How to multiply by 12, using Trachtenburg’s Method.
The exam paper referred to in this post can be found here. For each question which is compatible with Ratio Grids, I work through a similar example, then you can try the actual exam question. The answers to the exam paper can be found here. This is a calculator exam.
You will need to be able to complete a ratio grid to follow this page – so watch this 2 minute video!
Similar to Question 4 – write a fraction as a percentage
Similar to Question 13 – A machine filling containers with items – how many left over?
Similar to Question 14: Drawing a Pie Chart
Similar to Question 16. How many marks needed to pass an exam?
Similar to question 17: Making Orange Juice
Similar to question 17b: Simplify a ratio (Calculator method)
Similar to question 19: Sharing money without knowing the total
Similar to question 20: Shopping with a ratio
Similar to question 23: Different sized boxes
Similar to question 28: Exterior angles in a polygon
- For the video of instructions, click HERE
- Worksheet about factorising numbers click here
- To download the worksheet factorising quadratics both numbers positive click here
- For the answers, click here
- For more practice (includes negative coefficients) click here
- For harder questions (larger coefficient of x squared) click here
If you are not already confident using RATIO GRIDS then watch this video first!
What is 35% of £14?
What is 15% of £85?
My savings target is £5500. I have saved £2640. What percentage have I saved?
Jo scored 65% in a test. She scored 26 marks. What was the test marked out of?
A tree was 15m tall in January. Now it is 18m tall. What is the percentage increase in height?
Another tree has grown 15% since January. It is now 46m high. What was its height in January?
Now try some problems yourself:
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.
** 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.
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: