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Ratio and Proportion In this lesson, we will learn how to: • define ratio and direct proportion. • compare two quantities multiplicatively in terms of a ratio and proportion. • solve word problems involving ratios and proportions. Real life examples We use ratios and proportions in our daily life without realising it. You must have heard your mum saying “for every 2 cups of flour, we add half cup of sugar” whenever she shares a recipe with someone. Little friends, have you ever prepared a juice mixture from concentrated juice and water? If you ever have, what proportion of concentrated juice to water did you use? Ratios Ratios are used to compare two quantities of the same kind or quantities measured in the same unit. A ratio can be written in the form: a:b or a . b Example The ratio of Fidget Spinners to Top Spinners is 3 : 2 Example Write down the following quantities in terms of a (i) ratio and a (ii) fraction. (a) 4 girls to 3 boys (b) 12 blue pens to 17 red pens Solution (a) (i) Girls : Boys = 4 : 3 (ii) Girls : Boys = 4 3 (b) (i) Blue Pens : Red Pens = 12 : 17 (ii) Blue Pens : Red Pens = 12 17 Example of simplifying ratios The ratio Doughnuts: Cupcakes = 2 : 4 which can be simplified to: ÷ 2 2 : 4 ÷ 2 1 : 2 The H.C.F. of 2 and 4 is 2. So, we divide both numbers by 2 Answer: 1 : 2 Example Simplify the following ratios 13:21 (a) 5 : 15 (b) (c) 1.2 : 3.6 4 8 Solution (a) The H.C.F. of 5 and 15 is 5. So, we divide both numbers by 5. ÷ 5 5 : 15 ÷ 5 1 : 3 Answer : 1 : 3 Solution 13:21 7 :17 (b) = Convert to improper fraction 4 8 4 8 78:178 = 4 8 Multiply by 8, the L.C.M. of 4 & 8 = 14 : 17 Solution (c) 1.2 : 3.6 = 12 : 36 Multiply by 10 to obtain whole numbers = 1 : 3 Divide by 12 which is the H.C.F. of 12 and 36 Sharing In Ratio Example Share Rs 5 000 between Shania and Diya in the ratio 3 : 2. Solution Number of equal parts = 3 + 2 = 5 Amount in 1 part = 5 000 ÷ 5 = Rs 1 000 Shania’s share = Rs1 000 × 3 = Rs 3 000 Diya’s share = Rs1 000 × 2 = Rs 2 000 Example The heights of Ronny and his father are in the ratio 2 : 3. If Ronny is 120 cm tall, find the height of his father. 120cm ? Solution Ronny’s Height : Father’s height 2 : 3 × 60 × 60 120 cm : ? Ronny’s father’s height = 3 × 60 = 180 cm Example An orange drink is obtained by mixing orange juice and water in the ratio 2 : 5. If there is 15 ml more water than orange juice, find the amount of orange juice used. Solution Orange juice : Water = 2 : 5 Difference in ratios = 5 – 2 = 3 3 parts = 15 ml 1 part = 15 ÷ 3 = 5 ml Amount of orange juice = 2 parts × 5 = 10 ml Direct proportion Two quantities are in direct proportion if an increase or decrease in one quantity results in an increase or decrease in the other quantity in the same ratio. For example 1 box of chips costs Rs 25 2 boxes of chips will cost Rs 50
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