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Ratio

Ratio. Comparison of two numbers Expresses the relative size of two quantities as the quotient of one divided by the other Written in 3 ways: a:b or a/b or a to b. Example. Suppose there are 78 are women and 162 are men in a class

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Ratio

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  1. Ratio • Comparison of two numbers • Expresses the relative size of two quantities as the quotient of one divided by the other • Written in 3 ways: a:b or a/b or a to b

  2. Example • Suppose there are 78 are women and 162 are men in a class Numerically women to men would be expressed as: 78 : 162 78 to 162 78/162 Could reduce to 13/27 or decimal of 0.481481 • Would be the opposite putting the value for men first.

  3. The order in which the ratio is written is important because it defines the comparison • Ratios should be left in their original form to represent the size of the sample compared • In our example • Ratio of women to men is 78 to 162 • Notice that, in the expression "the ratio of women to men", “women" came first. • This order is very important, and must be respected:  whichever word came first, its number must come first. • If the expression had been "the ratio of men to women", then the ratio would have been “162 to 78"

  4. However… • This points out something important about ratios: the numbers used in the ratio might not be the absolute references. • The ratio “78 women to 162 men" refers to the absolute numbers of women and men, respectively. • But if we reduce the values , “13 to 27" just tells you that, for every 13 women, there are 27 men. • This also tells you that, in any representative set of 40 people (13 + 27 = 40) from this group, 13 will be women and 27 men.

  5. Units in Ratios • Ratios may or may not have units – it depends on what you are comparing • In some cases units may cancel out Express the ratio in simplest form: $10 to $45 This means that you should write the ratio as a fraction, and you should then reduce the fraction: 10/45 = 2/9 Note that the units "canceled" on the fraction, since the units, "$", were the same on both values. So there is no unit on the answer

  6. Ratios and Units • Express the ratio in simplest form: 240 miles to 8 gallons • In this case, you would have (240 miles)/(8 gallons) = (30 miles)/(1 gallon) In more common language, 30 miles per gallon. • Properly, this answer should have units on it, since the units, "miles" and "gallons", do not cancel out.

  7. Ratios are said to be in proportion when their corresponding fractions are equal 78/162 = 13/27 OR 78:162 = 13:27

  8. Write each ratio in simplest form. 32:20 15:33 149 21 48

  9. A statement that two ratios are equal. A comparison of one fraction to another For example: What is a Proportion? • = X • 162 193

  10. Solve the Problem • Cross Multiply and set up an equation • women = X women • 162 men 193 men (78) (193) = (162) X 15054 = 162 X 15054 = X 162 X = 92.9259 women X = 93 women

  11. Check your answer to see if the equations are equal 78 = 92.93 162 193 78/162 = 0.48 92.93/193 = 0.48 The Proportion is true if the both fractions reduce to the same value.

  12. Check your answer to see if the equations are equal 78 X 193 = 15054 92.9259 X 162 = 15054 15054 15054 • = 92.9259 • 162 193 = 1

  13. State whether the ratios are proportional. yes or no • = 2 7 28 2 = 6 11 33 7 = 30 10 21 40 = 4 50 5

  14. Practice • If 18 plums weigh 54 ounces, then 27 plums weigh _____ ounces. • If 40 nails hold 5 rafters, then 96 nails hold ______ rafters. • If 60 sliced mushrooms are on 4 pizzas, them ______ sliced mushrooms are on 15 pizzas.

  15. Making Pancakes This many? OR This many??

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