Multiplication and division
Multiplication
Estimate first, then calculate. The estimate is not extra work — it is what tells you whether your answer can possibly be right.
Always start with an estimate
Round each number to something easy, then multiply. For 56 × 27, estimate 60 × 30 = 1800. So the real answer should be near 1800. If your working gives 151 or 15 120, the estimate tells you instantly that something is wrong. It costs a few seconds and catches most mistakes.
The column method
Split the second number into tens and ones, multiply by each, then add. 56 × 27: 56 × 20 = 1120 56 × 7 = 392 1120 + 392 = 1512 Compare with the estimate of 1800 — close enough to be believable. You can do the two parts in either order; the answer is the same.
Multiplying by multiples of 10
Multiply the non-zero digits, then put the zeros back. 400 × 9: think 4 × 9 = 36, then add the two zeros → 3600. 60 × 8: think 6 × 8 = 48, then one zero → 480. 30 × 80: think 3 × 8 = 24, then two zeros → 2400. Count the zeros in the question and make sure the same number appears in the answer.
Different questions, same answer
Many different calculations give the same product. 30 × 80 = 2400 60 × 40 = 2400 120 × 20 = 2400 That is because 30 × 80 and 60 × 40 are the same numbers rearranged: doubling one and halving the other leaves the product unchanged. It is a useful trick for making a calculation easier.
Worked examples
56 × 27
- Estimate: 60 × 30 = 1800.
- 56 × 20 = 1120.
- 56 × 7 = 392.
- 1120 + 392 = 1512, which is close to the estimate.
Answer: 56 × 27 = 1512
400 × 9
- Multiply the non-zero digits: 4 × 9 = 36.
- The question has two zeros, so put two back.
Answer: 400 × 9 = 3600
The hummingbird
- It beats its wings about 75 times a second.
- There are 60 seconds in a minute.
- 75 × 60 = 4500.
Answer: About 4500 times a minute
The product of 31 and 76
- Estimate: 30 × 80 = 2400.
- 76 × 30 = 2280 and 76 × 1 = 76.
- 2280 + 76 = 2356.
Answer: 31 × 76 = 2356
Which give 2400?
- 30 × 80 = 2400.
- 60 × 40 = 2400.
- 120 × 20 = 2400.
- 30 × 60 = 1800 and 80 × 20 = 1600 do not.
Answer: 30 × 80, 60 × 40 and 120 × 20
Where you see this in real life
- Working out how many seats are in a hall with 27 rows of 56.
- Finding the cost of 24 items at $15 each.
- Calculating how far you travel at 75 km per hour for 6 hours.
Key words
- Product
- The result of multiplying numbers together.
- Estimate
- A rough answer used to check your working.
- Multiple
- The result of multiplying by a whole number.
- Column method
- Writing digits in place-value columns to calculate.
- Partition
- To split a number into easier parts.
- Digit
- One of the symbols 0–9.