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CBSE · Class 7 · Mathematics

Chapter 8: Working with Fractions

5 concepts · 40 practice questions with answers · Free to read

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Fraction times a whole number

From daily life

A recipe needs 3/4 cup of milk per glass. For 5 glasses you need 5 × 3/4 cups.

Simple definition

Multiplying a fraction by a whole number is repeated addition: multiply the numerator by the whole number and keep the denominator. The word "of" also means multiply.

½½½½½½3 ÷ ½ = 63 wholes hold 6 halves

In the figure: Three wholes cut in halves give six halves, as repeated addition shows.

Rule 1: Repeated addition — 3 × (1/4) = 1/4 + 1/4 + 1/4 = 3/4.

  • Easy: 4 × 2/9 = 8/9.
  • Medium: 5 × 3/4 = 15/4 = 3 3/4.
  • Exam-type: 7 × 5/6 = 35/6 = 5 5/6.

Rule 2: Cancel first — If the whole number and the denominator share a factor, cancel before multiplying.

  • Easy: 3/4 × 8 = 3 × 2 = 6.
  • Medium: 5/6 × 12 = 5 × 2 = 10.
  • Exam-type: 7/15 × 45 = 7 × 3 = 21.

Rule 3: Fraction "of" a quantity — Divide by the denominator, then multiply by the numerator.

  • Easy: 1/3 of 12 = 4.
  • Medium: 2/3 of 18 = 6 × 2 = 12.
  • Exam-type: 3/4 of ₹60 = 15 × 3 = ₹45.
Remember

Convert an improper answer to a mixed number only at the end.

Common mistake

Multiplying the denominator too: 3/4 × 8 ≠ 24/32 left as is; it equals 24/4 = 6.

Shortcut

Whole number ÷ denominator first makes numbers small. Memory clue: "Number on top, denominator stays."

Spot the difference

StepSlow wayFast way
3/4 × 824/4 = 63 × 2 = 6
2/5 × 1020/5 = 42 × 2 = 4

Practice questions

Easy
  1. 1Find 4 × 2/9.
  2. 2Find 1/3 of 12.
  3. 3Find 3/4 × 8.
Medium
  1. 4Find 5 × 3/4 as a mixed number.
  2. 5Find 2/3 of 18.
  3. 6Find 5/6 × 12.
Challenging
  1. 7A cloth costs ₹60 per metre. Find the cost of 3/4 m.
  2. 8Find 7/15 × 45.
Show answers (try them yourself first)
  1. 18/9
  2. 24
  3. 36
  4. 43 3/4
  5. 512
  6. 610
  7. 7₹45
  8. 821
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Fraction times a whole number

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Fraction times a fraction

From daily life

Half of a third of a chocolate bar is a sixth of the whole bar.

Simple definition

To multiply fractions, multiply the numerators and multiply the denominators, then simplify: a/b × c/d = (a × c)/(b × d). The product of two proper fractions is smaller than each of them.

1/2 × 1/3= 1/6red = 1 of 6 boxes

In the figure: Half of a third: the red box is 1 of 6 boxes, so 1/2 × 1/3 = 1/6.

Rule 1: Multiply across — Top × top over bottom × bottom.

  • Easy: 1/2 × 1/3 = 1/6.
  • Medium: 2/5 × 3/7 = 6/35.
  • Exam-type: 3/4 × 5/9 = 15/36 = 5/12.

Rule 2: Cross-cancel — Cancel a numerator against a different denominator before multiplying.

  • Easy: 2/3 × 3/4 = 1/2.
  • Medium: 4/9 × 3/8 = 1/6.
  • Exam-type: 5/6 × 12/25 = 2/5.

Rule 3: Area of a rectangle — Area = length × breadth, even when both are fractions.

  • Easy: 3/4 m by 2/3 m → 1/2 sq m.
  • Medium: 1/2 m by 1/2 m → 1/4 sq m.
  • Exam-type: 5/4 m by 4/5 m → 1 sq m.
Remember

Do not need a common denominator for multiplication.

Common mistake

Adding denominators: 1/2 × 1/3 is not 1/5. It is 1/6.

Shortcut

Cancel diagonally to avoid large numbers. Memory clue: "Across and cancel; no common ground needed."

Spot the difference

OperationCommon denominator?Example
Add / subtractYes1/2 + 1/3 = 5/6
MultiplyNo1/2 × 1/3 = 1/6

Practice questions

Easy
  1. 1Find 1/2 × 1/3.
  2. 2Find 2/5 × 3/7.
  3. 3Find 2/3 × 3/4.
Medium
  1. 4Find 3/4 × 5/9.
  2. 5Find the area of a 1/2 m by 1/2 m square.
  3. 6Find 4/9 × 3/8.
Challenging
  1. 7Find the area of a 3/4 m by 2/3 m rectangle.
  2. 8Find 5/6 × 12/25.
Show answers (try them yourself first)
  1. 11/6
  2. 26/35
  3. 31/2
  4. 45/12
  5. 51/4 sq m
  6. 61/6
  7. 71/2 sq m
  8. 82/5

Reciprocals and dividing a whole number

From daily life

How many half-litre bottles can you fill from 3 litres of water? 3 ÷ 1/2 = 6 bottles.

Simple definition

The reciprocal of a fraction is obtained by flipping it: the reciprocal of a/b is b/a. A number times its reciprocal is 1. Dividing by a fraction means multiplying by its reciprocal.

23⇄32× = 12/3 × 3/2 = 1

In the figure: Flip 2/3 to get 3/2; their product is 1.

½½½½½½3 ÷ ½ = 63 wholes hold 6 halves

In the figure: Counting halves: 3 wholes give 6 halves, so 3 ÷ 1/2 = 6.

Rule 1: Find the reciprocal — Swap the numerator and the denominator; a whole number n is n/1, so its reciprocal is 1/n.

  • Easy: 3/5 → 5/3.
  • Medium: 7 → 1/7.
  • Exam-type: 2 1/2 = 5/2 → 2/5.

Rule 2: Whole number ÷ fraction — Multiply the whole number by the reciprocal.

  • Easy: 3 ÷ 1/2 = 3 × 2 = 6.
  • Medium: 8 ÷ 2/3 = 8 × 3/2 = 12.
  • Exam-type: 15 ÷ 5/6 = 15 × 6/5 = 18.

Rule 3: Fraction ÷ whole number — Multiply the denominator by the whole number.

  • Easy: 1/2 ÷ 3 = 1/6.
  • Medium: 3/4 ÷ 6 = 3/24 = 1/8.
  • Exam-type: 4/5 ÷ 2 = 4/10 = 2/5.
Remember

Dividing by a number smaller than 1 makes the answer bigger.

Common mistake

Flipping the first number instead of the divisor: 3 ÷ 1/2 is not 1/3 ÷ 1/2.

Shortcut

Ask "how many halves fit in 3?" to check. Memory clue: "Keep, Change, Flip": keep first, change ÷ to ×, flip second.

Spot the difference

DivideRewriteAnswer
3 ÷ 1/23 × 26
8 ÷ 2/38 × 3/212
1/2 ÷ 31/2 × 1/31/6

Practice questions

Easy
  1. 1Write the reciprocal of 3/5.
  2. 2Find 3 ÷ 1/2.
  3. 3Write the reciprocal of 7.
Medium
  1. 4Find 8 ÷ 2/3.
  2. 5Find 1/2 ÷ 3.
  3. 6Find 15 ÷ 5/6.
Challenging
  1. 7How many 1/4 kg packets can be made from 5 kg of sugar?
  2. 8Find 3/4 ÷ 6.
Show answers (try them yourself first)
  1. 15/3
  2. 26
  3. 31/7
  4. 412
  5. 51/6
  6. 618
  7. 720
  8. 81/8

Dividing fractions

From daily life

A 3/4 m ribbon is cut into pieces of 1/8 m each. How many pieces? 3/4 ÷ 1/8 = 6.

Simple definition

To divide by a fraction, multiply by its reciprocal: a/b ÷ c/d = a/b × d/c. For mixed numbers, first change them to improper fractions.

3/4 ÷ 1/4 = 3how many quarters fit in three quarters

In the figure: Three quarters hold three pieces of one quarter: 3/4 ÷ 1/4 = 3.

Rule 1: Keep, change, flip — Keep the first fraction, change ÷ to ×, flip the second.

  • Easy: 3/4 ÷ 1/4 = 3/4 × 4 = 3.
  • Medium: 2/3 ÷ 4/9 = 2/3 × 9/4 = 3/2.
  • Exam-type: 5/6 ÷ 5/12 = 5/6 × 12/5 = 2.

Rule 2: Mixed numbers — Convert to improper fractions first, then divide.

  • Easy: 1 1/2 ÷ 3/4 = 3/2 × 4/3 = 2.
  • Medium: 2 1/4 ÷ 3/8 = 9/4 × 8/3 = 6.
  • Exam-type: 3 ÷ 1 1/2 = 3 × 2/3 = 2.

Rule 3: Check by multiplying back — Quotient × divisor must give the dividend.

  • Easy: 3/2 × 4/9 = 2/3 ✓.
  • Medium: 6 × 3/8 = 9/4 ✓.
  • Exam-type: 2 × 3/4 = 3/2 ✓.
Remember

Flip only the divisor (the number after ÷).

Common mistake

Flipping both fractions. Only the second one is flipped.

Shortcut

Cancel after flipping, before multiplying. Memory clue: "Keep, Change, Flip."

Spot the difference

CaseMethodExample
fraction ÷ fractionmultiply by reciprocal3/4 ÷ 1/4 = 3
mixed ÷ fractionimproper first1 1/2 ÷ 3/4 = 2

Practice questions

Easy
  1. 1Find 3/4 ÷ 1/4.
  2. 2Find 5/6 ÷ 5/12.
  3. 3Find 1/2 ÷ 1/8.
Medium
  1. 4Find 2/3 ÷ 4/9.
  2. 5Find 1 1/2 ÷ 3/4.
  3. 6A 3/4 m ribbon is cut into 1/8 m pieces. How many pieces?
Challenging
  1. 7Find 2 1/4 ÷ 3/8.
  2. 8Find 3 ÷ 1 1/2.
Show answers (try them yourself first)
  1. 13
  2. 22
  3. 34
  4. 43/2
  5. 52
  6. 66
  7. 76
  8. 82

Fraction word problems

From daily life

Sharing a cake, cutting cloth, filling tanks: real tasks mix "of", "how many" and "how much" with fractions.

Simple definition

Read the problem, decide the operation ("of" → ×, "how many pieces" → ÷, "total" → +, "left" → –), then compute. Follow the order: brackets, then × and ÷, then + and –.

3/4 m ÷ 1/8 m = 66 pieces

In the figure: A 3/4 m ribbon in 1/8 m pieces gives 6 pieces.

Rule 1: Fraction of the remainder — Find the part used, subtract, then take the next fraction of what is left.

  • Easy: Spend 1/4 of ₹80: ₹20; left ₹60.
  • Medium: Then 1/3 of the rest: ₹20; left ₹40.
  • Exam-type: Total spent = ₹40, which is 1/2 of ₹80.

Rule 2: Speed, time, distance — Distance = speed × time; time = distance ÷ speed.

  • Easy: 4 km/h for 3/4 hour → 3 km.
  • Medium: 6 km at 4 km/h → 6/4 = 1 1/2 hours.
  • Exam-type: 2 1/2 km in 1/2 hour → 5 km/h.

Rule 3: Order of operations — Brackets first, then × and ÷ left to right, then + and –.

  • Easy: 1/2 + 1/3 × 3/4 = 1/2 + 1/4 = 3/4.
  • Medium: (1/2 + 1/3) × 6 = 5/6 × 6 = 5.
  • Exam-type: 3/4 ÷ 3/8 – 1 = 2 – 1 = 1.
Remember

Write what each fraction stands for ("of the whole" or "of the remainder").

Common mistake

Taking the second fraction of the original amount instead of what is left.

Shortcut

Underline the amount each fraction applies to. Memory clue: "Of means times; how many means divide."

Spot the difference

WordsOperationExample
of×1/4 of 80
how many pieces÷3/4 ÷ 1/8
left–80 – 20

Practice questions

Easy
  1. 1Spend 1/4 of ₹80. How much is left?
  2. 2A boy walks at 4 km/h for 3/4 h. Distance?
  3. 3Find 1/2 + 1/3 × 3/4.
Medium
  1. 4How long to walk 6 km at 4 km/h?
  2. 5Find (1/2 + 1/3) × 6.
  3. 6A tank is 2/3 full. 1/4 of the water is used. What part of the tank is full now?
Challenging
  1. 7Of ₹80, 1/4 is spent, then 1/3 of the rest. How much is left?
  2. 8Find 3/4 ÷ 3/8 – 1.
Show answers (try them yourself first)
  1. 1₹60
  2. 23 km
  3. 33/4
  4. 41 1/2 h
  5. 55
  6. 61/2
  7. 7₹40
  8. 81