Proportions, Ratio, Rate and Unit Rate Review

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Proportions, Ratio, Rate and Unit Rate Review
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Ratio

• What is a ratio?
• A ratio is a comparison between two numbers.
• What is an example of a ratio?
• There are 15 boys in a class and 8 girls. A
  ratio to represent the class would be 15 8, 15
  to 8 and 15
• 
  8
• You drove 30 miles in 45 minutes. A ratio to
  represent this situation is 30 45, 30 to 45 and
  30
• 
  45
• Order DOES matter in a ratio!!! 4 5 is NOT the
  same as 5 4

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Ratio

• How do you find equivalent ratios?
• To find an equivalent ratio multiply the
  numerator and denominator by the SAME number.
• What is an example of equivalent ratios?
• You are given the ratio 4
• 5
• To find an equivalent ratio multiply the top and
  bottom by the SAME number. I am going to use 2
• 4 x 2 8
• 5 x 2 10

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Rate

• What is a rate?
• A rate is a ratio with 2 different units
  (measurement)
• What is an example of a unit?
• You ran 5 miles in 2 hours. A rate to represent
  you running would be 5 miles
• 2 hours
• 5 apples cost 2.00. A rate to represent the
  cost of the apples would be 2.00
• 5 apples
• REMEMBER ALWAYS put money in the numerator!

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Unit Rate

• What is a unit rate?
• A unit rate is a rate with a denominator of 1.
• Do unit rates of two different units?
• YES, unit rates are rates and rates have two
  different units!
• How do we find unit rate?
• 1st Set up a unit rate
• 2nd Divide by the denominator
• 3rd Write your answer in word form (the
  numerator PER the denominator).

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Unit Rate

• What is an example of a unit rate?
• A car drives 30 miles on 10 gallons. To write a
  unit rate follow the three step.
• 1st Set up a rate
  30 miles
• 
  10 gallons
• 2nd Divide by the denominator 30
  miles 10 3 miles
• 
  10 gallons 10 1 gallon
• 3rd Write in word form
  3 miles per gallon

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Proportion

• What is a proportion?
• Proportions are two ratios set equal to each
  other.
• What is an example of a proportion?
• Since a proportion are 2 equal ratios an example
  could be
• 4 8
• 5 10
• How do you know if it is a true proportion?
• The cross-products of the ratios must be equal.
• 4 x 10 40 and 5 x 8 40 It is a
  proportion!

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Proportion

• When a proportion contains a variable, how do you
  solve for the variable?
• To solve for the variable you cross multiply!
• Example 6 x
• 10 30
• 30(6) 10x
• 180 10x
• 18 x

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Proportion

• Now lets try write and solving a proportion.
• There is a ratio of 8 boys to 12 girls in a
  classroom. How many girls would there be if
  there were 12 boys in the classroom?

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Proportion

• If given a ratio how can you form a proportion?
• If given a ratio you can form a proportion by
  finding an equivalent ratio and setting them
  equal to each other.
• Given the ratio 2 to 3 form a proportion.