Using Inverse Operations

How to use an inverse to undo a repeated multiplication problem.

10 October, 2004

X 1.62.5 4 ÷1.6 2.5

So the inverse of

X 1.6 is ÷1.6

X 1.62.5 4 X 0.625 2.5

Remember that the inverse

X 1.6 is X 1/1.6 (1÷ 1.6 = 0.625)

X 1.62.5 4 X 1.2 4.8

1.6 X 1.2 = 1.92So replace the two operations with this

single operation

2.5 X 1.92 4.8

Find the single operation that replaces these two operations. Check your answers, in the same way as the previous

example, using a starting number of 2.5

First Second Replacement

X 1.2 X 2.5

X 1.4 X 0.5

X 1.7 X 2.3

X 1.6 X 0.5

X 1.9 X 1.5

X 1.7 X 1.9

X 0.2 X 0.4

X 0.5 X 0.5

X 1.62.5 4 X 1.2 4.8

First find 1.6 X 1.2 = 1.92

Find the reciprocal 1/1.92 = 0.5208333…

Multiply by 0.5208333…This is the single inverse

operation.

2.5 4.8X 0.52083333…….

Find the single inverse operation that replaces these two operations. Check your answers, in the same way as the

previous example, using a starting number of 2.5

First Second Single Inverse Operation

X 1.2 X 2.5

X 1.4 X 0.5

X 1.7 X 2.3

X 1.6 X 0.5

X 1.9 X 1.5

X 1.7 X 1.9

X 0.2 X 0.4

X 0.5 X 0.5