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Cut and Paste I am learning to solve multiplication problems using doubling and halving, thirding and trebling, and other proportional adjustments. 2 X2 3 X3 To start with lets use ‘doubling and halving’ to help us change a question and make it easier to answer. Below are 4 groups of 3 or 4 X 3 = 12 Now let’s halve the number of groups there are. Then double the amount you put in each group. 4 X 3 = 12 Do this by dividing by 2 So… 4 X 3 = 12 ÷2 and x2 2 X 6 = 12 2 X …. 6 = 12 Do this by multiplying by 2 Now let’s try a thirding and trebling example. Below are 3 groups of 27 or 3 X 27 = ? Now let’s triple the number of groups there are. Then third the amount you put in each group. 3 X 27 = …. Do this by multiplying by 3 9 X 9 = 81 so 3 X 27 =81 Do this by dividing by 3 81 9 = …. 9 X …. We can also adjust our problems more than once if it helps. 2 X 36 = ? ÷2 X2 Doubling and halving X4so we once didn’t help can do it again. 4 X 18 = ? X2 ÷4 ÷2 8 X 9 = 72 We could also have divided by 4 and multiplied by 4. This would have saved us the middle step and we would still have got the same answer. The questions on the left have a buddy question to the right where, doubling and halving or trebling and thirding has been used. Which questions do you think go together? 1) 5 X 14 = ? 9 X 8 = 72 2) 14 X 50 = ? 12 X 9 = 108 3) 6 X 18 = ? 10 X 7 = 70 4) 3 X 24 = ? 7 X 100 = 700 Click again when you have worked out which questions go together. Use doubling and halving to help you work out the answers to these questions. Click again when you have worked out all your answers. 1) 18 X 5 = ? 9 X 10 = 90 2) 21 X 3 = ? 7 X 9 = 63 3) 6 X 25 = ? 3 X 50 = 150 4) 33 x 3 = ? 11 X 9 = 99 5) 4 X 50 = ? 2 X 100 = 200 Need some more practise? Try Pg31 & 32 of Teacher Tools Multiplication and Division Book Numeracy resources