Key ideas
÷ 10, 100, 1000
The digits move right: 1 place for ÷ 10, 2 places for ÷ 100, 3 places for ÷ 1000.
48 ÷ 100 = 0.48
÷ a multiple of 10
Split it up: ÷ 80 = ÷ 8, then ÷ 10.
÷ 300 = ÷ 3, then ÷ 100.
The bus stop
Divide each digit from the left. Carry the remainder to the next digit as tens.
When it doesn't divide exactly
Put a decimal point after the number, add zeros and keep dividing. If it doesn't stop, round to something sensible.
158 ÷ 4 = 39.5
Only use a remainder when the question needs it: 75 pupils in minibuses of 8 needs 10 minibuses.
Breaking it down
Split the number into factors: ÷ 24 = ÷ 8, then ÷ 3.
÷ 4 = halve, halve.
Check
Check by multiplying back: if 936 ÷ 4 = 234, then 234 × 4 should give 936.
Dividing by 10, 100 and 1000
Calculate 5600 ÷ 100(1 mark)
Move the digits 2 places right.5600 ÷ 100 = 56✓1
In plain EnglishDividing by 100 makes the number 100 times smaller: each digit moves 2 places to the right.
Calculate 48 ÷ 100(1 mark)
Move the digits 2 places right.48 ÷ 100 = 0.48✓1
In plain EnglishThe 4 moves from tens to tenths and the 8 moves from units to hundredths. Put a 0 in the units place.
Dividing by multiples of 10, 100 and 1000
Calculate 7200 ÷ 80(2 marks)
Split the 80.÷ 80 = ÷ 8, then ÷ 10✓1
In plain English80 is 8 × 10, so divide by 8 and then by 10.
Calculate.7200 ÷ 8 = 900900 ÷ 10 = 90✓2
In plain English72 ÷ 8 = 9, so 7200 ÷ 8 = 900. Then divide by 10 by moving the digits one place right.
Calculate 4500 ÷ 300(2 marks)
Split the 300.÷ 300 = ÷ 3, then ÷ 100✓1
In plain English300 is 3 × 100.
Calculate.4500 ÷ 3 = 15001500 ÷ 100 = 15✓2
In plain English45 ÷ 3 = 15, so 4500 ÷ 3 = 1500. Then move the digits two places right.
The bus stop method
Calculate 936 ÷ 4(2 marks)
Set it out.936 inside the bus stop, 4 outside✓1
In plain EnglishThe number you are dividing goes inside. The number you divide by goes outside.
Divide each digit, from the left.
936 ÷ 4 = 234✓2
| 2 | 3 | 4 | |
| 4 | 9 | 13 | 16 |
In plain English9 ÷ 4 = 2 remainder 1: carry the 1 to make 13. 13 ÷ 4 = 3 remainder 1: carry the 1 to make 16. 16 ÷ 4 = 4. Check: 234 × 4 = 936.
Calculate 1575 ÷ 7(2 marks)
1 ÷ 7 won't go.Use the first two digits: 15 ÷ 7 = 2 r 1✓1
In plain English7 doesn't go into 1, so carry it: 15 ÷ 7 = 2 remainder 1.
Keep going.
1575 ÷ 7 = 225✓2
| 2 | 2 | 5 | ||
| 7 | 1 | 15 | 17 | 35 |
In plain EnglishCarry the 1 to make 17: 17 ÷ 7 = 2 remainder 3. Carry the 3 to make 35: 35 ÷ 7 = 5.
When it doesn't divide exactly
Calculate 158 ÷ 4(2 marks)
Bus stop.
15 ÷ 4 = 3 r 3, then 38 ÷ 4 = 9 r 2✓1
| 3 | 9 | . | 5 | ||
| 4 | 1 | 15 | 38 | . | 20 |
In plain EnglishThere are 2 left over, but we don't stop there. Put a decimal point after 158 and in the answer, then add a zero: 158 = 158.0.
Keep dividing.20 ÷ 4 = 5, so 158 ÷ 4 = 39.5✓2
In plain EnglishCarry the 2 to make 20, and 20 ÷ 4 = 5. Check: 39.5 × 4 = 158.
Calculate 158 ÷ 6. Give your answer to 2 decimal places.(2 marks)
Bus stop past the point.
158 ÷ 6 = 26.333…✓1
| 2 | 6 | . | 3 | 3 | 3 | ||
| 6 | 1 | 15 | 38 | . | 20 | 20 | 20 |
In plain EnglishAdd zeros after the decimal point and keep dividing. The 3s keep going for ever, so stop once you have 3 decimal places.
Round.26.333… = 26.33 to 2 decimal places✓2
In plain EnglishFor 2 decimal places, look at the third decimal place. It is a 3, so the second decimal place stays the same.
75 pupils are going on a trip. Each minibus holds 8 pupils. How many minibuses are needed?(2 marks)
Divide.
75 ÷ 8 = 9 r 3✓1
| 9 | r 3 | ||
| 8 | 7 | 75 |
In plain English9 minibuses carry 72 pupils, with 3 pupils left over.
Think about the remainder.The 3 pupils still need a minibus: 10 minibuses✓2
In plain EnglishHere we round up. If the question were "how many £8 tickets can you buy with £75?", you would round down to 9.
Breaking it down
Calculate 1440 ÷ 24(2 marks)
Split 24 into factors.24 = 8 × 3✓1
In plain EnglishDividing by 24 is the same as dividing by 8 and then by 3.
Divide by each factor in turn.
1440 ÷ 8 = 180180 ÷ 3 = 60✓2
| 1 | 8 | 0 | ||
| 8 | 1 | 14 | 64 | 0 |
In plain EnglishUse a bus stop for 1440 ÷ 8. Then 18 ÷ 3 = 6, so 180 ÷ 3 = 60. Check: 60 × 24 = 1440.
Calculate 1008 ÷ 12(2 marks)
Split 12 into factors.12 = 4 × 3, and ÷ 4 = halve, halve✓1
In plain EnglishHalving twice is the same as dividing by 4.
Divide.1008 → 504 → 252
252 ÷ 3 = 84✓2
| 8 | 4 | ||
| 3 | 2 | 25 | 12 |
In plain EnglishHalf of 1008 is 504, and half of 504 is 252. Then 252 ÷ 3 = 84 with a bus stop.
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