Decimals - Multiplying and dividing by less than 1
Multiplying by a number between 0 and 1
The multiplication sign can be replaced by 'lots of'.
For example,
2 × 3 means 2 lots of 3
6 × 8 means 6 lots of 8
So, 1/2 × 10 means 1/2 of 10
And 1/3 × 12 means 1/3 of 12
When you multiply by a number greater than 1, you get an answer that is greater than the original number. But when you multiply by a number between 0 and 1, the answer is smaller than the original number.
In general:
m × 1/n = m ÷ n
Example
8 × 1/4 = 8 ÷ 4 = 2
20 × 1/5 = 20 ÷ 5 = 4
Dividing by a number between 0 and 1
Imagine that you had 10 bars of chocolate that you wanted to share amongst some children.
If you gave the children 2 bars each, you would have enough for 5 children.
10 ÷ 2 = 5
If you gave the children 1/2 bar each, you would have enough for 20 children.
10 ÷ 1/2 = 20
The pattern
Can you see what's happening?
10 ÷ 2 = 5
10 ÷ 1/2 = 20
When you divide by a whole number the answer is less than the original number. When you divide by 1/2 the answer (20) is greater than the original number (10).
It's the opposite of multiplying. When we divide by a number greater than 1, we get an answer that is less than the original number. But when we divide by a number between 0 and 1 the answer is larger than the original number.
So, 10 ÷ 1/2 = 20
Similarly, 10 ÷ 1/3 = 30 and 10 ÷ 1/4 = 40
In general:
m ÷ 1/n = mn
Questions
Q1. What is 10 ÷ 1/7 ?
Q2. Find the value of: 4 ÷ 1/3
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