You can find the Exterior angle in a regular polygon by using Ratio Grids if you want to.
Angles in a Regular Polygon
Category: Proportional Reasoning
Currency Conversion using Ratio Grids
Check out the Introduction to Ratio Grids if you are not already an expert!
When you are asked to do a currency conversion, you will usually be given an exchange rate first, as in this question:
“George changes some pounds into Euros. The exchange rate is £1=€1.18. If he changes £350 into Euros, how many Euros will he receive?”
Draw a simple Ratio Grid and give headings of £ and €. Put the numbers 1 and 1.18 in the correct columns. Then, the final number from the question, £350, goes in the £ column under the 1. Putting the numbers into their correct places is easy if you have headings! Put a ring around the empty space – that is where your answer will go.
In this grid, the 2 multiplying numbers are the “1.18” and the “350”, and you will divide by 1. So the sum will be 1.18×350÷1.
The answer is 413, and it is clearly in the Euros column, so give your answer as €413.
It’s easy if you get the headings right!
If you want lots of practice, Mr Corbett has a great set of currency conversion questions.
For lots of simple questions click here and the answers are here
Exam-style questions are here** and the answers are here. (Mr Corbett doesn’t use Ratio Grids so his methods won’t look the same, but the answers are all the same, obviously!)
** Some of these questions are really challening – they may require 2 ratio grids, so think carefully! If an exchange rate changes, you will need a new grid for the new rate.
Introduction to Percentages
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.
Solving Ratio Problems
If you don’t yet know how to work out the 4th number in a ratio grid, watch this video first!
The videos on this page use the worksheet “Ratio Problems” which you can download:
Answers
Introduction to Ratio Grids
Ratio Grids can be used whenever you have a problem that starts with 3 numbers, and you have to times and divide. They are a clear way of laying out your working, and knowing which order to do the calculation.
You will need a calculator to do the practice questions, but first, here are 2 videos. The first shows you how to solve a small ratio grid, the second deals with the larger ones:
Your comments are very welcome – please use the box below.
Now you can use Ratio Grids to solve a Maths Problems, here are some types of problem you can try:
Recommending mathsbot.com
I am grateful to Mr. Holding who teaches locally for this link. So simple! Lots of GCSE questions presented one at a time. A couple of examples are reproduced below.
http://mathsbot.com/gcseQuestionshttp://mathsbot.com/gcseQuestions
The Proof Questions on this site are invaluable – the best collection I have seen.
Ratio Grids Topic Overview
I invented “Ratio Grids” to help students who struggle with Proportional Reasoning. The philosophy includes:
- All proportional reasoning sums are essentially the same – times 2 numbers and divide by a third. If one of the numbers is one, then it’s just a multiply or a divide.
- Students who get used to working a problem “forwards” often struggle to work backwards, but mathematically there is no difference!
- Skills gained working with ratios can be applied to shopping, percentages, similar shapes, stratified sampling, speed, density, and other “per” problems, Direct and Inverse proportion, currency conversions, unit conversions and the Sine Rule, without learning shed loads of new stuff.
- Students often get in a muddle because they do sums and lose hold of the units of numbers so although they get a correct answer they don’t realise what it means! Ratio hold the units of numbers as well as the numbers themselves.
- Students sometimes try to mix different units inappropriately in their working. With ratio grids this is much less likely.
- Start at the beginning with the Introduction to Ratio Grids
Maths Tutor Bournemouth 
