Multiplying & dividing fractions & decimals
Multiplying decimals by whole numbers
Take the decimal point out of the way, do an ordinary multiplication, then put it back. The estimate tells you where it belongs.
Estimate first
Round the decimal to the whole numbers either side and multiply both. For 12.9 × 6: 10 × 6 = 60 and 20 × 6 = 120. So the answer must be between 60 and 120. Now you know roughly where the decimal point goes before you even start.
Take the point out, then put it back
12.9 × 6 Multiply by 10 to remove the point: 129 × 6 = 774. Now divide by 10 to put it back: 774 ÷ 10 = 77.4 And 77.4 sits between 60 and 120, as the estimate predicted. Whatever you do to get rid of the point, undo at the end.
Counting the decimal places
There is a shortcut: the answer has the same number of decimal places as the question. 12.9 has ONE decimal place, so the answer has one: 77.4 0.5 × 90: 5 × 90 = 450, and one decimal place gives 45.0, which is 45. Count the digits after the point in the question and make sure the same number appears in your answer.
Counting in decimal steps
Counting up in decimals is repeated addition, and the same pattern appears. 0.3, 0.6, 0.9, 1.2, 1.5, … Each step adds 0.3. Notice how it carries past 0.9 into 1.2 — three tenths added to nine tenths makes twelve tenths, which is one whole and two tenths.
Worked examples
12.9 × 6
- Estimate: between 10 × 6 = 60 and 20 × 6 = 120.
- Remove the point: 129 × 6 = 774.
- Put it back: 774 ÷ 10 = 77.4.
Answer: 12.9 × 6 = 77.4
0.5 × 90
- 0.5 is a half, so this is half of 90.
- Or: 5 × 90 = 450, then one decimal place gives 45.0.
Answer: 0.5 × 90 = 45
3.4 × 5
- Estimate: 3 × 5 = 15 and 4 × 5 = 20, so between 15 and 20.
- 34 × 5 = 170.
- One decimal place: 17.0.
Answer: 3.4 × 5 = 17
Counting in steps of 0.3
- Start at 0.3 and keep adding 0.3.
- 0.3, 0.6, 0.9 — then 9 tenths plus 3 tenths is 12 tenths.
Answer: 0.3, 0.6, 0.9, 1.2, 1.5
Checking with the estimate
- 7.2 × 4: estimate between 7 × 4 = 28 and 8 × 4 = 32.
- 72 × 4 = 288, so 28.8.
- 28.8 sits inside the estimate.
Answer: 7.2 × 4 = 28.8
Where you see this in real life
- Buying 6 items at $12.90 each.
- Working out the total length of 5 planks each 3.4 m long.
- Finding the cost of 4 kg of something priced at $7.20 per kg.
Key words
- Decimal
- A number written with a decimal point.
- Decimal place
- A digit position after the decimal point.
- Estimate
- A rough answer used to check your working.
- Product
- The result of multiplying.
- Tenth
- The first place after the decimal point.
- Whole number
- A number with no fractional part.