# Unitary Method

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

##### Level 1Level 2ProportionExam-StyleDescriptionHelpRatio

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 £8 how much would nine lamps cost? Working: pounds If 90g of pumpkin can make enough soup for three people, what weight of pumpkin is needed to make soup for seven people? Working: g If nine tins of paint are enough for twenty seven doors, how many doors would two tins of paint cover? Working: doors A student can jog 5km in 15 minutes. At the same speed how long would it take him to jog 2km? Working: minutes A student can swim seven lengths in 21 minutes. At the same speed how long would it take her to swim six lengths? Working: minutes A recipe for samosas requires 300g of flour for six samosas. How much flour will be needed for five samosas? Working: g Two carpenters are buying wood to make some shelves. If 25m of wood is needed for five shelves how much wood do they need for four shelves? Assume all of the shelves are the same length and width. Working: m The song "Out of Reach" is put on repeat play. If eight plays of the track last 28 minutes how many minutes would six plays take? Working: minutes 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 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 7 times in 42 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.

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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