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Ratio Developed by Ivan Seneviratne

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What is a ratio? A ratio is a comparison of two or more numbers. We generally separate the two numbers in the ratio with a colon (:). Remember when writing a ratio, ORDER matters. Example Suppose we want to write the ratio of 8 and 12. We can write this as 8:12 or as a fraction 8/12, and we say the ratio is eight to twelve.

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**Comparing Ratios Example**

To compare ratios, write them as fractions. The ratios are equal if they are equal when written as fractions. Example Are the ratios 3 to 4 and 6:8 equal? The ratios are equal if 3/4 = 6/8.

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What’s the Use? Ratio can be used to solve many different problems, for example recipes, scale drawing and map work. Example A map scale is 1 : On the map the distance between two shopping centers is 4 cm. What is the actual distance between the shopping centers? Give your answer in km.

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**Simplifying Ratios Example**

We can often make the numbers in ratios smaller so that they are easier to compare. You do this by dividing each side of the ratio by the same number, the highest common factor. This is called simplifying. Example In a class the ratio of female to male members is 12:18. Both 12 and 18 can be divided by :9 To make the ratio simpler again, we can divide both 6 and 9 by :3 These are all equivalent ratios.

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Problem Solving The ratio of the number of Malay pupils to the number of Indian pupils is 7 : 4. There are 84 more Malay pupils than Indian pupils. How many Malay pupils are there? Malay Indian 84 ? 7 units – 4 units = 3 units 3 units = 84 pupils 1 unit = 84 ÷ 3 = 28 pupils 7 units = 7 × 28 = 196 pupils There are 196 Malay pupils

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**Ratio Try these: Challenge 1 1 4 4**

The ratio of the number of cows to the number of sheep on a farm is 8 : 5. If there are 120 more cows than sheep, how many cows and sheep are there altogether? The ratio of Jane’s mass to Merlin’s mass is 3 : 5. If their total mass is 96kg, find the difference between Jane’s mass and Merlin’s mass. Sally and Maria shared 180 sweets in the ratio 7 : 2. How many more sweets did Sally get than Maria? A box of paper clips was shared between Ann and Lisa in the ratio of 4 : 11. Ann gave of her paper clips to Lisa. Then Lisa gave of her new number of paper clips to Ann. In the end, Lisa had 60 more paper clips than Ann. How many paper clips did Ann have in the end? Challenge 1 4 1 4

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Ratio Hale, Randy and Ali shared a sum of money in the ratio : 9 : 7. If the largest share was $36, find the smallest share and the total sum of money. Hale Randy Ali ? $36 Largest share is 9 units Smallest share is 4 units 9 units = $ units = 4 × $ 1 unit = 36 ÷ = $ 16 = $ 4 Total sum of money = = 20 units 20 units = 20 × $ 4 = $ 80 The smallest share was $ 16. The total sum of money was $ 80.

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Ratio Try these: Kenny, Roland and Willy shard 250 marbles in the ratio 6 : 8 : 11. How many marbles did Kenny and Roland receive altogether? The lengths of the sides of a triangle are in the ratio : 9 : 6. if the longest side is 54 cm long, find the perimeter of the triangle. 3 boys shared a box of paper clips in the ratio 2 : 9 : 5. If the largest share was 90 paper clips. Find the smallest share and the total number of paper clips.

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This presentation is developed by Ivan Seneviratne © 2006 purely for personal use.

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