3.2 Multiplying and dividing
To multiply and divide by 10, 100, 1000, etc., write the digits in their place value columns. To multiply, move the digits to the left (replacing the numbers on the right with zeros) and to divide move them to the right (putting in a decimal point, and any zeros necessary for the place value).
Multiplication and division by whole numbers in general can be carried out by combining this technique with a knowledge of the multiplication tables up to 10.
Example 12
A machine in a factory puts tops on bottles at the rate of 1 every second.
(a) How many bottles does it top in a 10 hour working day?
(b) How many bottles does it top in a 30 day month, at 10 hours a day?
Answer
(a) There are 60 seconds in a minute and so it puts on 60 tops a minute. There are 60 minutes in an hour so it puts on 60 × 60 tops in an hour, which gives 3600.
There are many ways to do this e.g. think of 60 × 60 as 6 × 10 × 6 × 10, which is 6 × 6 × 10 × 10, i.e. 36 × 100, giving 3600 as before.
However you tackle it, the important thing is to remember the place values of the numbers.
So it tops 3600 bottles an hour. In 10 hours it tops 3600 × 10 = 36 000 bottles.
It tops 36 000 bottles in a 10 hour day.
(b) To find out how many bottles it tops in 30 days, multiply 36 000 by 30.
This is 36 000 × 3 × 10 = 1 080 000.
So the factory machine tops 1 080 000 bottles a month (just over a million).
The factory puts on 1 080 000 bottle tops in 30 days.