Ratio Objective: Use a multiplier to find an unknown value in a ratio that is proportional similar to a ratio given in its lowest terms Terms and Conditions: To the best of the producer's knowledge, the presentation’s academic content is accurate but errors and omissions may be present and Brain-Cells: E.Resources Ltd cannot be held responsible for these or any lack of success experienced by individuals or groups or other parties using this material. The presentation is intended as a support material for GCSE maths and is not a comprehensive pedagogy of all the requirements of the syllabus. The copyright proprietor has licensed the presentation for the purchaser’s personal use as an educational resource and forbids copying or reproduction in part or whole or distribution to other parties or the publication of the material on the internet or other media or the use in any school or college that has not purchased the presentation without the written permission of Brain-Cells: E.Resouces Ltd.
A ratio is a way of comparing things from their numerical values. On the Titanic, for example, there were, approximately 325 first, 300 second and 700 third class passengers. We could use a ratio to show a comparison as a ratio in this way… First : Second : Third 325 : 300 : 700 65 : 60 : 140 13 : 12 : 28 We usually write a ratio in its lowest terms The colons are used instead of the word ‘to’ Divide all by 25 Divide all by 5
Write these ratios in their lowest terms 1. 12 : 60 2. 45 : 150 3. 12 : 36 : 72 4. 9 : 81 : 270 5. 15 : 100 : 225 6. 18 : 54 : 144 7. 21 : 84 : 133 8. 24 : 108 : 228 Write these ratios in their lowest terms
Write these ratios in their lowest terms 1. 12 : 60 1 : 5 2. 45 : 150 3 : 10 3. 12 : 36 : 72 1 : 3 : 6 4. 9 : 81 : 270 1 : 9 : 30 5. 15 : 100 : 225 3 : 20 : 45 6. 18 : 54 : 144 1 : 3 : 8 7. 21 : 84 : 133 3 : 12 : 19 8. 24 : 108 : 228 2 : 9 : 19 Write these ratios in their lowest terms
Finding unknown values in a ratio that is proportionally similar to a ratio given in its lowest terms
We can also do the reverse and multiply all the numbers in a ratio We can also do the reverse and multiply all the numbers in a ratio. Here, for example, we start with… …and then multiply each number by 4 1 : 3 : 5 x 4 x 4 x 4 We can use this fact to solve ratio problems like… 4 : 12 : 20 This is the same ratio increased by the multiplier 4
Cement : Sand : Pebbles 1 : 3 : 6 14 : 42 : 84 Concrete is made from cement, sand and pebbles in the ratio 1 : 3 : 6. How much cement and sand will be required to mix with 84 kg of pebbles? Cement : Sand : Pebbles Find the multiplier that increases 6 to 84 84 ÷ 6 = 14 1 : 3 : 6 x 14 x 14 x 14 Check 14 : 42 : 84 Now, use the same multiplier to find the unknown values
A cleaning fluid contains three chemical – X, Y and Z - in the ratio 3 : 5 : 12. What amounts of chemicals X and Z will be needed to mix with 32 litres of chemical Y? Multiply 3 and 5 by 6.4 to find the missing numbers Find the multiplier from 5 to 12 X : Y : Z 3 : 5 : 12 x 6.4 x 6.4 x 6.4 32 ÷ 5 = 6.4 Want these two numbers 19.2 : 32 : 76.8 Check that it works
Find the missing numbers for these ratios: 1. 4. 1 : 3 : 7 4 : 5 : 7 4 : 12 : 28 17 : 21.25 : 29.75 2. 5. 5 : 6 : 11 3 : 7 : 13 40 : 48 : 88 10.5 : 24.5 : 45.5 3. 6. 4 : 5 : 7 7 : 11 : 15 12 : 15 : 21 17.5 : 27.5 : 37.5
Here are two questions that are similar to ones that have been on exam papers….
T. Glue : Handle : Screws 2 : 12 : 27 450 : 2700 : 6075 A firm makes flat pack furniture and each pack contains tubes of glue, handles and screws in the ratio 2 : 12 : 27. How many tubes of glue and screws will be required for 2700 handles? T. Glue : Handle : Screws Find the multiplier that increases 12 to 2700 Check 2 : 12 : 27 x 225 x 225 x 225 450 : 2700 : 6075 Now, use the same multiplier to find the unknown values 2700 ÷ 12 = 225
Find the multiplier from 7 to 94.5 A paint contains three chemical – A, B and C - in the ratio 5 : 7 : 17. What amounts of chemicals A and B will be needed to mix with 94.5 litres of chemical B? 94.5 ÷ 7 = 13.5 Find the multiplier from 7 to 94.5 A : B : C 5 : 7 : 17 Check that it works x 13.5 x 13.5 x 13.5 Multiply 5 and 17 by 13.5 67.5 : 94.5 : 229.5