Long division

For grown-ups: this lesson in words

Year 6 · Maths

Long division: I can divide a 4-digit number by a 2-digit number using long division, and say what the remainder means.

1. Dividing means making equal groups. Here are 30 pencils in groups of 15: 2 groups. 30 ÷ 15 = 2

   With big numbers we cannot count out the groups, so we use a written method: long division.

   Picture: Group 1: 15 pencils and Group 2: 15 pencils. 30 pencils altogether.

2. Long division shares big numbers into groups. Today we divide by 15. First, we list the multiples of 15.

   Count up in 15s: 15, 30, 45, 60, 75.

   The line goes on: 90, 105, 120, 135, 150. Add 15 each time.

   Write this list at the side of your page. It tells you how many 15s fit.

   Picture: A number line from 0 to 150 with a tick every 15, labelled every 15. The frog hops from 0 to 15, then to 30, then to 45, then to 60, then to 75.

3. Now 345 ÷ 15. The 3 is less than 15, so 15 does not fit into 3. Start with 34.

   The biggest multiple of 15 that fits in 34 is 30: 2 × 15. Write 2 above the 4. 34 − 30 = 4

   Bring down the 5 to make 45. 45 is 3 × 15. Write 3 above the 5. 45 − 45 = 0

   Nothing is left. 345 ÷ 15 = 23

   Picture: 345 divided by 15 worked out as a long division: the answer is 23.

4. Your turn: Here are multiples of 15: 15, 30, 45, 60. The dot is at 34. Which is the biggest multiple of 15 that fits in 34?

   Picture: A number line from 0 to 60 with a tick every 15, labelled every 15. A dot at a point between 30 and the next tick.

   Choose one:

   • 15
   • 30
   • 45

   Answer

   The answer: 30

   30 is the biggest multiple of 15 that fits in 34. 2 × 15 = 30, and 34 − 30 = 4

   Picture: A number line from 0 to 60 with a tick every 15, labelled every 15. A dot at a point between 30 and the next tick. The frog hops from 0 to 15, then to 30.