Four operations with decimals | Year 7

01 / LEARN

The idea, step by step

Adding and subtracting place values

Write tenths below tenths and hundredths below hundredths. Trailing zeros are useful placeholders: 4.7 and 4.70 name the same amount. Regroup across the decimal point as you would regroup whole-number places.

An estimate gives a target size. If an amount near 8 has an amount near 4 removed, a result near 4 is reasonable. It is not enough to place a decimal point where it happens to look tidy.

Multiplication and division

For multiplication, first calculate with whole-number digits, then account for the decimal place values of both factors. For division, multiplying both numbers by the same power of ten can make the divisor a whole number.

Scale dividend and divisor together. Check the quotient by multiplying it by the divisor. Include the practical unit in an answer, and use two decimal places when displaying an ordinary money amount.

A common trap

When adding decimals, line up their last digits.

Instead: Line up decimal points so the same place values are combined. Write 0.8 as 0.80 before adding it to 0.35.

02 / WORKED EXAMPLES

See the thinking

Example 1

Subtract with regrouping

Calculate $8.2 - 3.76$ .

Write 8.20 and 3.76 in aligned columns.
Regroup and subtract to obtain 4.44.
Check: 3.76 + 4.44 = 8.20.

4.44

Example 2

Make the divisor whole

Calculate $4.68 \div 0.6$ .

Multiply both numbers by 10 to obtain 46.8 divided by 6.
46.8 divided by 6 is 7.8.
Check: 7.8 times 0.6 equals 4.68.

7.8

Check your understanding

Calculate $0.24 \times 3$ .

Show answer

0.72

Three groups of 24 hundredths make 72 hundredths.

03 / WORKSHEET

Your turn

6 questions · 14 marks · Work at your own pace.

Worksheet PDF 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 is 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 divided by 9.
7
$1.75 \times 4 + 2.6$
3 marks
Multiply first: 1.75 times 4 is 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 ↗

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