Unitary Method

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

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This is level 1: calculations that can be done without a calculator. You will be awarded a trophy if you get at least 7 answers correct and you do this activity online.

 1) If four bicycle lamps cost £24 how much would five lamps cost? Working: pounds 2) If 400g of pumpkin can make enough soup for five people, what weight of pumpkin is needed to make soup for six people? Working: g 3) If three tins of paint are enough for twelve doors, how many doors would two tins of paint cover? Working: doors 4) A student can jog 5km in 25 minutes. At the same speed how long would it take him to jog 3km? Working: minutes 5) A student can swim six lengths in 24 minutes. At the same speed how long would it take her to swim five lengths? Working: minutes 6) A recipe for samosas requires 540g of flour for nine samosas. How much flour will be needed for seven samosas? Working: g 7) Two carpenters are buying wood to make some shelves. If 54m of wood is needed for nine shelves how much wood do they need for four shelves? Assume all of the shelves are the same length and width. Working: m 8) The song "Out of Reach" is put on repeat play. If eighteen plays of the track last 63 minutes how many minutes would fourteen plays take? Working: minutes 9) 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 10) 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 9 times in 45 minutes. How many minutes would it take to complete 4 versions of this page assuming the student did not get any faster with practice? Working: minutes
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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.

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?

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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