Multiplication and division (2)
Dividing decimals
Here you learn to estimate and then divide a number with 1 or 2 decimal places by a 1-digit or a 2-digit whole number. Keep the decimal point lined up and always estimate before you calculate.
Estimate first
Round the numbers to friendly values to make a rough answer before you divide. This tells you how big the answer should be. Example: for 55.2 ÷ 24, round to 50 ÷ 25 = 2, so the answer will be a little more than 2.
Dividing by a 1-digit number
Divide each part in turn, keeping the decimal point in the answer directly above the decimal point in the number. Example: 37.2 ÷ 4. 37 ÷ 4 = 9 with 1 left over, then the remaining 1.2 ÷ 4 = 0.3, giving 9.3.
Dividing by a 2-digit number
Use short or long division. Take away multiples of the divisor and record the answer place by place. Example: 55.2 ÷ 24. There are two 24s in 55.2 (24 × 2 = 48), leaving 7.2. Then 7.2 ÷ 24 = 0.3, so 55.2 ÷ 24 = 2.3.
Sharing money and measures
Dividing decimals is useful for sharing amounts of money equally or for finding the length of one part. Example: a regular pentagon with perimeter 26.25 m has 5 equal sides, so each side is 26.25 ÷ 5 = 5.25 m.
Worked examples
Estimate before dividing
- You want 55.2 ÷ 24.
- Round 55.2 to 50 and 24 to 25.
- Divide the rounded numbers: 50 ÷ 25.
Answer: Estimate: 50 ÷ 25 = 2, so the answer is a little more than 2.
Divide a decimal by a 1-digit number
- Calculate 37.2 ÷ 4.
- Divide the whole part: 37 ÷ 4 = 9 with 1 left over.
- Carry the 1 to make 1.2, then 1.2 ÷ 4 = 0.3.
- Keep the decimal point lined up.
Answer: 37.2 ÷ 4 = 9.3
Divide a decimal by a 2-digit number
- Calculate 55.2 ÷ 24.
- There are two 24s in 55.2 (24 × 2 = 48). Subtract 48 from 55.2 to leave 7.2.
- 7.2 ÷ 24 = 0.3, because 72 ÷ 24 = 3. Write 3 in the tenths place.
- Check the answer is close to the estimate of 2.
Answer: 55.2 ÷ 24 = 2.3
Sharing money equally
- Three friends share $29.52 equally.
- Divide the amount by 3: 29.52 ÷ 3.
- 29 ÷ 3 = 9 with 2 left over; then 2.52 ÷ 3 = 0.84.
Answer: 29.52 ÷ 3 = $9.84 each
Where you see this in real life
- Sharing a food bill equally between friends.
- Finding the price of one orange or one pot of paint from a multi-pack price.
- Working out the length of one side of a shape from its perimeter.
- Comparing two packs to see which is the better deal.
Key words
- Dividend
- The number being divided, such as 55.2 in 55.2 ÷ 24.
- Divisor
- The number you divide by, such as 24 in 55.2 ÷ 24.
- Quotient
- The answer to a division.
- Decimal point
- The dot that separates the whole part from the fraction part of a number.
- Estimate
- A rough answer found by rounding, used to check the real answer.