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Transcript
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.
these questions.