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Ratio

Use ratio notation, simplify ratios, and divide a quantity into parts based on a given ratio.
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This is level 8: using ratios in real life. You will be awarded a trophy if you get at least 9 answers correct and you do this activity online.

1

A recipe requires mixing flour and sugar in the ratio 7:2 by volume.
How much sugar will be required to mix with 21 cups of flour?

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2

The ratio of the number of red cubes to the total number of small plastic cubes in a classroom is 3:14. How many red cubes are there if there are 560 cubes altogether in the classroom?

Cubes

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3

The number of supporters of two teams at a football match are in the ratio of 5:3. Calculate the number of supporters of the smaller team as a percentage of the number of supporters of the larger team.

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4

Hot dog rolls
Hot dog rolls come in packets of 6
Hot dog sausages come in tins of 8

What ratio of packets of rolls to tins of sausages should I buy to ensure nothing will be left over when making hot dogs (one sausage in each roll)? Give your answer as a ratio in its simplest form.

Hot dog sausages

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5

As a rough approximation the ratio of the circumference to the diameter of any circle is 22:7. Using this approximation find the length of the circumference of a circle if its diameter is 21mm. Give your answer in cm.

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6

Suzie the cat is proud that her picture hangs on the wall in the front room. The ratio of the width to the height of the picture is 10:13. The height is 15cm longer than the width. How wide is Suzie's picture?

Suzie the cat

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7

The ratios of the ages of Maureen, Noreen and Doreen is 2:5:7. If Maureen is 15 years younger than Noreen, how old is Doreen?

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8

A model car is a scale replica of the real car. The ratio of the lengths of the model to the real car is 2:95. If the width of the real car is 2.85 metres, how wide is the model car in centimetres?

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9

Find w if the ratio w:3 is equivalent to the ratio 80:120.

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10

Find y if the ratio y:4 is equivalent to the ratio 3:5.

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11

The angles of a triangle are in the ratio 2:3:4. What is the size of the largest angle?

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12

The scale of a map is 1:50,000. The distance between two road junctions on the map is 7cm. How far are they apart in real life? Give your answer in kilometres.

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Check

This is Ratio level 8. You can also try:
Level 1 Level 2 Level 3 Level 4 Level 5 Level 6 Level 7

There is also a related exercise on the Unitary Method.

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.
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?

Comment recorded on the 17 November 'Starter of the Day' page by Amy Thay, Coventry:

"Thank you so much for your wonderful site. I have so much material to use in class and inspire me to try something a little different more often. I am going to show my maths department your website and encourage them to use it too. How lovely that you have compiled such a great resource to help teachers and pupils.
Thanks again"

Comment recorded on the 14 September 'Starter of the Day' page by Trish Bailey, Kingstone School:

"This is a great memory aid which could be used for formulae or key facts etc - in any subject area. The PICTURE is such an aid to remembering where each number or group of numbers is - my pupils love it!
Thanks"

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Monday, November 9, 2020

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Description of Levels

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Level 1 - Identifying ratios from pictures

Level 2 - Simplifying ratios

Level 3 - Simplifying ratios with mixed units

Level 4 - Reducing a ratio to the form 1:n or n:1

Level 5 - Simplifying ratios with fractional parts

Level 6 - Dividing a quantity in a given ratio

Level 7 - Comparing the parts of a ratio

Level 8 - Using ratios in real life

Retro: Real life problems adapted from an old Mathematics textbook

Exam Style Questions - A collection of problems in the style of GCSE or IB/A-level exam paper questions (worked solutions are available for Transum subscribers).

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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Curriculum Reference

See the National Curriculum page for links to related online activities and resources.

Introduction to Ratios

Please be aware that the levels referenced in this video pertain to the structure of the exercise when it consisted of only seven levels. Following the production of the video, I introduced a new Level 4, focused on simplifying ratios to the form 1:n. Consequently, the previous Level 4 was reassigned as Level 5, Level 5 advanced to Level 6, and this pattern continued accordingly. I am confident you will be able to navigate these changes; my apologies for any inconvenience caused.

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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