Set it out as usual
To work out 9.6 ÷ 4, set it out for short division exactly as you would set out 96 ÷ 4, with the point in its place between the 9 and the 6. 9.6 is 9 ones and 6 tenths. Short division shares out the ones first, then the tenths.
9.6 ÷ 4 set out for short division: 4 outside the bar, and 9.6 under it.
Share the ones
4 goes into 9 twice, because 4 × 2 = 8. Write 2 above the 9. That shares out 8 of the 9 ones, and 1 one is left over.
The 1 left over cannot be shared among 4 as a whole one, so break it into tenths: 1 one is 10 tenths. Carry it past the point into the tenths column, where it joins the 6 tenths already there. Together they make 16 tenths.
2 is written above the 9, and the 1 left over is carried to the 6, making 16 tenths.
Share the tenths, and bring the point up
16 tenths ÷ 4 = 4 tenths, so write 4 above the 6. The point in the answer goes straight above the point in 9.6, because the 2 counts ones and the 4 counts tenths. So 9.6 ÷ 4 = 2.4.
Check by multiplying back: 2.4 × 4 = 9.6. An estimate helps as well. 8 ÷ 4 = 2 and 12 ÷ 4 = 3, and 9.6 lies between 8 and 12, so the answer must lie between 2 and 3.
The point rises straight up from 9.6 into the answer: 9.6 ÷ 4 = 2.4.
Four equal hops of 2.4 land exactly on 9.6, so 9.6 shared into 4 equal parts is 2.4 each.
Keep going past the point
A whole number can be divided the same way, even when it does not divide exactly. For 7 ÷ 2, 2 goes into 7 three times, with 1 left over. Instead of stopping with a remainder, write 7 as 7.0. It is the same number, with 0 tenths. Carry the 1 past the point: it is 10 tenths, and 10 tenths ÷ 2 = 5 tenths. So 7 ÷ 2 = 3.5, with nothing left over.
Write as many zeros after the point as the division needs. 3 is 3.00, so 3 ÷ 4 = 0.75: 4 does not go into 3, so write 0 above it and carry the 3 as 30 tenths. 30 tenths ÷ 4 = 7 tenths with 2 tenths left over, and those are 20 hundredths, which share out as 5 hundredths each.
7 is written 7.0, and the 1 left over from the ones is carried into the tenths: 7 ÷ 2 = 3.5.
Where the point goes
Leaving the point out gives 24 for 9.6 ÷ 4, but sharing 9.6 into 4 parts cannot give more than 9.6 itself. Putting the point one place too far along gives 0.24, which is ten times too small: 0.24 × 4 is only 0.96. The point goes straight up, no further.
Worked example: Equal Spacing Along a Line
Question Twelve lamp posts stand in a straight line along a road, equally spaced. The distance from the first lamp post to the last is 46.2 m. (a) What is the distance between two neighboring lamp posts? (b) What is the distance from the 3rd lamp post to the 9th?
1.Count the gaps, not the posts. Twelve posts in a line have 12 − 1 = 11 gaps between them.
Twelve posts in a line have 11 gaps between them. 2.The 11 equal gaps make 46.2 m, so one gap is 46.2 ÷ 11 = 4.2 m.
(a) One gap is 46.2 ÷ 11 = 4.2 m. 3.(a) Neighboring lamp posts are 4.2 m apart.
4.From the 3rd post to the 9th there are 9 − 3 = 6 gaps.
From the 3rd post to the 9th there are 9 − 3 = 6 gaps. 5.(b) The distance is 6 × 4.2 = 25.2 m.
(b) 6 × 4.2 = 25.2 m.
Answer: (a) 4.2 m; (b) 25.2 m
Common mistakes
- Dividing 46.2 by 12, the number of posts. The distance is made of 11 gaps.
- Counting 7 gaps from the 3rd post to the 9th because there are 7 posts in that stretch. Seven posts have 6 gaps between them.