Introduction to Percentages

Finding a percentage of a number using Ratio Grids

The left hand column of a percentage Ratio Grid will be headed “%” and the right hand one will be for the numbers that you are working with. For example if you are asked to “Find 65% of £40”, you are starting with £40, so the right hand column will be labelled “£” and the number 40 will be on the top line, beside the 100%:

“100 Percent” is a phrase everyone knows and uses, and that’s great because when you solve a percentage problem using a Ratio Grid, you will need to put the number 100 into one corner of the grid.

Once the numbers are all in the right places, (assuming you know how to complete a ratio grid!!) , you will know the sum you need to do is 40×65÷100 and the answer is 26. Because the answer is in the column headed “£”, then it must mean £26. Headings are really useful in Ratio Grids because they will always help you to put Units in your answers.

Questions about Percentage Increase and Decrease are easy if you use Ratio Grids. For example:

“A tree increases from 15m to 17m in height over one year. What is the percentage increase?”

The 2 columns of the ratio grid will be headed % and m. The first percentage will be 100, which is for the start of the story. In the story about the tree, it starts at a height of 15, so put 15 beside the 100, in the metres column. It grows to 17m, so that goes underneath the 15.

The missing number is found from this ratio grid by working out 100×17÷15, on a calculator, which is 113.33333333… It’s usually fine to round percentages to one decimal place, so the missing number is 113.3%.

Because the question is asking for a percentage increase, you need to find the difference between 100% and 113.3%, so the answer is 113.3%-100%=13%.

Here is a worksheet you can try, and here are the workings and answers.

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