How would you divide 6.9 by 0.3?

Multiplying or dividing by two decimals is often more difficult than multiplying or dividing by whole numbers. Therefore, if presented with a question that asks us to divide or multiply by two decimals, we want to find a way to convert both these decimals into whole numbers. How are we going to do this?

6.9/0.3

We can multiply both the numerator and denominator of this fraction to obtain whole numbers both in the numerator and the denominator. Here we can multiply top and bottom of the fraction by 10:

Now we have obtained a fraction that is much easier to simplify, 69/3. We can use short division to simplify. Alternatively, we can try to think about what number 3 must be multiplied to yield an answer of 69, or how many times 3 can be fitted into 69. A fun way to think about this is to imagine an individual, Alice, who loves lollipops. Each lollipop costs £3. Alice has £69 in her wallet. How many lollipops can Alice buy with the money she has?

Using the short division technique, we can see that 3 fits into 69 a total of 23 times, without producing a remainder. That means that 69 is exactly divisible by 3.

Because we have established that 6.9/0.3 = 69/3 and that 69/3 = 23, we can conclude that:

6.9/0.3 = 23.