Key ideas
× 10, 100, 1000
The digits move left: 1 place for × 10, 2 places for × 100, 3 places for × 1000.
Fill empty places before the point with zeros.
× a multiple of 10
Split it up: × 40 = × 4, then × 10.
× 300 = × 3, then × 100.
The grid method
Split each number into hundreds, tens and units. Multiply each pair in a grid, then add up everything inside the grid.
Chimney sums
Bigger number on top. Multiply each digit from the right, carrying as you go.
For a two-digit number, do one row for the units and one row for the tens, then add.
Breaking it down
Split the number into factors: × 24 = × 8, then × 3.
× 4 = double, double. × 8 = double, double, double.
Multiplying by 10, 100 and 1000
Calculate 47 × 100(1 mark)
Move the digits 2 places left.47 × 100 = 4700✓1
In plain EnglishMultiplying by 100 makes the number 100 times bigger. Each digit moves 2 places to the left, and the empty tens and units places are filled with zeros.
Calculate 6.4 × 1000(1 mark)
Move the digits 3 places left.6.4 × 1000 = 6400✓1
In plain EnglishThe 6 moves from units to thousands and the 4 moves from tenths to hundreds. Fill the empty tens and units with zeros.
⚠ A common mistake: "just add zeros". 6.4 × 1000 is not 6.4000. The digits move: the point stays where it is.
Multiplying by multiples of 10, 100 and 1000
Calculate 23 × 400(2 marks)
Split the 400.× 400 = × 4, then × 100✓1
In plain English400 is 4 × 100, so multiply by 4 and then by 100.
Calculate.23 × 4 = 9292 × 100 = 9200✓2
In plain EnglishMultiply by 4 first. Then multiply by 100 by moving the digits two places left.
Calculate 60 × 700(2 marks)
Multiply the non-zero digits.6 × 7 = 42✓1
In plain EnglishTake away the zeros for now: 60 is 6 × 10 and 700 is 7 × 100.
Multiply by 10 and 100.× 10 × 100 = × 100042 × 1000 = 42 000✓2
In plain EnglishAltogether that is × 1000, so the digits of 42 move three places left.
The grid method
Calculate 47 × 36(3 marks)
Split and fill the grid.
47 = 40 + 7 and 36 = 30 + 6✓1
| × | 40 | 7 |
|---|---|---|
| 30 | 1200 | 210 |
| 6 | 240 | 42 |
In plain EnglishSplit each number into tens and units. Multiply each pair: 40 × 30 = 1200, 7 × 30 = 210, 40 × 6 = 240, 7 × 6 = 42.
Add everything in the grid.
47 × 36 = 1692✓3
| 1 | 2 | 0 | 0 | |
| 2 | 4 | 0 | ||
| 2 | 1 | 0 | ||
| + | 4 | 2 | ||
| 1 | 6 | 9 | 2 |
In plain EnglishUse a chimney sum to add the four answers, biggest on top. Estimate to check: 50 × 40 = 2000, so 1692 is sensible.
Calculate 236 × 7(2 marks)
Split and fill the grid.
236 = 200 + 30 + 6✓1
| × | 200 | 30 | 6 |
|---|---|---|---|
| 7 | 1400 | 210 | 42 |
In plain English236 = 200 + 30 + 6. Multiply each part by 7: 1400, 210 and 42.
Add.
236 × 7 = 1652✓2
| 1 | 4 | 0 | 0 | |
| 2 | 1 | 0 | ||
| + | 4 | 2 | ||
| 1 | 6 | 5 | 2 |
In plain EnglishAdd the three answers together.
Chimney sums
Calculate 386 × 7(2 marks)
Set it out.Bigger number on top, 7 under the units✓1
In plain EnglishWrite 386 on top and 7 underneath, lined up with the 6.
Multiply each digit, carrying.
386 × 7 = 2702✓2
| 6 | 4 | |||
| 3 | 8 | 6 | ||
| × | 7 | |||
| 2 | 7 | 0 | 2 |
In plain English7 × 6 = 42: write 2, carry 4. 7 × 8 = 56, + 4 = 60: write 0, carry 6. 7 × 3 = 21, + 6 = 27: write 27.
Calculate 54 × 23(3 marks)
Multiply by the 3 units.54 × 3 = 162✓1
In plain EnglishThe first row is 54 × 3.
Multiply by the 2 tens.54 × 20 = 1080✓2
In plain EnglishThe 2 is really 20. Put a 0 in the units first, then multiply by 2.
Add the two rows.
54 × 23 = 1242✓3
| 1 | ||||
| 5 | 4 | |||
| × | 2 | 3 | ||
| 1 | ||||
| 1 | 6 | 2 | ||
| + | 1 | 0 | 8 | 0 |
| 1 | 2 | 4 | 2 |
In plain EnglishAdd 162 and 1080. Estimate to check: 50 × 20 = 1000, so 1242 is sensible.
Breaking it down
Calculate 15 × 24(2 marks)
Split 24 into factors.24 = 8 × 3✓1
In plain EnglishPick factors that are easy to multiply by. 24 = 8 × 3 (or 4 × 6, or 2 × 12).
Multiply by each factor in turn.15 × 8 = 120120 × 3 = 360✓2
In plain English15 × 8: double 15 three times: 30, 60, 120. Then × 3.
Calculate 35 × 12(2 marks)
Split 12 into factors.12 = 4 × 3✓1
In plain English× 4 is easy: double, then double again.
Multiply by each factor.35 × 4: 70, 140140 × 3 = 420✓2
In plain EnglishDouble 35 is 70, double again is 140. Then 140 × 3 = 420.
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