Warm up – back of your books

1. Three businessmen sell a Car for £2451. They decide to divide the money evenly between themselves. How much do each get?

2. Mr Dad has seven sons. Each is to receive an equal share of his land, totalling 8022 acres. How many acres does each son get to keep?

• Three businessmen sell a Car for £2451. They decide to divide the money evenly between themselves. How much do each get? Use the ‘bus shelter’ method...

2 4 5 132 2

0 8 1 7

Each would get £817...

• Mr Dad has seven sons. Each is to receive an equal share of his land, totalling 8022 acres. How many acres does each son get to keep?

8 0 2 271 4

1 1 4 6

Each would get 1146 acres...

3

Multiples

We will be discovering how to identify if a BIG number is a multiple of a SMALL number

You will be able to identify multiples of 2,3,4,5 and 6

Tests of Divisibility

• Which of these numbers divide by 2? How do you know?

18

123

2341

9

32568.4 190

266

Numbers that are divisible by 2 end in a 0, 2, 4, 6 or 8 (ie) They are even!)

Tests of Divisibility

• Which of these numbers divide by 3? How do you know?

30 6

321

61

1653003 224

17

Numbers that are divisible by 3 have digits that add up to a multiple of 3...

3 + 0 = 3

3 + 2 + 1 = 6

6 = 6

3 + 0 + 0 + 3 = 6

6 + 1 = 7

1 + 6 + 5 = 12

1 + 7 = 8

2 + 2 + 4 = 8

Tests of Divisibility

• Which of these numbers divide by 4? How do you know?

16 312

224

509

918732

342

5604

Numbers are divisible by 4 if their last 2 digits are divisible by 4...

16 ÷ 4 = 4

42 cannot divide by 4

18 cannot divide by 432 ÷ 4 =

8

24 ÷ 4 = 6

04 ÷ 4 = 1

09 cannot divide by 412 ÷ 4 =

3

Tests of Divisibility

• Which of these numbers divide by 5? How do you know?

23 2735

540

730

295732

502

71

Numbers are divisible by 5 if their last digit is either 0 or 5...

Tests of Divisibility

• Which of these numbers divide by 6? How do you know?

12 123

540

152

9246732 51

258

Numbers are divisible by 6 if they are divisible by both 2 and 3...So they must be even, and their digits add up to a multiple of 3...

1 + 2 = 3

5 + 1 = 6But not Even

9 + 2 + 4 + 6

5 + 4 + 0 = 9 7 + 3 + 2 =

12

2 + 5 + 8 = 15

1 + 5 + 2 = 81 + 2 + 3 =

6But not Even

Plenary• A number is divisible by 6 if it is divisible by both 2

and 3

• Why does this work?• Because 2 x 3 = 6 (ie 2 and 3 are the factors of 6)

• If a number is divisible by 3 and 5, what bigger number will it also divide by?

• 15 as 3 x 5 = 15

• If another number is divisible by 3 and 7, what will it also divide evenly by?

• 21 as 3 x 7 = 21

Summary

• We have learnt how check whether certain numbers are divisible by 2, 3, 4, 5, or 6

• As said, this can be useful for checking answers

• The patterns can also be used to work out factors of bigger numbers...