Year 7AC9M7N06

Adding and Subtracting Decimals

Use the 4 operations with positive rational numbers including fractions, decimals and percentages to solve problems using efficient calculation strategies.

One rule carries this whole topic: line up the decimal points. Get that right and it becomes ordinary column addition.

Builds onYr 7 · Decimal Place Value and Ordering

Method

Line up the points, not the last digits

Right-aligning the digits is the classic error. Align the decimal points instead.

Fill the gaps with zeros

3{,}4 \ \rightarrow\ 3{,}400

Every column then has a digit to work with.

The point in the answer sits under the others

It never moves when adding or subtracting.

Estimate first

Round each number to the nearest whole and add. Your answer should be close.

Worked example

e.g.

12{,}5 + 3{,}47

Estimate before you start. $13 + 3 = 16 \quad \text{so expect about } 16$
Write the numbers with their decimal points lined up. $\begin{array}{r} 12{,}5\phantom{0} \\ +\ 3{,}47 \end{array}$
Add a zero so both have the same number of places. $\begin{array}{r} 12{,}50 \\ +\ 3{,}47 \end{array}$
Add each column from the right, carrying as usual. $0+7 = 7 \quad 5+4 = 9 \quad 2+3 = 5 \quad 1$
Bring the decimal point straight down. $12{,}50 + 3{,}47 = 15{,}97$
Check against your estimate. $15{,}97 \approx 16 \quad\checkmark$

Practice

Estimate first, then line up the points.

4{,}6 + 2{,}75

Answer

7{,}35

9{,}3 - 1{,}84

Answer

7{,}46

0{,}75 + 0{,}8

Answer

1{,}55

15 - 3{,}62

Answer

11{,}38

\text{A book costs } 12{,}99 \text{ and a pen } 3{,}50. \text{ Find the total.}

Answer

16{,}49

\text{Why does } 3{,}4 + 0{,}25 = 3{,}29 \text{ show the digits were aligned wrongly?}

Answer

\text{The 4 was added to the 2. Aligning the points gives } 3{,}65.