CALCULATING • DIVISION 129Division is repeated subtraction
Division is also like taking away one number from
another number again and again. We call this repeated
subtraction. Let’s see what happens when our robots
start removing their apples from the barn.Division is the opposite of multiplication
If we know a multiplication fact, we can use it to find a division
fact. This is because division is the opposite, or inverse, of
multiplication. We can show this with our robots and apples.The 3 robots are storing
their apples. Each robot
takes a basket of 4 apples
and empties it into the barn.
The total number of apples
in the barn is 12, because
4 multiplied by 3 is 12.One robot takes
her 4 apples out
of the barn. There
are 8 apples left.The second
robot removes
his 4 apples, leaving
4 apples in the barn.The third
robot takes
the last 4 apples
out of the barn.The multiplication to store the apples
(4 × 3 = 12) is the inverse of the division
we did to share them out (12 ÷ 3 = 4).
The 3 stays where it is, but the other
numbers change places. So, if you know
the multiplication, you just rearrange the
numbers to find the division, and vice versa.4 × 3 = 12
4 × 3 = 12 12 ÷ 3 = 4
12 apples in
the barn4 apples in
a basket3 robots12 12 − 4 = 8 8 4 0
Repeated subtraction is
the inverse of repeated
addition, which we looked
at on page 99.The barn is
now empty.
This shows us
that 12 ÷ 3 = 48 − 4 = 4 4 − 4 = 0
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