YEAR 7 · FRACTIONS AND DECIMALS · 15 MIN

Four operations with decimals

Calculate with positive decimals using place value, equivalent calculations and sensible checks.

In this lesson

Use all four decimal operations
Check a decimal answer using an estimate or inverse operation

Before you start

Decimal place value
Whole-number operations

01 / LEARN

Understand the idea.

Adding and subtracting place values

For addition or subtraction, align place values: ones with ones, tenths with tenths and hundredths with hundredths. Adding trailing zeros gives useful placeholders without changing a value, so $8.2$ can be written as $8.20$ .

Regroup between adjacent places when needed: one tenth is ten hundredths, and one whole is ten tenths. Estimate the difference first, then check by adding the result back to the amount subtracted.

Multiplication and division

For multiplication, account for the place value of both factors. For example, 24 hundredths multiplied by three gives 72 hundredths. Whole-number multiplication supplies the digits, but the original factors determine their scale.

For division, multiply both numbers by the same power of ten to make the divisor whole. The quotient stays the same because the size of each group and the total scale equally. Check by multiplying the quotient by the original divisor.

02 / WORKED EXAMPLES

See the method in action.

EXAMPLE 01

Subtract with regrouping

Calculate $8.2 - 3.76$ .

Worked solution

1
Write both amounts as hundredths.
$8.2 = 8.20, 3.76 = \frac{376}{100}$
The same-sized hundredth units can be subtracted directly.
2
Subtract the counts of hundredths.
$\begin{aligned} 8.20 - 3.76 & = \frac{820 - 376}{100} \\ = \frac{444}{100} = 4.44 \end{aligned}$
Regrouping in the whole-number subtraction preserves the hundredth unit.
3
Check with addition.
$3.76 + 4.44 = 8.20$
The amount removed plus the difference recovers the original value.

Answer

4.44

EXAMPLE 02

Make the divisor whole

Calculate $4.68 \div 0.6$ .

Worked solution

1
Scale both numbers by ten.
$4.68 \div 0.6 = 46.8 \div 6$
Multiplying the dividend and divisor equally leaves the quotient unchanged.
2
Divide by the whole-number divisor.
$\begin{aligned} 46.8 \div 6 & = (42 + 4.8) \div 6 \\ = 7 + 0.8 = 7.8 \end{aligned}$
Both parts divide exactly by 6, so their quotients add.
3
Check with the original divisor.
$7.8 \times 0.6 = 4.68$
Multiplication reverses the division and confirms the decimal scale.

Answer

7.8

03 / YOUR TURN

Try it yourself.

Check your understanding

Calculate $0.24 \times 3$ .

Show answer & reasoning

0.72

The number $0.24$ represents 24 hundredths. Three lots contain 72 hundredths, so $0.24 \times 3 = 0.72$ .

Keep practising

6 worksheet questions · 14 marks

Open worksheet Worked solutions

Read the questions online

$3.45 + 0.8$
2 marks
$12 - 4.65$
2 marks
$2.4 \times 0.35$
2 marks
$6.3 \div 0.9$
2 marks
$1.75 \times 4 + 2.6$
3 marks
Five notebooks cost 2.35 dollars each. Find the change from 20 dollars.
3 marks

Read the worked solutions

Equivalent correct methods earn the corresponding marks. Include units where asked.

$3.45 + 0.8$
2 marks
Write 0.8 as 0.80; $3.45 + 0.80 = 4.25$ .
4.25
$12 - 4.65$
2 marks
Write 12 as 12.00 and subtract 4.65.
7.35
$2.4 \times 0.35$
2 marks
$24 \times 35 = 840$ . Account for three decimal places to get 0.840.
0.84
$6.3 \div 0.9$
2 marks
Scale both by 10 to obtain $63 \div 9$ .
7
$1.75 \times 4 + 2.6$
3 marks
Multiply first: $1.75 \times 4 = 7$ . Then add 2.6.
9.6
Five notebooks cost 2.35 dollars each. Find the change from 20 dollars.
3 marks
The cost is $5 \times 2.35 = 11.75$ dollars.
20.00 minus 11.75 is 8.25 dollars.
8.25 dollars

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Curriculum reference & lesson scope

Australian Curriculum v9 / SA Curriculum Mathematics

Equivalent fractions and mixed numbers; ordering rational numbers on number lines; adding/subtracting fractions; multiplying/dividing fractions; four operations with decimals; converting between fractions and decimals; multi-step problems and checking estimates.

Official curriculum source ↗

In this lesson

Understand the idea.

Adding and subtracting place values

Multiplication and division

See the method in action.

Subtract with regrouping

Write both amounts as hundredths.

Subtract the counts of hundredths.

Check with addition.

Make the divisor whole

Scale both numbers by ten.

Divide by the whole-number divisor.

Check with the original divisor.

Try it yourself.

Check your understanding

Keep practising