WJEC MATHEMATICS INTERMEDIATE NUMBER RATIO AND PROPORTION

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1 WJEC MATHEMATICS INTERMEDIATE NUMBER RATIO AND PROPORTION 1

2 Contents Simplifying Ratio Simplifying Scale Ratio Sharing in a given Ratio Reverse Ratio Recipes Proportion Credits WJEC Question bank 2

3 Understanding Ratio Ratio shows the proportion between two things. It is represented by two numbers separated by : 2: 3 The above ratio shows that for every 2 of object A there is three of object B Simplifying Ratio Simplifying Ratio is extremely similar to simplifying fractions. Make sure you understand that process in the 'Equivalent Fractions' booklet. Consider the following ratio 24: 36 To simplify this ratio, we need to understand what we can divide 24 and 36 by. They are both even so we can divide them both by 2. 12: 18 Again, these are both even numbers. So divide them both by 2. 6: 9 This time, we cannot divide both numbers by 2. However, both numbers are in the 3 times table so divide them both by 3. 2: 3 This is now fully simplified. Exercise N25 Simplify the following ratios a. 20:35 d. 80:100 b. 20:24 e. 64:56 c. 36:40 f. 49:56 g. 81:63 h. 99:66 i. 12:17 3

4 Simplifying Scale Ratio You may be required to simplify a ratio that involve different units Before simplifying make sure both sides are in the SAME UNITS Example 1 Simplify the following 500g: 3kg The first step is to get the units the same. To answer these questions you will need to know your units and conversions. You can find these in the booklet 'Metric and Imperial Units & Conversions' 500: 3000 There is now no need to write the units as the units are the same. Divide both numbers by 100: 5: 30 Divide both numbers by 5 1: 6 Example 2 Simplify 30 secs 3 mins Putting them both into seconds 30: 180 3: 18 1: 6 Exercise N26 a. 5kg:500g b. 5m:150cm c. 2mins:40secs d. 3litres:600ml e. 5km:900m f. 8kg:1.6kg 4

5 Sharing in a given ratio Very commonly, you are given an amount and instructed to share it in a given ratio. Example Share 49 in the ratio 5:2 The PURSES Method Total amount to share out This means we will give 5 purses to one person and 2 purses to another We have 7 purses and 49 to share equally between them so we need to put 7 in each one So we now know how much each person gets by adding the amounts on each side 35: 14 After completing a few of these questions you won't need to draw purses. The next page shows the same question with the workings shown that you would need to show in an exam. 5

6 Share 49 in the ratio 5:2 5+2=7 (Total purses) 49 7 = 7 (Each Purse) 7 5: : 14 Exercise N27 1. Share 63 in the ratio 7:2 2. Share 56 in the ratio 4:3 3. Share 80 in the ratio 3:1 4. Share 135 in the ratio 3:2 5. Share 147 in the ratio 4:2:1 6. Share 520 in the ratio 5:2:1 7. Share 445 in the ratio 5:3:2 Reverse Ratio For some questions, you won't be given the total, but the value of a proportion from the ratio. When an amount is shared in the ratio 2:3 the largest share is 24. How much was shared in total? Consider the purses for this question These three purses must add to 24 Total amount shared = = 40 6

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8 Recipes You may be given the recipe for making food for a number of people and use proportion to increase the ingredients for more people. Example The ingredients for 12 cakes are as follows: 300g flour 180g butter 150g sugar 2 eggs How much is needed of each of the above ingredients for 30 cakes. There's nothing we can multiply 12 by to get 30, so we need to work out the amount of ingredients needed for a smaller amount first. Working out the ingredients for 6 works because it's easy to get from 12 to 6 ( 2) and easy to get from 6 to 30 ( 5) 6 cakes 150g flour 90g butter 75g sugar 1 egg 30 cakes 750g flour 450g butter 375 sugar 5 eggs 8

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11 Proportion Here's an example question It takes 3 men 6 days to dig 4 gardens. How long will it take 24 men to dig 12 gardens? Begin by putting the information in a table. This makes it easier to see. Men Time (Days) Gardens ? 12 If the same three men dig twelve gardens, it will take 3 times as long. So if the amount of men did not change we can fill in the middle row of the table Men Time (Days) Gardens ? 12 This time we will keep the number of gardens the same, but we have 24 men working (This is 8 times as many). So they should be able to complete the job 8 times as fast. To calculate the number of days, we divide 18 by 8. Men Time (Days) Gardens

12 Exercise N28 1. It takes 6 workers 2 days to build 4 cars. How many days does it take 4 workers to build 8 cars? 2. It takes 4 men 12 days to dig 1 hole. How many days will it take 6 men to dig 3 holes? 3. It takes 15 Robots 6 days working 5 hours a day to complete a job. How many days will it take 25 robots, working 6 hours a day, to complete the same job? 12