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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 3: miscellaneous questions. 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

If two-thirds of the pupils in a class are right-handed, what is the ratio of left-handed to right-handed pupils?

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2

Anthony and Declan share some money. If Anthony gets three-eighths of the money express the ratio of Anthony's share to Declans share.

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3

Earth Topographic Map (public domain)
Roughly seven-tenths of the Earth's surface is covered by sea water. Express the ratio of sea covered land to dry land as a ratio.

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4

Write the ratio of the area of dry land to the Earth's total surface area.

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5

In Stan's Soap Shop twice as many bars of soap were white than pink. Half as many bars of soap were yellow than pink. What is the ratio of yellow to white bars of soap?

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6

A pencil is of length 13.5cm and a pen is of length 14.5cm. What is the ratio of the length of the pencil to the length of the pen?

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7

What fraction of the length of the pen is the difference between their lengths?

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8

Sal keeps a record of the colours of cars passing under a bridge. There were 72 light-coloured cars, 75 dark-coloured cars and 78 mixed-coloured cars. Express this data as a ratio of light-coloured to dark-coloured to mixed-coloured cars.

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9

What fraction of the cars were not mixed-coloured cars?

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10

A basket contains a number of balls. \( \frac{6}{11} \) of the balls are red and the rest are green. What is the ratio of the number of red to green balls?

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11

A box contains a number of counters. \( \frac{15}{32} \) of the counters are blue and the rest are yellow. What is the ratio of the number of blue to yellow counters?

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12

Express the ratio of A to B if:
$$ A = \frac{3}{4} \text{ and } B = \frac{4}{7} $$

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Check

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

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 10 April 'Starter of the Day' page by Mike Sendrove, Salt Grammar School, UK.:

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

Comment recorded on the 24 May 'Starter of the Day' page by Ruth Seward, Hagley Park Sports College:

"Find the starters wonderful; students enjoy them and often want to use the idea generated by the starter in other parts of the lesson. Keep up the good work"

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Description of Levels

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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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