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Unitary Method

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

Menu Level 1 Level 2 Level 3 Proportion Exam Help Ratio

This is level 3: problems requiring an algebraic solution. You will be awarded a trophy if you get at least 7 answers correct and you do this activity online.

Give each answer as an algebraic fraction like this: \( \dfrac{ab}{c}\)

Use the forward slash (/) for the fraction line.

1) If \(x\) litres of water is enough for \(y\) people on a sailing passage, how many litres of water is needed for \(z\) people on a passage for the same amount of time?	litres
2) If \(a\) grams of cheese is enough to make \(b\) sandwiches, how many grams of cheese is needed to make \(c\) sandwiches?	grams
3) If \(p\) textbooks weigh \(q\) kilograms altogether, how many kilograms would \(r\) textbooks weigh at the same rate?	kg
4) In a 'Back To School' sale, \(m\) pencils cost \(n\) pence, how many pence would \(k\) pencils cost?	pence
5) If a train travels \(p\) kilometres in \(q\) hours, how many kilometres does it travel in \(r\) hours at the same speed?	km
6) If \(a\) metres of fabric costs \(b\) pounds, how much does \(c\) centimetres of the same fabric cost?	pounds
7) If \(e\) identical machines produce \(f\) items in \(g\) hours, how many items will \(h\) identical machines produce in \(g\) hours at the same rate?	items
8) If \(p\) people eat \(q\) loaves of bread in \(r\) days, how many loaves of bread would \(s\) people eat in \(t\) days, assuming the same rate of consumption per person? *	loaves
9) If \(e\) identical machines produce \(f\) items in \(g\) hours, how many items will \(h\) identical machines produce in \(i\) hours at the same rate? *	items
10) If it costs \(v\) dollars to hire \(w\) thingamabobs for \(x\) minutes, how much would it cost to hire \(y\) thingamabobs \(z\) hours? *	dollars

* groups of letters being multiplied together should be in alphaberical order, for example \( \frac{ace}{bd} \).

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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.

Level 3 - Problems requiring an algebraic solution.

Unit Pricing Learn how to compare prices of items in shops.

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.

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)

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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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