Multiplication, multiples & factors
Multiplication
In this section you multiply whole numbers by a 1-digit number. You group numbers in different ways, estimate first, and use methods like the grid method.
Multiply in any order
The associative law lets you group and multiply numbers in any order. A bar of chocolate could be 6 lots of 4 or 4 lots of 6 — either way it is 24 pieces, because 4 × 6 = 24 and 6 × 4 = 24. For 16 × 2 × 5, doing 2 × 5 = 10 first makes it easy: 16 × 10 = 160.
Using factors to multiply
You can split a number into factors to make multiplying easier. To work out 18 × 5, use 18 = 9 × 2. Then 18 × 5 = 9 × 2 × 5 = 9 × 10 = 90, because multiplying by 10 is simple.
Estimate first
Always estimate the size of the answer before you calculate, so you can check your answer is about right. For 27 × 4, round 27 to 30: 30 × 4 = 120, so the answer will be a little less than 120.
The grid method
Partition the number into tens and ones, then multiply each part. For 27 × 4, split 27 into 20 and 7: 20 × 4 = 80 and 7 × 4 = 28. Add the parts: 80 + 28 = 108.
Multiplying larger numbers
The grid method also works for 3-digit numbers. For 174 × 4, split 174 into 100, 70 and 4: 100 × 4 = 400, 70 × 4 = 280, 4 × 4 = 16. Add them: 400 + 280 + 16 = 696.
Worked examples
Multiplying in any order
- Look at 16 × 2 × 5.
- Multiply 2 × 5 = 10 first.
- Then 16 × 10 = 160.
Answer: 16 × 2 × 5 = 160
Using factors: 18 × 5
- Split 18 into factors: 18 = 9 × 2.
- So 18 × 5 = 9 × 2 × 5.
- Do 2 × 5 = 10, then 9 × 10 = 90.
Answer: 18 × 5 = 90
Estimating 27 × 4
- Round 27 to the nearest ten: 30.
- Multiply 30 × 4 = 120.
- So the answer is a little less than 120.
Answer: 27 × 4 is about 120 (the exact answer is 108).
The grid method for 27 × 4
- Partition 27 into 20 and 7.
- Multiply: 20 × 4 = 80 and 7 × 4 = 28.
- Add the parts: 80 + 28 = 108.
Answer: 27 × 4 = 108
The grid method for 174 × 4
- Partition 174 into 100, 70 and 4.
- Multiply: 100 × 4 = 400, 70 × 4 = 280, 4 × 4 = 16.
- Add the parts: 400 + 280 + 16 = 696.
Answer: 174 × 4 = 696
Where you see this in real life
- Working out the cost of 4 packs of pencils at 95 cents each.
- Sharing a chocolate bar that is 6 lots of 4 pieces.
- Counting cans stacked in equal rows on a shelf using an array.
Key words
- Product
- The answer when you multiply numbers together.
- Associative law
- You can group and multiply numbers in any order and get the same answer.
- Factor
- A number that divides into another number exactly.
- Partition
- To split a number into parts, such as 27 into 20 and 7.
- Grid method
- A way to multiply by partitioning a number, multiplying each part, then adding.
- Estimate
- A sensible guess of the size of an answer, often by rounding.