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