Addition and subtraction
Adding & subtracting decimals
Line up the decimal points, not the ends of the numbers. Almost every mistake in this topic comes from getting that one thing wrong.
Line up the points
Write the calculation in columns with the decimal points directly underneath each other. The point in the answer goes underneath them too. 3.4 + 1.8 āāā 5.2 If you line up the ENDS of the numbers instead, the digits land in the wrong columns and the answer will be wrong.
Fill the gaps with zeros
When one number has fewer decimal places, add a zero to hold the column. 7.25 + 15.50 is easier to see written as: 7.25 + 15.50 āāāāā 22.75 The zero changes nothing about the value ā it just means every column has a digit to add.
Subtracting works the same way
6.5 ā 2.7 āāā 3.8 Points lined up, and exchange from the next column when you need to. Here 5 ā 7 will not go, so exchange one whole from the 6, making 15 tenths ā 7 tenths = 8 tenths. A common error is to subtract the smaller digit from the bigger one in each column regardless of which is on top. That gives 4.2 instead of 3.8.
Check your answer is sensible
Round both numbers and add them in your head first. For 3.4 + 1.8, think 3 + 2 = 5. So the answer should be near 5 ā and 5.2 is. If you had got 4.2 or 12.2 you would know something was wrong. This takes two seconds and catches most slips.
Worked examples
3.4 + 1.8
- Line up the decimal points.
- 4 tenths + 8 tenths = 12 tenths, which is 1 whole and 2 tenths.
- Carry the 1: 3 + 1 + 1 = 5.
Answer: 3.4 + 1.8 = 5.2
6.5 ā 2.7
- Line up the points.
- 5 tenths ā 7 tenths will not go, so exchange one whole into 10 tenths.
- 15 ā 7 = 8 tenths, then 5 ā 2 = 3.
Answer: 6.5 ā 2.7 = 3.8
Fatima's money
- She has $7.25 and is given $15.50.
- Write them in columns with the points lined up.
- 7.25 + 15.50.
Answer: She has $22.75
Taking $2.25 off a $6.65 book
- Line up the points: 6.65 ā 2.25.
- Subtract each column: 5 ā 5 = 0, 6 ā 2 = 4, 6 ā 2 = 4.
Answer: The sale price is $4.40
Spotting Alana's mistake
- Alana wrote 3.4 + 1.8 = 4.2.
- Estimate first: 3 + 2 = 5, so the answer should be near 5.
- She forgot to carry the extra whole from 12 tenths.
Answer: The correct answer is 5.2
Where you see this in real life
- Adding up prices at a till ā every total is a decimal addition.
- Working out change from $20 means writing it as 20.00 before subtracting.
- Adding two distances in kilometres, such as 3.4 km and 1.8 km.
Key words
- Decimal point
- The dot separating whole numbers from parts of a number.
- Column method
- Writing digits in place-value columns to calculate.
- Place holder
- A zero written to fill an empty column.
- Exchange
- Swapping one whole for ten tenths when subtracting.
- Tenth
- The first place after the decimal point.
- Estimate
- A rough answer used to check your working.