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RATIO

RATIO. Simplifying ratios. Ratios are used to compare one quantity with another quantity. If there are 6 red sweets and 2 green sweets then the ratio of red to green can be written as red : green = 6 : 2. Rearranging the sweets shows that for every 3 red sweets there is 1 green sweet.

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RATIO

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  1. RATIO

  2. Simplifying ratios Ratios are used to compare one quantity with another quantity. If there are 6 red sweets and 2 green sweets then the ratio of red to green can be written as red : green = 6 : 2 Rearranging the sweets shows that for every 3 red sweets there is 1 green sweet. red : green = 3 : 1 Ratios are simplified in a similar way to fractions. 6 : 2 Divide both sides of the ratio by the common factor 2. ÷ 2 ÷ 2 = 3 : 1 A ratio in its simplest form (lowest terms) has integer values that cannot be cancelled further.

  3. Examples • 1 Simplify these ratios. • a 49 : 28 b 36 : 48 49 : 28 36 : 48 ÷ 7 ÷ 7 ÷ 12 ÷ 12 = 7 : 4 = 3 : 4 • 2 Simplify these ratios. • a 0.6 : 0.7 b 1.2 : 3.4 0.6 : 0.7 1.2 : 3.4 × 10 × 10 ×10 × 10 = 12 : 34 = 6 : 7 ÷ 2 ÷ 2 = 6 : 17

  4. 3 Simplify these ratios. • ab × 4 × 4 × 15 × 15 = 3 : 2 = 10 : 12 ÷ 2 ÷ 2 = 5 : 6 • 4 Simplify these ratios. • a 9 cm : 2 m b 3 kg : 200 g 9 cm : 2 m 3 kg : 200 g = 9 : 200 = 3000 : 200 ÷ 100 ÷ 100 = 30 : 2 ÷ 2 ÷ 2 = 15 : 1

  5. Dividing quantities in a given ratio Paulo wants to share $20 between Alano and Bernardo in the ratio 3 : 2. This means that the $20 is divided into 3 + 2 = 5 parts. Each part is worth $20 ÷ 5 = $4. Alano receives 3 parts. Bernardo receives 2 parts. $4 $4 $4 $4 $4 Alano receives $12. Bernardo receives $8.

  6. Example Paulo wants to share $54 between Alano, Bernardo and Carlos in the ratio 2 : 1 : 3. How much does each receive? Total number of parts = 2 + 1 + 3 = 6 Value of 1 part = $54 ÷ 6 = $9 $9 $9 $9 $9 $9 $9 Alano Bernardo Carlos Alano receives $18. Bernardo receives $9. Carlos receives $27.

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