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

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.

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:

Using Ratio Grids
Larger Ratio Grids

Click here for asnwers

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:

Points of view (changing the subject of an equation)

This post is practicing simple equations. In 3 days there will be another one to change the subject of more simple equations. If you write your answers in the box at the bottom I will check them and reply to you. I won’t publish them on the page though!

  • “I am forty-one years older than you” is my point of view. In algebra language I would write R=C+41
  • What’s your point of view?
  • C=R-41

Looking at some of the people in my family then,

  • R=D+26 (I am 26 years older than D, my oldest daughter)
  • What’s her point of view?
  • D=R-26

Now let’s look at another relationship in my family,

  • R=G+28
  • Who is older? R or G?
  • R is older than G, by 28 years.
  • so how would G see it?
  • G=R-28

Now here’s something you can work out,  given I am 54 at the moment,

  1. How old is C?
  2. How old is D?
  3. How old is G?
  4. One more person in my family is T. R=T (that’s my point of view) How old is T?
  5. What is T’s point of view, in other words write T=…

 

Not SOH CAH TOA

Dear H,

We have just spent 2 lessons on Trigonometry and here is the writeup as promised. You were getting everything right but these notes are in case you forget a small step and need to revise.

Sorry you couldn’t remember SOH CAH TOA, but it’s really quite complicated, what with labelling the triangle, writing out SOH CAH TOA, remembering which way round they go, what they mean and how to use them…

So anyway we were just using the SINE RULE and CROSS SUMS to find the missing side or the missing angle.

Before you start, make sure you have revised

  • Cross Sums
  • Pythagoras’ Theorem

Finding an unknown side, given a right angled triangle, with one known side and one known angle.

      1. Work out the value of the missing angle and write it into the correct corner. (For example, the 3rd angle in a 90/42/? triangle would be found by doing 180-90-42=)
      2. Draw a cross sum. In the top line, write the KNOWN SIDE and an x (or ?, or whatever the exam is calling the side you are looking for. In the images below we labelled it “?”)
      3. Underneath the KNOWN SIDE write down the sin of its opposite angle
      4. Underneath the “?” side, write the sine of its angle. That’s sin(?)
      5. Write down the sum you plan to type into your calculator
      6. And do it!
      7. Write the answer back on the diagram and check it looks sensible

Finding an unknown angle given a right angled triangle, with two known sides.

  1. If the Hypotenuse is unknown you will have to use PYTHAGORAS’ Theorem to find it, first.
  2. Draw a cross sum. In the top line, write the KNOWN SIDES and an x (or ?, or whatever the exam is calling the side you are looking for. In the images below we labelled it “?”)
  3. underneath the known sides, write sin(of their opposite angle), one should be sin(90), the other will be sin(?)
  4. Write down the sum you plan to type into your calculator
  5. This time the cross sum’s answer will be weird (0.67834 in the example below) and you need to write sin(?)= 0.67834 or whatever.
  6. You found the sine of the angle – to find the angle itself, press Shift, Sin, ANS, =
  7. Write the answer onto the diagram and check it looks reasonable.

If the hypotenuse and one other side is given, then you wont need Pythagoras. So its easier.

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.

This slideshow requires JavaScript.

Game – Prime Number Recognition

You will need:

2 dice and a pen and paper.

Take in turns to:

  • Throw the dice
  • From the dice, construct 2 or perhaps 3 numbers. For example, if you throw a two and a three, you can make 5, 23 and 32 (3+2=5, two followed by three is 23 and three followed by two is 32)
  • Score one point for each prime number you have made (so this example scores one for the 5 and one for the 23, scoring two points in total).
  • If you need to use a calculator, then a Casio fx-83GT PLUS can tell you whether a number is prime. This is *not* cheating – students will soon start to recognise the primes they need, rather than having to check using the calculator!

The Winner Is:

The person who has the most points.

Things to discuss:

  • Why are two even numbers always such bad news? (even+even=even and the only even prime number is two)
  • Is it possible to score three points with one throw?
  • If there is a six in your throw, what happens?

This sample space diagram may help:

Sample Space Diagram for 2 Dice

1

2

3

4

5

6

1

(1,1)

(2,1)

(3,1)

(4,1)

(5,1)

(6,1)

2

(1,2)

(2,2)

(3,2)

(4,2)

(5,2)

(6,2)

3

(1,3)

(2,3)

(3,3)

(4,3)

(5,3)

(6,3)

4

(1,4)

(2,4)

(3,4)

(4,4)

(5,4)

(6,4)

5

(1,5)

(2,5)

(3,5)

(4,5)

(5,5)

(6,5)

6

(1,6)

(2,6)

(3,6)

(4,6)

(5,6)

(6,6)

 

 

 

How to Factorise a Number (Or Check that is Prime) using a CASIO fx-83GT PLUS calculator

On the CASIO fx-83gt PLUS factorising is done like this:

  • Entering the number,
  • press equals,
  • SHIFT and ., ,,, (this has “FACT” written above it in yellow).
  • The Prime Factor Form is displayed as the answer.
  • If the number is Prime, then the number itself is displayed.

This is a natural way to introduce what indices mean, because the CASIO gives the answers in index form eg 34 rather than 3x3x3x3

Understanding Mean and Median

For a collection of questions that encourages students to *think* about mean and median rather than just crunch numbers, there’s no resource to beat this one that is available free to download from the TES site. (You will need to create a TES login account – that’s free too).

https://www.tes.com/teaching-resource/mean-and-median-problems-and-practice-11180656