Year 7AC9M7N06

Multiplying and Dividing Decimals

Use the 4 operations with positive rational numbers including fractions, decimals and percentages to solve problems using efficient calculation strategies.

For multiplying, ignore the decimal points until the very end. For dividing, get rid of the point in the divisor first. Two different tricks, and mixing them up is the usual problem.

Builds onYr 7 · Adding and Subtracting Decimals

Method

Multiplying: count the places, then place the point

Total decimal places in the question equals decimal places in the answer.

Do not line up points when multiplying

That rule belongs to addition only. Multiplying ignores the points until the end.

Dividing: make the divisor a whole number

\frac{a}{0{,}4} = \frac{a \times 10}{4}

Move the point in both numbers the same number of places.

Multiplying by a number under 1 makes it smaller

6 \times 0{,}5 = 3

The same surprise as with fractions.

Worked example

e.g.

1{,}2 \times 0{,}03 \quad \text{and} \quad 7{,}2 \div 0{,}4

To multiply, first ignore the decimal points completely. $12 \times 3 = 36$
Count the decimal places in the question. $1{,}2 \ \text{has } 1 \quad 0{,}03 \ \text{has } 2 \quad \text{total } 3$
Put that many decimal places into the answer. $1{,}2 \times 0{,}03 = 0{,}036$
Now to divide. Move the point in the divisor to make it whole. $0{,}4 \ \rightarrow\ 4 \quad \text{(one place right)}$
Move the point in the other number the same way. $7{,}2 \ \rightarrow\ 72$
Divide as normal. $72 \div 4 = 18$
Check it makes sense. Dividing by less than 1 gives a bigger answer. $18 > 7{,}2 \quad\checkmark$

Practice

Count places for multiplying. Shift the point for dividing.

0{,}6 \times 0{,}4

Answer

0{,}24

2{,}5 \times 1{,}2

Answer

3{,}0

0{,}07 \times 0{,}3

Answer

0{,}021

4{,}8 \div 0{,}6

Answer

48 \div 6 = 8

0{,}96 \div 0{,}04

Answer

96 \div 4 = 24

\text{Why is } 8 \div 0{,}5 = 16 \text{ and not } 4?

Answer

\text{You are asking how many halves fit into 8. Sixteen do.}