Working with Fractions – Class 7 Mathematics notes, important questions and MCQs

Chapter overview

Fractions are multiplied and divided using simple rules. "Of" means multiply, and dividing by a fraction means multiplying by its reciprocal.

Multiplication

• a/b × c/d = (a × c)/(b × d); simplify before multiplying when possible.
• "of" means ×: 2/3 of 12 = 8.
• A proper fraction times a number gives less than the number.

Division

• Reciprocal of a/b is b/a.
• a/b ÷ c/d = a/b × d/c.
• Mixed numbers: convert to improper fractions first (2½ = 5/2).

Key terms

Reciprocal

the number which multiplied by the given number gives 1

Improper fraction

numerator greater than or equal to denominator

Mixed fraction

a whole number and a proper fraction together, e.g. 2¾

Formulas

• a/b ÷ c/d = ad/bc
• Reciprocal of a/b = b/a

Important questions with answers

Quick revision

• "Of" = multiply.
• Divide = multiply by reciprocal.
• Convert mixed numbers first.

Exam tips

• Cancel common factors across numerator and denominator first.
• Dividing by a fraction less than 1 gives a bigger answer.

Practice MCQs

1. 1/2 × 3/5 equals

   1. 4/7
   2. 3/10
   3. 3/7
   4. 5/6
   Show answer

   Answer: (b) 3/10. (1 × 3)/(2 × 5).

2. The reciprocal of 4/7 is

   1. 7/4
   2. 4/7
   3. −4/7
   4. 1
   Show answer

   Answer: (a) 7/4. Flip it.

3. 3/4 of 36 is

   1. 12
   2. 9
   3. 27
   4. 48
   Show answer

   Answer: (c) 27. 36 ÷ 4 × 3.

4. 2/3 ÷ 4/9 equals

   1. 8/27
   2. 3/2
   3. 2/3
   4. 1
   Show answer

   Answer: (b) 3/2. 2/3 × 9/4 = 18/12 = 3/2.

5. 2/3 × 3/4 equals

   1. 6/7
   2. 1/2
   3. 5/7
   4. 8/9
   Show answer

   Answer: (b) 1/2. 6/12.

6. 2½ × 1⅓ equals

   1. 3
   2. 2⅔
   3. 3⅓
   4. 3½
   Show answer

   Answer: (c) 3⅓. 5/2 × 4/3 = 20/6 = 10/3.

7. How many 3/4-litre bottles can be filled from 9 litres?

   1. 9
   2. 6
   3. 27/4
   4. 12
   Show answer

   Answer: (d) 12. 9 ÷ 3/4 = 12.

8. How many 3/4-litre bottles can be filled from 9 litres

   1. 12
   2. 6
   3. 27/4
   4. 9
   Show answer

   Answer: (a) 12. 9 ÷ 3/4 = 12.