Inverse Operations

One of the most important concepts that your child needs to understand is that of inverse operations. It sounds complicated but is really quite simple. Basically,

Inverses are just Opposites.

Inverse operations are useful because they reverse the effect of whatever operation
you used and get you back to where you started.

The inverse operation of multiplication is division. The inverse operation of division is multiplication.

For example, if we performed the addition 5 + 4 = 9, we could undo the addition by using the inverse, subtraction, 9 - 4 and get back to 5.

or if we performed the multiplication 8 x 7 =56, we could undo the multiplication by using the inverse, division, 56 ÷ 7- and get back to 8.

This idea comes up again and again , especially in algebra and when using function machines.

Inverse operations are also used to check that calculations are correct.

Lets say that we divided 425 by 5 and got the answer 85. We could check this by using the inverse of division which is multiplication by multiplying 85 x 5. If the answer is 425, we know that our original calculation was correct. The "Inverse Operation" of multiplication reversed the division, and returned the number we started with.

Number Facts

A number fact can contains three numbers, for example 9, 5 and 4

What calculations can be made up of these three numbers?

4 + 5 = 9,     5 + 4 = 9,    9 - 5 = 4   and   9 - 4 = 5

these calculations demonstrate that addition and subtraction are inverse.

try the numbers 5, 3 and 15

What calculations can be made up of these three numbers?

5 x 3 =15,     3 x 5 = 15,    15 ÷ 3 = 5  and   15 ÷ 5 = 3

these calculations demonstrate that multiplication and division are inverse.

Try giving your child three numbers and see if they can work out the
four different number facts relating to each set of three.

Multiply/Divide facts for   2 5 10,    3 4 12,    4 10 40,    15 4 60,    4 25 100

Check understanding with these worksheets -

Inverse Operations -

Inverse A - Inverse B

Division and Multiplication 1

Division and Multiplication 2

from Mathsblog.