Addition and subtraction of decimals | Year 6

01 / LEARN

The idea, step by step

Match the units first

A decimal point separates whole units from parts of one unit. When adding or subtracting, place ones under ones, tenths under tenths and hundredths under hundredths. Align the decimal points rather than the final digits.

You may add trailing zeros without changing a value: 4.6 and 4.600 describe the same amount. These zeros can make a written calculation easier to organise.

Aligned place values for 12.8 + 5.67
Tens	Ones	Tenths	Hundredths
1	2	8	0
0	5	6	7

Regroup and check

Ten hundredths make one tenth, and ten tenths make one whole. Regroup in the same way as with whole numbers, keeping each digit in its place-value column. Write the decimal point in the answer beneath the others.

Before calculating, make a rough estimate. For 12.8+5.67, a result near 19 is sensible. A result such as 6.947 or 184.7 signals a place-value error. Keep the original units with a measurement answer.

A common trap

Writing the last digits beneath one another even when the numbers have different decimal lengths.

Instead: Align decimal points so equal place values match. For example, 2.4 is 2.40, not 0.24.

02 / WORKED EXAMPLES

See the thinking

Example 1

Worked example 1

Calculate $5.67 + 12.8$ .

Write 12.8 as 12.80 and align the decimal points.
Hundredths: 7+0=7. Tenths: 6+8=14, so write 4 tenths and regroup 1 whole.
Whole parts: 5+12+1=18. The sum is 18.47.

18.47.

Example 2

Worked example 2

Calculate $20.05 - 7.86$ .

Write 20.05 as 20 ones and 5 hundredths. Regroup across the zero tenths so the small columns can be subtracted.
Equivalently, take away 7.80 to get 12.25, then take away the remaining 0.06.
12.25−0.06=12.19. Adding 7.86 back gives 20.05.

12.19.

Check your understanding

Calculate $4.5 + 0.37$ .

Show answer

4.87.

Write 4.5 as 4.50, then add 0.37.

03 / WORKSHEET

Your turn

6 questions · 12 marks · Work at your own pace.

Worksheet PDF Worked solutions

Read the questions online

Calculate $8.4 + 2.67$ .
2 marks
Calculate $15.03 - 6.8$ .
2 marks
Calculate $3.075 + 0.96$ .
2 marks
Calculate $10 - 2.478$ .
2 marks
A rope is made by joining lengths of 2.85 m and 1.975 m, with no overlap. Find the total length.
2 marks
Harper says $6.4 + 0.28 = 0.92$ . Explain the error and give the correct answer.
2 marks

Read the worked solutions

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

Calculate $8.4 + 2.67$ .
2 marks
8.40+2.67=11.07.
11.07.
Calculate $15.03 - 6.8$ .
2 marks
15.03−6.80=8.23.
8.23.
Calculate $3.075 + 0.96$ .
2 marks
Align thousandths: 3.075+0.960=4.035.
4.035.
Calculate $10 - 2.478$ .
2 marks
10.000−2.478=7.522.
7.522.
A rope is made by joining lengths of 2.85 m and 1.975 m, with no overlap. Find the total length.
2 marks
2.850+1.975=4.825.
4.825 m.
Harper says $6.4 + 0.28 = 0.92$ . Explain the error and give the correct answer.
2 marks
Harper treated 6.4 as 0.64. The answer must be greater than 6.4.
6.4 means 6.40, so the correct sum is 6.68.

Checking saved progress…

Continue learning

Multiplication/division by multiples of powers of ten

Next lesson

Curriculum reference & lesson scope

Australian Curriculum v9 and SA Curriculum Mathematics

Addition/subtraction; multiplication/division by multiples of powers of ten; estimation.

Official curriculum source ↗

Back to Decimals