Reciprocals and Division of Fractions

Reciprocals

The reciprocal of a number is the number that gives a product of 1 when multiplied
by the original number.

For a fraction:

ab
→ reciprocal →
ba

Examples

• Reciprocal of 4 =
  14
• Reciprocal of
  23
  =
  32
• Reciprocal of 1
  35
  =
  58

Division of Fractions

To divide by a fraction, multiply by its reciprocal.

Rule:

ab
÷
cd
=
ab
×
dc

Example 1.24

Evaluate:
89
÷
23

=
89
×
32
=
43
= 1
13

Example 1.25

Evaluate: 4 ÷
25

=
41
×
52
= 10

Example 1.26

Evaluate:
512
÷ 3

=
512
×
13
=
536

Example 1.27

Evaluate: 1
23
÷ 1
13

=
53
×
34
=
54
= 1
14

Flip or Not?

Question:

Flip the second fraction
Do NOT flip

Reciprocal Match

Click two cards to match a number with its reciprocal

Exercise

Question 1

(a)
23
÷
13

(b)
56
÷ 3

(c) 1
1112
÷ 4

(d) 2
45
÷ 1
25

(e) 6 ÷ 1
23

(f) 4 ÷ 2
45

Check Answer
Show Working
(a) 2/1 (b) 5/18 (c) 23/48 (d) 14/5 (e) 18/5 (f) 10/7
Each question is solved by multiplying by the reciprocal of the divisor.

Question 2

Musa drank orange juice from a 500 ml bottle.
If
25
was remaining, how much did he drink?

Check Answer
Show Working
Answer: 300 ml
Remaining = 2/5 of 500 = 200 ml
Drunk = 500 − 200 = 300 ml

Question 3

Out of a class of 150 learners,
13
opted for Mandarin,
25
for Italian.
How many opted for French?

Check Answer
Show Working
Answer: 40 learners
Mandarin: 1/3 × 150 = 50
Italian: 2/5 × 150 = 60
French = 150 − (50 + 60) = 40

Question 4

Fifty divided by half minus forty. What is the answer?

Check Answer
Show Working
Answer: 60
50 ÷ 1/2 = 100
100 − 40 = 60