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Ratios vs Fractions

Exercises on the language of ratios and calculations involving fractions and linear functions.

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This is level 4: graphs of linear functions describing ratios. You will be awarded a trophy if you get at least 9 answers correct and you do this activity online.

Type in fractions using a forward slash like this 3/8 for three eighths.  Give ratios and fractions in their lowest terms.


Frozen orange juice concentrate was introduced when scientists discovered a method to remove the water from fresh orange juice, creating a concentrate. When you are thirsty simply add chilled water to the concentrate in the ratio 6:1 (water to concentrate)

The graph below represents this six to one ratio

Linear function
Use the graph to answer the following questions:

How many glasses of water would be needed to mix with 7 glasses of concentrate?


How many jugs of concentrate would be needed to mix with 18 jugs of water?


The Someday printing company has a logo which fits into a rectangular space.
Someday logo
The graph show the possible dimensions of the logo.

Linear function
What is the ratio of the width to the height of this logo?


What is the height in centimetres of a copy of the logo that is 15cm wide?


The graph below shows how various quantities of a certain hue of green paint can be made by mixing together yellow and blue paint.

Linear function
What is the ratio of yellow to blue paint represented by this graph?


What fraction of a tin of blue paint would be needed to mix with one tin of yellow paint to produce the same hue of green paint?


The graph shows the recommended minimum ratio of instructors to young people for hill walking activities. The graph is a line segment from (13,2) to (78,12).
Linear function
What ratio of instructors to young people does the graph represent?


When using the graph above to work out the number of instructors for a particular number of young people it would not be possible to have a faction on an instructor so the number of instructors should always be rounded up to the next whole number.

How many instructors would be required for a group of 60 young people?


The ratio \(y:x\) is equal to \(2:1\).
On squared or graph paper draw the graph of \(y\) as a function of \(x\) for \(x \le 10\).

What is the equation of your graph?


The ratio \(y:x\) is equal to \(7:1\).

What is the equation of the graph of this relationship?


The ratio \(y:x\) is equal to \(1:5\).

What is the gradient of the graph of this relationship?


The ratio \(y:x\) is equal to \(3:2\).

What is the equation of the graph of this relationship?


This is Ratios vs Fractions level 4. You can also try:
Level 1 Level 2 Level 3


Try your best to answer the questions above. Type your answers into the boxes provided leaving no spaces. As you work through the exercise regularly click the "check" button. If you have any wrong answers, do your best to do corrections but if there is anything you don't understand, please ask your teacher for help.

When you have got all of the questions correct you may want to print out this page and paste it into your exercise book. If you keep your work in an ePortfolio you could take a screen shot of your answers and paste that into your Maths file.

Why am I learning this?

Mathematicians are not the people who find Maths easy; they are the people who enjoy how mystifying, puzzling and hard it is. Are you a mathematician?

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"A really useful set of resources - thanks. Is the collection available on CD? Are solutions available?"

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Learning and understanding Mathematics, at every level, requires learner engagement. Mathematics is not a spectator sport. Sometimes traditional teaching fails to actively involve students. One way to address the problem is through the use of interactive activities and this web site provides many of those. The Go Maths page is an alphabetical list of free activities designed for students in Secondary/High school.

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Are you looking for something specific? An exercise to supplement the topic you are studying at school at the moment perhaps. Navigate using our Maths Map to find exercises, puzzles and Maths lesson starters grouped by topic.


If you found this activity useful don't forget to record it in your scheme of work or learning management system. The short URL, ready to be copied and pasted, is as follows:

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Description of Levels


Ratio - Try this exercise first if you are unsure about ratio

Fractions - Try this exercise first if you are unsure about fractions

Level 1 - Questions with pictures (no cancelling required)

Level 2 - Questions without pictures (cancelling required)

Level 3 - Miscellaneous Questions

Level 4 - Graphs of linear functions describing ratios

More on this topic including lesson Starters, visual aids, investigations and self-marking exercises.

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

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Help Video For Basic Ratio

This video was made for the basic Ratio exercise. If you are unsure abour ratios or fractions you may want to try the following exercises first:

Ratio   Fractions

Don't wait until you have finished the exercise before you click on the 'Check' button. Click it often as you work through the questions to see if you are answering them correctly. You can double-click the 'Check' button to make it float at the bottom of your screen.

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

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