# Percentages

### Finding percentages

The word percentage hopefully triggers some associations for you. If not here are some ideas to get you thinking:

Now practise working out some percentages of amounts by trying out this problem. Using the digits 0 to 9 at most once each, fill in the boxes to create a correct sentence

Hint: The answer is a whole number with two digits. Use this to focus in on possible solutions.

How many different solutions can you find? Share your solutions with someone else if you can. Or use a calculator to check.

### Use of percentages

Percentages are used in a wide variety of contexts, often so that comparisons can be made. In this activity, cars go in for MOT tests at different garages. This activity may be attempted with or without a calculator.

### Increase and decrease problems

In A Change in Code, you need to try to identify what digit each of the letters represents, where the first column have all been increased by the same percentage to give the second column.

Hint: Notice that all of these two digit whole numbers have stayed as two digit whole numbers after the increase.

Once you’ve got the idea, try the second part of the problem. The third and final part of the problem is much more challenging.

In GCSE exam questions, ideas of sales and profit often come up. These ideas are developed through this next activity Percentage Sales.

Or you may do just one step, using a decimal multiplier to perform this percentage increase calculation. Instead of using 0.25 to find 25%, you can find the final answer by using 1.25, since the selling price is 125% (100% plus 25%). Check for yourself that 1.25 multiplied by £2.20 equals £2.75.

If you need to spend some more time on multipliers, watch the Corbettmaths clip here.

Once you are confident using multipliers, use this method to work through the first five problems below. In the second group of questions there is a reduction in a sale so these are percentage decrease problems. Can you figure out how to work through these? Either by using a two step method, or by using multipliers. If you want to go through

### Mixed problems

Here is a problem linking fractions and percentages with shape.

If you want to try and create your own problem like this, you can download this with further ideas here. Then submit your square dissection to Student Showcase

### Further ideas

For a quick entertaining run through of some of the basic ideas about fractions, decimals and percentages, watch the Maths Show with Matt Parker here.

Percentages are widely used by everyone but they can sometimes be misused or misinterpreted. An example of this was an advertising campaign by a toothpaste brand that claimed that 80% of dentists recommended their brand. It is discussed in this BBC article.

This paragraph is taken from a Guardian article by David Spieglelhalter:

The word rate is crucial here – it does refer to a percentage, although it is further complicated by how it is defined:

This excerpt is from a Full Fact article. Full Fact is an independent fact checking charity.

In Statistics and Geography other rates, such as birth rates, are commonly used when looking at population changes. The birth rate is the number of births per 1000 of the population. So this is an example of a rate that is not a percentage.

Finding percentages
• There are many answers including:
• 5% of 260 = 13
• 5% of 620 = 31
• 2% of 650 = 13
• 6% of 350 = 21
• 5% of 320 = 16

Use of percentages
Increase and decrease problems

A Change in Code solution here

Mixed problems