More multiplication & division
Extending multiplication and division
Now the numbers get bigger! You can multiply and divide numbers up to 100 by estimating first, using the grid method, and understanding what a remainder means.
Estimate first
Before you calculate, make an estimate by rounding. For 27 × 4, round 27 to 30: 30 × 4 = 120. Your real answer should be close to 120, so an estimate helps you check.
The grid method
Split the two-digit number into tens and ones. For 27 × 4, split 27 into 20 and 7. Multiply each piece: 20 × 4 = 80 and 7 × 4 = 28. Then add: 80 + 28 = 108.
Dividing bigger numbers
You can divide numbers up to 100 by 2, 3, 4 or 5. For example 72 ÷ 4 = 18. Dividing by a smaller number gives a greater answer: 72 ÷ 3 = 24 is more than 72 ÷ 4 = 18.
What a remainder means
Sometimes a division leaves a remainder, and the problem tells you what to do with it. If 46 balls go 4 to a tube, 46 ÷ 4 = 11 remainder 2. The 2 leftover balls still need a tube, so you round up to 12 tubes.
Worked examples
Grid method for 27 × 4
- Estimate: 30 × 4 = 120.
- Split 27 into 20 and 7.
- Multiply: 20 × 4 = 80 and 7 × 4 = 28.
- Add the products: 80 + 28 = 108.
Answer: 27 × 4 = 108
Grid method for 58 × 3
- Estimate: 60 × 3 = 180.
- Split 58 into 50 and 8.
- Multiply: 50 × 3 = 150 and 8 × 3 = 24.
- Add the products: 150 + 24 = 174.
Answer: 58 × 3 = 174
A remainder that rounds up
- There are 46 balls, 4 to a tube.
- Divide: 46 ÷ 4 = 11 remainder 2.
- The 2 extra balls still need a tube, so round up.
- You need 12 tubes.
Answer: 12 tubes are needed
Comparing two divisions
- Work out 72 ÷ 4 = 18.
- Work out 72 ÷ 3 = 24.
- Dividing by the smaller number (3) makes bigger groups.
- So 72 ÷ 3 gives the greater answer.
Answer: 72 ÷ 3 = 24 is greater
Where you see this in real life
- Packing tennis balls into tubes and working out how many tubes you need.
- Sharing a box of marbles between children and seeing how many are left over.
- Working out how many benches are needed to seat a whole class.
Key words
- Estimate
- A sensible guess made by rounding, used to check an answer.
- Grid method
- Splitting a number into tens and ones to multiply each part.
- Remainder
- The amount left over when a number does not divide equally.
- Round up
- To go up to the next whole number when there is a leftover.
- Interpret
- To decide what a remainder means in a real problem.