet

Ganita Prakash Part-II, Grade 7

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• Another Peek Beyond the Point Class 7 Maths Worksheet
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