RATIO AND PROPORTION

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UNIT 15

• RATIO AND PROPORTION

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RATIOS

• A ratio is the comparison of two like quantities
• The terms of a ratio must be compared in the
  order in which they are given
• The first term is the numerator of a fraction,
  and the second term is the denominator
• A ratio should be expressed in lowest fractional
  terms
• Express 3 feet to 18 inches as a ratio in lowest
  terms
• Change the quantities to a common unit
• We will change the 3 feet to 36 inches
• Then write the ratio as a fraction and reduce

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PROPORTIONS

• A proportion is an expression that states the
  equality of two ratios
• The product of the means equals the product of
  the extremes
• Solve the proportion below for A

1.2A (14.8)(2.4) Cross Multiply
Divide both sides by 1.2
A 29.6 Ans
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DIRECT PROPORTIONS

• Two quantities are directly proportional if a
  change in one produces a change in the other in
  the same direction
• When setting up a direct proportion in fractional
  form, numerator of first ratio must correspond to
  numerator of second ratio. Denominator of first
  ratio must correspond to denominator of second
  ratio

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DIRECT PROPORTION EXAMPLE

• If reducing calorie intake by 2,000 calories
  results in a weight loss of one pound, how many
  pounds would a person lose if he/she ate 14,500
  less calories?
• Since an increase in calorie reduction will
  result in an increase in weight loss, the
  proportion is direct
• Set calories as the numerator and pounds as the
  denominator in both ratios
• Solve by cross multiplication

x 7.25 pounds Ans
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INVERSE PROPORTIONS

• Two quantities are inversely or indirectly
  proportional if a change in one produces a change
  in the other in the opposite direction
• If an increase in one produces a decrease in the
  other, or if a decrease in one produces an
  increase in the other, the two quantities are
  inversely proportional
• When inverse proportion is set up in fractional
  form, numerator of first ratio must correspond to
  denomi-nator of the second ratio. Denominator of
  first ratio must correspond to numerator of
  second ratio

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INVERSE PROPORTION EXAMPLE

• It takes 3.5 hours for the 12 workers at Bettys
  Bakery to prepare the baked goods sold each day.
  How many hours would it take 15 workers to
  produce the same goods?
• Since more workers would require less time to
  bake the goods, this problem is an inverse
  proportion
• Set numerator of first ratio equal to 3.5 hours
  and set corresponding 12 workers equal to
  denominator of second ratio. Denominator of first
  ratio will be the variable (x hours) and
  numerator of second ratio will be the
  corresponding 15 workers

Now, solving by cross multiplication
x 2.8 hours Ans
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PRACTICE PROBLEMS

• Express the following ratios in lowest terms
• 1. 1628
• 2. 2/5 to 1/3
• 3. 20 min to 1 hour
• Solve the following proportions

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PRACTICE PROBLEMS

• 7. The fifteen workers in the Fly-By-Night
  Machine Shop produce 1200 widgets daily. How many
  widgets would twenty workers produce daily?
• 8. The scale on a given map is 1 inch 32
  miles. How many miles would there be between two
  cities that are 3 inches apart on the map?
• 9. Two gears are in mesh. The driver gear has
  30 teeth and revolves at 250 revolutions per
  minute. Determine the number of revolutions per
  minute of a driven gear with 12 teeth.
• 10. If six identical machines can produce 1000
  parts in 7 hours, how many hours will it take
  four of these machines to produce the same 1000
  parts?

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PROBLEM ANSWER KEY

• 1. 4/7
• 2. 6/5
• 3. 1/3
• 4. 5.6
• 5. 277.55
• 6. 20
• 7. 1600 widgets
• 8. 112 miles
• 9. 625 rpm
• 10. 10.5 hours