Multiplication and division (1)
Multiplication
In Stage 6 we multiply whole numbers up to 10 000 by 1-digit or 2-digit numbers. Always make an estimate first, so you can check that your answer is reasonable. The answer to a multiplication is called the product.
Estimate first
Before you calculate, round the numbers to make an easy multiplication. This gives you a range your answer should be near. Example: for 1347 × 8, round 1347 to 1000 and to 1500. Then 1000 × 8 = 8000 and 1500 × 8 = 12 000, so the answer is between 8000 and 12 000.
Multiply by a 1-digit number
Use short multiplication. Work from the ones column to the left, and carry into the next column when a digit is 10 or more. Keep the columns lined up neatly.
Multiply by a multiple of 10
To multiply by 30, first multiply by 3, then multiply the result by 10 (the digits move one place left and a zero appears at the end). The same idea works for 50, 70 and so on.
Multiply by a 2-digit number
Split the 2-digit number into its tens and ones. For × 19, work out × 10 and × 9 separately, then add the two products together.
Worked examples
Estimating before you multiply
- You want to work out 1347 × 8.
- Round 1347 to 1000: 1000 × 8 = 8000.
- Round 1347 up to 1500: 1500 × 8 = 12 000.
Answer: The answer will be between 8000 and 12 000.
Multiplying a 4-digit number by a 1-digit number
- Multiply the ones: 7 × 8 = 56. Write 6, carry 5 tens.
- Multiply the tens: 40 × 8 = 320, add the 50 carried to make 370. Write 7, carry 3 hundreds.
- Multiply the hundreds: 300 × 8 = 2400, add the 300 carried to make 2700. Write 7, carry 2 thousands.
- Multiply the thousands: 1000 × 8 = 8000, add the 2000 carried to make 10 000.
Answer: 1347 × 8 = 10 776.
Multiplying by a multiple of 10
- Work out 5489 × 30.
- First multiply by 3: 5489 × 3 = 16 467.
- Then multiply by 10, so the digits move one place left and a zero is added.
Answer: 5489 × 30 = 164 670.
Multiplying by a 2-digit number
- Work out 1356 × 19 by splitting 19 into 10 + 9.
- Multiply by 10: 1356 × 10 = 13 560.
- Multiply by 9: 1356 × 9 = 12 204.
- Add the two products: 13 560 + 12 204.
Answer: 1356 × 19 = 25 764.
A multiplication word problem
- Each display cabinet has 7 shelves and each shelf holds 18 figures.
- One cabinet holds 7 × 18 = 126 figures.
- There are 25 full cabinets, so multiply 126 × 25.
Answer: There are 3150 figures in the 25 cabinets.
Where you see this in real life
- Counting stamps: 10 columns × 16 rows on each sheet, across many sheets.
- Working out how many times a heart beats in a day (about 79 beats a minute).
- Astronomers, scientists, teachers and doctors all multiply numbers in their work.
Key words
- Product
- The answer when you multiply two or more numbers together.
- Estimate
- A sensible, rounded guess used to check that an answer is reasonable.
- Factor
- A number that is multiplied by another to make a product.
- Multiple of 10
- A number like 10, 30 or 50 that you can make by multiplying by 10.