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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 Proportion   Exam     Help     Ratio  

This is level 2: calculations requiring written working and the use of a calculator. You will be awarded a trophy if you get at least 7 answers correct and you do this activity online.

1) If fifteen bricks weigh 105kg. What would eighteen bricks weigh?

Bricks

Working:

kg Correct Wrong
2) If nineteen girls can plant 228 trees in a day. How many trees could twenty nine girls plant in a day?

Trees

Working:

trees Correct Wrong
3) If twenty one workers can dig 420 holes in an hour. How many holes could twenty eight workers dig in an hour?

Building Site

Working:

holes Correct Wrong
4) If nineteen coins weigh 209g. What would thirty coins weigh?

Working:

g Correct Wrong
5) If thirteen buses can seat 663 people. How many people could fourteen buses seat?

Working:

people Correct Wrong
6) Twenty three identical pipes laid end to end make a length of 414m. What length would thirty eight pipes make if they are laid end to end?

Working:

m Correct Wrong
7) 27 toy building blocks placed one on top of another reach a height of 270cm. How high would 73 blocks be if placed one on top of the other?

Working:

cm Correct Wrong
8) 720g of flour is needed to make a special cake for 16 people. How much flour would be needed to make a cake for 33 people?

Working:

g Correct Wrong
9) A vehicle travels three hundred and twenty two km on 23 litres of fuel. How far would it travel on thirty eight litres?

Working:

km Correct Wrong
10) Another vehicle travels two hundred and seventeen km on 31 litres of fuel. How far would it travel on fifty seven litres?

Working:

km Correct Wrong
Check

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.

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.

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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.

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