6.4

# Increasing by an amount: further example

In the previous step we showed how to increase an amount by a percentage. Here we will identify a common mistake that occurs when increasing by small percentages i.e. an increase of less than 10%.

## Question

In the UK, electricity bills have 5% tax added to them. If the cost of the electricity used is £38. How much is the final bill, with 5% tax?

You might like to try out one of the methods used in the previous step first.

We are going to multiply £38 by 105% (100% of the original amount plus 5% tax). We know that 0.05 is equivalent to 5% ($\frac{5}{100}$). Therefore, to get our final answer we multiply £38 by 1.05.

Our percentage increase is a single digit, 5%. A common mistake students make is to multiply by 1.5, an increase of 50%, rather than 1.05, an increase of 5%. It is always worth exploring single digit percentage increases to expose this misconception.

A further example could be to ask students what multiplier they would use to increase by 7$\frac{1}{2}$%. Here we are combining single digit whole percentages with a fraction of a percent.

## Discuss

What other types of percentage increases could you use to discover student misconceptions about applying their understanding of fractions, decimals and percentages?

Come up with three questions you could ask students, along with the misconception or common mistake you are intending to identify. Post to the comments below.