Unitary Method

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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)

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1) If three bicycle lamps cost £15 how much would eight lamps cost?	Working: pounds
2) If 160g of pumpkin can make enough soup for two people, what weight of pumpkin is needed to make soup for five people?	Working: g
3) If five tins of paint are enough for fifteen doors, how many doors would three tins of paint cover?	Working: doors
4) A student can jog 9km in 45 minutes. At the same speed how long would it take him to jog 2km?	Working: minutes
5) A student can swim six lengths in 30 minutes. At the same speed how long would it take her to swim five lengths?	Working: minutes
6) A recipe for samosas requires 480g of flour for eight samosas. How much flour will be needed for three samosas?	Working: g
7) Two carpenters are buying wood to make some shelves. If 42m of wood is needed for seven shelves how much wood do they need for two 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 twelve plays of the track last 42 minutes how many minutes would ten 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 7 times in 42 minutes. How many minutes would it take to complete 5 versions of this page assuming the student did not get any faster with practice?	Working: minutes

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 Proportion Exam Help Ratio

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