Division
Division as a missing factor, then bigger exact divisions.
Best in your head · no pen, no calculator why?
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the idea
Division undoes multiplication. 56 ÷ 8 asks: 8 times what makes 56? So every times-table fact you know is also a division fact.
Bigger divisions come down to small ones. You can cross the same zeros off both numbers, or split a big number into pieces that divide cleanly.
Dividing by a number below 1 makes the answer bigger. 10 ÷ 0.5 asks how many halves fit in 10, and there are 20 of them.
techniques
Missing factor, then zeros
- Read 56 ÷ 8 as 8 × ? = 56. The missing factor is the answer.
- If both numbers end in zeros, cross the same number of zeros off each.
- Find the fact that fits the front digits. In 3,000 ÷ 6, that is 30 ÷ 6 = 5.
- Each zero after those digits goes on the end of the answer: 500.
worked example
3,500 ÷ 70
- Cross one zero off each: 350 ÷ 7.
- 35 ÷ 7 = 5, and one zero is left: 50.
Answer: 50
Split the number into pieces
- Take out 10 lots of the divisor, or 20 lots if that still fits.
- Divide what is left with a fact.
- Add the two answers.
worked example
195 ÷ 13
- 10 × 13 = 130, so split 195 into 130 + 65.
- 130 ÷ 13 = 10, and 65 ÷ 13 = 5.
- 10 + 5 = 15.
Answer: 15
Count halves and quarters
- ÷ 0.5 asks how many halves fit. Each whole holds 2, so double the number.
- ÷ 0.25 asks how many quarters fit. Each whole holds 4, so multiply by 4.
- Check the size: the answer is bigger than the number you started with.
worked example
13 ÷ 0.25
- Each whole holds 4 quarters.
- 13 × 4 = 52.
Answer: 52
watch out for
- Mixing up which number divides. 56 ÷ 8 asks how many 8s make 56, which is 7.
- Cancelling a zero from only one number. 2,400 ÷ 60 becomes 240 ÷ 6, not 2,400 ÷ 6.
- Dividing the leftover and forgetting the first piece. 156 ÷ 12 is 10 from the 120, plus 3 from the 36.
- Dividing by 4 when the question says ÷ 0.25. That gives 4.5 for 18 ÷ 0.25, instead of 72.
practice
Division facts
worked example
16 ÷ 8
Answer: 2
- Read it as a missing factor: 8 × ? = 16. Since 8 × 2 = 16, the answer is 2.
Divide with zeros
worked example
120 ÷ 60
Answer: 2
- Cancel a zero from both numbers: 120 ÷ 60 = 12 ÷ 6.
- 12 ÷ 6 = 2, because 6 × 2 = 12.
Split the dividend
worked example
225 ÷ 15
Answer: 15
- Split 225 into 150 + 75.
- 150 ÷ 15 = 10 and 75 ÷ 15 = 5, so the answer is 15.
÷ 0.5 and ÷ 0.25
worked example
35 ÷ 0.25
Answer: 140
- Dividing by 0.25 asks how many quarters fit. Each whole holds 4 quarters, so 35 × 4 = 140.