What is a ratio

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What is a ratio?

• The ratio of male students to female students at
  a school is 23.
• The ratio of juice concentrate to water is 13.
• Josie rode her skateboard 5 miles per hour.

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What is the difference between a ratio and a
fraction?

• Can a ratio always be interpreted as a fraction?

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Some ratios or rates cant be written as fractions

• Josie rode her skateboard 5 miles per hour.
• There is no whole, and so a fraction does not
  really make sense.

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What is a proportion?
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Proportions

• A comparison of equal fractions
• A comparison of equal rates
• A comparison of equal ratios

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Ratios and Rates

• If a b c d, then a/b c/d.
• If a/b c/d, then a b c d.
• Example
• 35 boys 50 girls 7 boys 10 girls
• 5 miles per gallon 15 miles using 3 gallons

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Exploration 6.3

• 1 Do a and b on your own. Then, discuss with a
  partner.

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Additive vs Multiplicative relationships

• This year Briana is making 30,000. Next year
  she will be making 32,000.
• How much more will she be making next year?
• What is her increase in salary?
• How does her salary next year compare with her
  salary this year?

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We can add fractions, but not ratios

• On the first test, I scored 85 out of 100 points.
• On the second test, I scored 90 out of 100
  points.
• Do I add 85/100 90/100 as
• 175/200 or 175/100?

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Exploration 5.18

• When will a fraction be equivalent to a repeating
  decimal and when will it be equivalent to a
  terminating decimal?
• Why does a fraction have to have a repeating or
  terminating decimal representation?
• 5

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What is the meaning of?

• proportional to

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To determine proportional situations

• Start easy
• I can buy 3 candy bars for 2.00.
• So, at this rate, 6 candy bars should cost
• 9 candy bars should cost
• 30 candy bars should cost
• 1 candy bar should cost this is called a unit
  rate.

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To determine proportional situations

• Cooking If a recipe makes a certain amount, how
  would you adjust the ingredients to get twice the
  amount?
• Maps (or anything with scaled lengths) If 1 inch
  represents 20 miles, how many inches represent 30
  miles?
• Similar triangles.

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To solve a proportion

• If a/b c/d, then ad bc. This can be shown by
  using equivalent fractions.
• Let a/b c/d. Then the LCD is bd.
• Write equivalent fractionsa/b ad/bd and c/d
  cb/db bc/bd
• So, if a/b c/d, then ad/bd bc/bd.

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To set up a proportion

• I was driving behind a slow truck at 25 mph for
  90 minutes. How far did I travel?
• Set up equal rates miles/minute
• 25 miles/60 minutes x miles/90 minutes.
• Solve 25 90 60 x x 37.5 miles.

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Reciprocal Unit Ratios

• Suppose I tell you that can be exchanged for 3
  thingies.
• How much is one thingie worth?
• 4 doodds/3 thingies means 1 1/3 doodads per
  thingie.
• How much is one doodad worth?
• 3 thingies/4 doodads means3/4 thingie per doodad.

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Exploration 6.4

• Part 1 a, b, c, e, f
• Solve each of these on your own and then discuss
  with your partner/group.

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Ratio problems

• Suppose the ratio of men to women in a room is
  23
• If there are 10 more women than men, how many men
  are in the room?
• If there are 24 men, how many women are in the
  room?
• If 12 more men enter the room, how mnay women
  must enter the room to keep the ration of men to
  women the same?

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Strange looking problems

• I see that 1/4 of the balloons are blue, and
  there are 6 more red balloons than blue.
• Let x number of blue balloons, and so x 6
  number of red balloons.
• Also, the ratio of blue to red balloons is 1 3
• Proportion x/(x 6) 1/3
• Alternate way to think about it. 2x 6 4x

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Lets look again at proportions

• Explain how you know which of the following rates
  are proportional?
• 6/10 mph
• 1/0.6 mph
• 2.1/3.5 mph
• 31.5/52.5 mph
• 240/400 mph
• 18.42/30.7 mph
• 60/100 mph