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Unitary Method

Test your understanding of the Unitary Method for solving real life proportion problems with this online, self-marking quiz.

Level 1 Level 2 Proportion Exam-Style Description Help Ratio

This is level 1: calculations that can be done without a calculator You can earn a trophy if you get at least 7 questions correct.

If two bicycle lamps cost £12 how much would three lamps cost?

Bicycle Lamp

Working:

pounds Correct Wrong
If 180g of pumpkin can make enough soup for three people, what weight of pumpkin is needed to make soup for eight people?

Pumpkin

Working:

g Correct Wrong
If five tins of paint are enough for twenty five doors, how many doors would six tins of paint cover?

Working:

doors Correct Wrong
A student can jog 8km in 32 minutes. At the same speed how long would it take him to jog 5km?

Working:

minutes Correct Wrong
A student can swim nine lengths in 27 minutes. At the same speed how long would it take her to swim eight lengths?

Working:

minutes Correct Wrong
A recipe for samosas requires 270g of flour for nine samosas. How much flour will be needed for eight samosas?

Working:

g Correct Wrong
Two carpenters are buying wood to make some shelves. If 15m of wood is needed for three shelves how much wood do they need for two shelves? Assume all of the shelves are the same length and width.

Working:

m Correct Wrong
The song "Out of Reach" is put on repeat play. If eighteen plays of the track last 63 minutes how many minutes would ten plays take?

Working:

minutes Correct Wrong
Given the information in the previous question, how many times would the track have to be repeated to last three and a half hours?

Working:

times Correct Wrong
Each time this page is refreshed you will get slightly different questions although it should take about the same amount of time to answer all ten questions. If a student refreshed and answered all the questions on this page 8 times in 32 minutes. How many minutes would it take to complete 3 versions of this page assuming the student did not get any faster with practice?

Working:

minutes Correct Wrong
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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.

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Description of Levels

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Level 1 - Calculations that can be done without a calculator.

Level 2 - Calculations requiring written working and the use of a calculator.

Proportion Direct and inverse proportion questions.

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

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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These problems can be solved using the unitary method. This is a technique in mathematics for solving particular types of problems. It involves scaling down one of the variables to a single unit, i.e. 1, and then performing the operation necessary to alter it to the desired value.

For example if six coins weigh 66g. What would seventeen coins weigh?

Coin Coin Coin
Coin Coin Coin

Consider the weight of one coin first

1 coin weighs 11g  (66 ÷ 6)

Now it is easy to calculate the cost of seventeen coins

17 coins weigh 187g (17 x 11)

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.

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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