Add & subtract decimals - Different decimal places
Theory
When decimals have different numbers of places, line up the decimal points and fill the gaps with zeros so every number has the same number of places. Then add or subtract as usual. This Year 6 maths page shows how, including taking a decimal away from a whole number.
Adding zeros at the end of a decimal does not change its value: \(3.6 = 3.60\) and \(6 = 6.00\).
Before adding or subtracting, write each number with the same number of decimal places: \(7.3 - 2.48\) becomes \(7.30 - 2.48\).
A whole number has its decimal point after the ones digit: \(6 = 6.00\).
Lining up the last digits instead of the points puts tenths under hundredths and gives wrong answers.
Zeros that do not change the value:
Different numbers of places
- Line up the decimal points.
- Fill empty places with zeros.
- Add or subtract from the right, carrying or trading.
- Check with an estimate.
| \(3.60 + 1.25\) | \(=\) | \(4.85\) |
\(4.85\).
| \(7.30 - 2.48\) | \(=\) | \(4.82\) |
\(4.82\).
| \(6.00 - 2.35\) | \(=\) | \(3.65\) |
\(3.65\).
| \(0.700 + 0.135\) | \(=\) | \(0.835\) |
\(0.835\).
| \(12.400 - 5.875\) | \(=\) | \(6.525\) |
\(6.525\).
(i) How much is in the jug after adding?
(ii) How much is left at the end?
| \(2.50 + 0.65\) | \(=\) | \(3.15\) |
| \(3.15 - 1.40\) | \(=\) | \(1.75\) |
(i) \(3.15\) L
(ii) \(1.75\) L
(i) What is the total?
(ii) What is the change from \(\$10\)?
| \(4.50 + 2.35\) | \(=\) | \(6.85\) |
| \(10.00 - 6.85\) | \(=\) | \(3.15\) |
(i) \(\$6.85\)
(ii) \(\$3.15\)
He put tenths under hundredths. Line up the points: \(3.60 + 1.25 = 4.85\).
Common pitfalls
Frequently asked questions
Why can I add zeros to a decimal?
Zeros at the end of a decimal do not change its value: \(3.6 = 3.60\).
How do I subtract a decimal from a whole number?
Write the whole number with zeros: \(6 - 2.35 = 6.00 - 2.35 = 3.65\).
What must line up?
The decimal points.
What is 0.7 + 0.135?
\(0.835\).
How do I check?
Round each number and estimate.