Nines and threes

1. Nines and threes I am learning to decide if a number is divisible by nine or three. Can the number be shared evenly between 9 or 3.

2. To work out whether a number is divisible by nine add the digits together. If the number you make is on your nine times table then your original number is divisible by nine. e.g. 72 7 + 2 = 9, 9 is on my 9 times table so 72 is divisible by 9. Let’s find out why this works. 72 is shown below. If we remove 1 from all the groups of ten then they will all have 9. 9 can easily be shared between 9 (9 ÷ 9 = 1) You can see from this that 72 is divisible by 9. Now there are 9 ones left. (9 ÷ 9 = 1) 72 10 10 10 10 10 10 10 + 2 = 9 7 9 9 9 9 9 9 9

3. 119 is shown below. Can 119 be divided by 9? If we remove 1 from the 100 we will have 99. This amount can be evenly shared between 9 (99 ÷ 9 = 11) If we remove 1 from the group of ten we will have 9 in the group. This amount can be shared between 9 (9 ÷ 9 = 1) . Now there are 11 ones left. 11 can’t be evenly shared among 9 groups so 119 is not divisible by 9. 119 1 + 1 + 9 = 11 100 10 So 119 is not divisible by 9 99 9

4. Use this strategy to work out whether the numbers below are divisible by 9. The first one has been done for you. Click again when you have worked out all your answers. 1) 333 2) 252 3) 114 4) 432 5) 227 Yes, (3 + 3 + 3 = 9) Yes, (2 + 5 + 2 = 9) No, (1 + 1 + 4 = 6) Yes, (4 + 3 + 2 = 9) No, (2 + 2 + 7 = 11) Need some more practise? Try Pg47 & 48 of Teacher Tools Multiplication and Division Book Numeracy resources