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Ratios

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Ratios

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  1. Ratios

  2. What is a Ratio? A ratio is a way of writing how much of something there is compared to another thing. e.g. If you have 3 apples and 2 oranges the ratio of apples to oranges is; 3 : 2

  3. e.g. A basket has 30 biscuits, 5 apples, 1 cake and 7 mandarins. What is the ratio of; • Apples to mandarins? • Mandarins to apples? • Cake to biscuits? • Apples to cake? • Biscuits to mandarins to apples? 5 : 7 7 : 5 1 : 30 5 : 1 30 : 7 : 5

  4. Simplifying Ratios Sometimes ratios have very large numbers. We can use smaller numbers to write equal ratios. We do this by dividing both numbers by the same amount. 10 : 5 divide both by 5 = 2 : 1 8 : 6 divide both by 2 = 4 : __ 4 : 12 divide both by __ = __ : 3 15 : 9 divide both by __ = __ : __ 200 : 300 divide both by __ = __ : __ 3 4 1 3 5 3 100 2 3

  5. Simplify these ratios • 1 : 2 • 1 : 3 • 3 : 4 • 3 : 1 • 7 : 3 • 7 : 2 • 3 : 2 • 10 : 1 • 3 : 8 • 3 : 7 • 16 : 24 • 6 : 33 • 55 : 15 • 13 : 39 • 36 : 18 • 24 : 28 • 8 : 24 • 44 : 444 • 0.5 : 4 • 20 : 0.1 • 2 : 3 • 2 : 11 • 11 : 3 • 1 : 3 • 2 : 1 • 6 : 7 • 1 : 3 • 11 : 111 • 1 : 8 • 200 : 1 • 5 : 10 • 7 : 21 • 12 : 16 • 9 : 3 • 21 : 9 • 49 : 14 • 36 : 24 • 100 : 10 • 33 : 88 • 6 : 14

  6. Using Ratios The first way to use ratios is if you are given an amount of for one of the numbers you can figure out how much there is of the other. e.g. Apples : Oranges 2 : 1 If you have 2 Apples you have 1 Orange If you have 4 Apples you have ___ Oranges If you have 200 Apples you have ___ Oranges If you have 30 Oranges you have ___ Apples If you have 58 Oranges you have ___ Apples 2 100 60 116

  7. Ratios are used to change money from one type to another. e.g. NZ dollars to US dollars 1 : 0.42 How many US dollars is… • 10 NZD • 30 NZD • 400 NZD • 300.5 NZD • 1 million NZD $4.20 USD $12.60 USD $168.00 USD $128.10 USD $420 000 USD

  8. e.g. On New Zealand roads the number of each colour car can be shown as a ratio. The two most common colour cars are red and white. The ratio of red to white is 5 : 8. How many white cars would you expect to see if you saw; • 10 red cars cars? • 50 red cars? How many red cars would you expect to see if you saw; • 64 white cars? • 1176 white cars? 16 80 40 735

  9. Using Ratios to Split Totals Ratios can be used to split total amounts of things. e.g. Use the ratio of 1:3 to split up 440 goats. Step 1 Write the ratio as two fractions. The top number of each fraction is the number in the ratio. The bottom number is the total. 1 : 3 5 : 3 ¼ and ¾ ⅝ and ⅜

  10. Write these ratios as fractions • 2 : 3 • 5 : 9 • 7 : 12 • 13 : 1 • 6 : 2 • 7 : 11 • 100 : 3 • 6 : 93 • 19 : 27 • 12 : 4 : 3

  11. Step 2 Multiply the total by each fraction. This is the a mounts it is split into. e.g. Use the ratio of 1:3 to split up 440 goats. 1 : 3 is ¼ and ¾ ¼ x 440 = 110 goats ¾ x 440 = 330 goats

  12. Rachel and Hemi buy a instant kiwi ticket. Rachel pays $5 and Hemi pays $3. They win $500. They agree to split the winnings according to the ratio of how much they paid for the ticket. • What ratio will they use? • What two fractions does their ratio make? • How much does Rachel win? • How much does Hemi win.