If we are given the answer to a calculation, we can use this to find the answer to a related calculation in which the numbers have been multiplied or divided by a power of ten.

We can also use the fact that division is the inverse of multiplication.

e.g. If we know that 52.3 x 4.8 = 251.04 then we can find the answer to many related calculations such as:

a) 523 x 48 - Both numbers in the original calculation have been multiplied by 10 therefore the answer must be multiplied by 100.

So the answer is 25104.

b) 0.523 x 480 - One number has been divided by 100 and the other multiplied by 100 which cancel each other out.

So the answer remains unchanged as 251.04.

c) 251.04 ÷ 48 - The first number is the same as the answer of the original and the second has been multiplied by 10.

Since this is division, the answer will have the inverse operation applied, which is divide by 10.

So the answer is 5.23.

Note that when answering question like this, estimation is also a useful technique.

You can round the numbers to 1 or 2 significant figure and then estimate the answer, remembering that the digits will be the same as in the original calculation.

e.g. For c) above: 251.04 ÷ 48 ≈ 250 ÷ 50 = 5

So the answer **must** be 5.23 as it is close to our estimated guess of 5.

In this activity, you will use information given in a calculation to enable you to work out related calculations by applying your knowledge of place value.

Good luck, place value superstar!