Topic 5 of 9
Step 7: Fraction and decimal arithmetic
Adding, subtracting, multiplying, and dividing decimals
Step 7 · Fraction and decimal arithmetic topics
Add and subtract decimals by lining up the points, multiply them by counting decimal places, and divide a decimal by a whole number or by another decimal.
Adding and subtracting decimals
Line up the decimal points, so tenths sit under tenths and hundredths under hundredths. Fill any gaps with zeros, then add or subtract as with whole numbers.
Example: Adding
What is 4.75 + 2.6?
- Write 2.6 as 2.60.
- Hundredths: 5 + 0 = 5. Tenths: 7 + 6 = 13, write 3 and carry 1. Ones: 4 + 2 + 1 = 7.
Answer7.35
Example: Subtracting
What is 10 − 3.45?
- Write 10 as 10.00.
- 10.00 − 3.45 = 6.55.
Answer6.55
Multiplying decimals
Multiply as if there were no decimal points, then put the point back: the answer has as many decimal places as the two numbers have together.
Example: Multiplying
What is 2.4 × 0.3?
- 24 × 3 = 72.
- 2.4 has 1 decimal place and 0.3 has 1: 2 in all.
- 72 becomes 0.72.
Answer0.72
Multiplying by a decimal less than 1 gives a smaller answer, just as with fractions: 0.5 × 8 = 4.
Dividing decimals
To divide a decimal by a whole number, divide as usual and keep the point in the same place: 7.2 ÷ 3 = 2.4.
To divide by a decimal, multiply both numbers by 10 or 100 until you are dividing by a whole number. The answer does not change.
Example: Dividing by a decimal
What is 4.8 ÷ 0.6?
- Multiply both by 10: 48 ÷ 6.
- 48 ÷ 6 = 8.
Answer8
Example: Sharing money
Three friends share a bill of $25.50 equally. How much does each pay?
- 25.50 ÷ 3.
- 25 ÷ 3 = 8 remainder 1.
- Trade the 1 for 10 tenths: 10 + 5 = 15 tenths, and 15 ÷ 3 = 5 tenths.
Answer$8.50
Try it yourself
Work each one on paper first, then open the answer to check.
What is 3.5 + 1.28?
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4.78.
What is 6.2 − 2.75?
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3.45.
What is 1.5 × 4?
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6.
What is 0.4 × 0.7?
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0.28.
What is 9.6 ÷ 0.3?
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32. Multiply both by 10: 96 ÷ 3 = 32.