# Ratios vs Fractions

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

##### Menu  Level 1Level 2Level 3Graphs  Help    More

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.

 1 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 ratioUse the graph to answer the following questions:How many glasses of water would be needed to mix with 5 glasses of concentrate? ☐ ☐ ✓ ✗ 2 How many jugs of concentrate would be needed to mix with 12 jugs of water? ☐ ☐ ✓ ✗ 3 The Someday printing company has a logo which fits into a rectangular space.The graph show the possible dimensions of the logo.What is the ratio of the width to the height of this logo? ☐ ☐ ✓ ✗ 4 What is the height in centimetres of a copy of the logo that is 24cm wide? ☐ ☐ ✓ ✗ 5 The graph below shows how various quantities of a certain hue of green paint can be made by mixing together yellow and blue paint.What is the ratio of yellow to blue paint represented by this graph? ☐ ☐ ✓ ✗ 6 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? ☐ ☐ ✓ ✗ 7 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).What ratio of instructors to young people does the graph represent? ☐ ☐ ✓ ✗ 8 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 70 young people? ☐ ☐ ✓ ✗ 9 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? ☐ ☐ ✓ ✗ 10 The ratio $$y:x$$ is equal to $$7:1$$.What is the equation of the graph of this relationship? ☐ ☐ ✓ ✗ 11 The ratio $$y:x$$ is equal to $$1:5$$.What is the gradient of the graph of this relationship? ☐ ☐ ✓ ✗ 12 The ratio $$y:x$$ is equal to $$3:2$$.What is the equation of the graph of this relationship? ☐ ☐ ✓ ✗
Check

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

## Instructions

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.

## Transum.org

This web site contains over a thousand free mathematical activities for teachers and pupils. Click here to go to the main page which links to all of the resources available.

## More Activities:

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?

Comment recorded on the 3 October 'Starter of the Day' page by Mrs Johnstone, 7Je:

"I think this is a brilliant website as all the students enjoy doing the puzzles and it is a brilliant way to start a lesson."

Comment recorded on the 1 May 'Starter of the Day' page by Phil Anthony, Head of Maths, Stourport High School:

"What a brilliant website. We have just started to use the 'starter-of-the-day' in our yr9 lessons to try them out before we change from a high school to a secondary school in September. This is one of the best resources on-line we have found. The kids and staff love it. Well done an thank you very much for making my maths lessons more interesting and fun."

Each month a newsletter is published containing details of the new additions to the Transum website and a new puzzle of the month.

The newsletter is then duplicated as a podcast which is available on the major delivery networks. You can listen to the podcast while you are commuting, exercising or relaxing.

Transum breaking news is available on Twitter @Transum and if that's not enough there is also a Transum Facebook page.

#### Car Park Puzzle

Can you get your car out of the very crowded car park by moving other cars forwards or backwards? There are five levels of increasing difficulty and the interactive interface makes this a fun problem solving exercise.

There are answers to this exercise but they are available in this space to teachers, tutors and parents who have logged in to their Transum subscription on this computer.

A Transum subscription unlocks the answers to the online exercises, quizzes and puzzles. It also provides the teacher with access to quality external links on each of the Transum Topic pages and the facility to add to the collection themselves.

Subscribers can manage class lists, lesson plans and assessment data in the Class Admin application and have access to reports of the Transum Trophies earned by class members.

Subscribe

## Go Maths

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.

## Maths Map

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.

## Teachers

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:

Alternatively, if you use Google Classroom, all you have to do is click on the green icon below in order to add this activity to one of your classes.

It may be worth remembering that if Transum.org should go offline for whatever reason, there are mirror sites at Transum.com and Transum.info that contain most of the resources that are available here on Transum.org.

When planning to use technology in your lesson always have a plan B!

Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for those learning Mathematics anywhere in the world. Click here to enter your comments.

For Students:

For All:

Scan the QR code below to visit the online version of this activity.

https://Transum.org/go/?Num=631

## Description of Levels

Close

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.

## 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:

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.

Close