Topic 9 of 12

Decimal operations

Step 8 · Ratios and negative numbers topics

Add, subtract, multiply and divide decimals accurately. Line up the decimal points to add and subtract, count places to multiply, and clear the decimal in the divisor to divide.

Adding and subtracting

Decimals add and subtract like whole numbers, as long as digits of the same place value are lined up. That means lining up the decimal points. Fill any gap with zeros so that both numbers have the same number of decimal places.

Example: Adding

Find $12.5 + 3.75$ .

Write $12.50$ so both numbers have two decimal places.
Line up the points and add: $12.50 + 3.75 = 16.25$ .

Answer16.25

Example: Subtracting

Find $8 - 2.46$ .

Write 8 as $8.00$ .
Line up the points and subtract: $8.00 - 2.46 = 5.54$ .

Answer5.54

Multiplying

To multiply decimals, ignore the points and multiply as whole numbers. Then put the point in so that the answer has as many decimal places as the two numbers have together.

Example: Multiplying

Find $0.6 \times 0.07$ .

Multiply $6 \times 7 = 42$ .
0.6 has 1 decimal place and 0.07 has 2, so the answer has 3 decimal places.
Write 42 with three places: 0.042.

Answer0.042

Example: A check by estimating

Find $2.4 \times 1.5$ .

Multiply $24 \times 15 = 360$ .
There are 1 + 1 = 2 decimal places, so the answer is 3.60, which is 3.6.
Check: 2.4 is a little under 2.5 and 1.5 is one and a half, so the answer should be a bit under 3.75. 3.6 fits.

Answer3.6

Dividing by a whole number

Divide as usual and keep the decimal point in the answer straight above the point in the number you are dividing.

Example: Dividing

Find $9.84 \div 4$ .

$9 \div 4 = 2$ remainder 1, so the first digit is 2, then the point.
$18 \div 4 = 4$ remainder 2, then $24 \div 4 = 6$ .
So $9.84 \div 4 = 2.46$ . Check: $4 \times 2.46 = 9.84$ .

Answer2.46

Dividing by a decimal

Dividing by a decimal is easier once the divisor is a whole number. Multiply both numbers by the same power of 10. This does not change the answer, because the quotient stays the same when both parts are scaled equally.

Example: Dividing by a decimal

Find $7.2 \div 0.06$ .

Multiply both numbers by 100 to make the divisor whole: $7.2 \times 100 = 720$ and $0.06 \times 100 = 6$ .
Now divide: $720 \div 6 = 120$ .

Answer120

Problems with money

Example: At the shop

Three notebooks cost $2.35 each, and a pen costs $1.80. How much is the total? How much change is there from $10?

Notebooks: $3 \times 2.35 = 7.05$ .
Total: $7.05 + 1.80 = 8.85$ .
Change: $10 - 8.85 = 1.15$ .

AnswerThe total is $8.85 and the change is $1.15.

Try it yourself

Work each one on paper first, then open the answer to check.

Find $4.8 + 0.76$ .
Show answer
5.56
Find $10 - 3.07$ .
Show answer
6.93
Find $0.5 \times 0.8$ .
Show answer
0.4, because $5 \times 8 = 40$ with two decimal places is 0.40.
Find $3.2 \times 0.15$ .
Show answer
0.48, because $32 \times 15 = 480$ with three decimal places is 0.480.
Find $6.3 \div 0.9$ .
Show answer
7, because multiplying both by 10 gives $63 \div 9 = 7$ .
A bottle holds 1.5 litres. How many 0.25-litre glasses can it fill?
Show answer
6, because $1.5 \div 0.25 = 150 \div 25 = 6$ .