Addition and subtraction (2)
Adding and subtracting decimals
In this section we add and subtract numbers with up to 3 decimal places, even when they have different numbers of decimal places. The secret is to line up the decimal points and use trailing zeros — and to estimate first.
Estimate first
Before you calculate, round the numbers to whole numbers to estimate the answer. For example, 4.49 + 3.09 is about 4 + 3 = 7. The estimate helps you check your final answer is sensible.
Decompose decimals by place value
Every digit after the decimal point has a value — tenths, hundredths and thousandths. For example, 6.075 = 6 + 0.07 + 0.005.
Line up the decimal points
Write the numbers with their decimal points underneath each other. Fill any empty places with trailing zeros so every number has the same number of decimal places, such as writing 14.8 as 14.800.
Adding decimals
Once the decimal points are lined up, add each column from the right. When a column reaches 10, carry into the next column on the left.
Subtracting decimals
Line up the decimal points and use trailing zeros. Then subtract each column, regrouping (borrowing) from the next column when you need to.
Worked examples
Estimating first
- Round 4.49 to 4 and 3.09 to 3.
- Add the rounded numbers: 4 + 3 = 7.
- Then 10 − 7 = 3.
Answer: The change will be close to $3.
Adding decimals with different decimal places
- Write 14.8 as 14.800 so both numbers have 3 decimal places.
- Line up the decimal points.
- Add each column: 14.800 + 5.678.
Answer: 14.8 + 5.678 = 20.478
Subtracting decimals
- Write 56.1 as 56.10 so both numbers have 2 decimal places.
- Line up the decimal points.
- Subtract each column, regrouping where needed: 56.10 − 26.64.
Answer: 56.1 − 26.64 = 29.46
Finding change (add then subtract)
- Add the two prices: 4.49 + 3.09 = 7.58.
- Write 10 as 10.00.
- Subtract: 10.00 − 7.58.
Answer: Jyoti gets $2.42 change.
Decomposing a decimal
- Look at each place value in 6.075.
- It has 6 ones, 0 tenths, 7 hundredths and 5 thousandths.
Answer: 6.075 = 6 + 0.07 + 0.005
Avoiding a common mistake
- To add 0.7 + 0.41, line up the place values.
- Write 0.7 as 0.70 so both have 2 decimal places.
- Add: 0.70 + 0.41.
Answer: 0.7 + 0.41 = 1.11 (not 0.48)
Where you see this in real life
- Working out change when shopping.
- Adding the weights of two suitcases and checking a luggage limit.
- Measuring and comparing heights in metres.
- Working out how much more money is needed to reach a fundraising target.
Key words
- Decimal place
- A position after the decimal point: tenths, hundredths or thousandths.
- Sum
- The result of adding numbers together.
- Difference
- The result of subtracting one number from another.
- Decompose
- To break a number into the value of each digit.
- Regroup
- To carry or borrow between columns when adding or subtracting.
- Trailing zero
- A zero added to the end of a decimal to fill an empty place, such as writing 14.8 as 14.800.
- Estimate
- A sensible rough answer, often found by rounding to whole numbers.