Transcript Proportions, Ratio, Rate and Unit Rate Review

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
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
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
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).
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

2nd: Divide by the denominator

3rd: Write in word form
30 miles
10 gallons
30 miles ÷ 10 = 3 miles
10 gallons ÷ 10
1 gallon
3 miles per gallon
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!
Proportion
 When a proportion contains a variable, how do you
solve for the variable?
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To solve for the variable you cross multiply!
Example: 6 = x
10
30
30(6) = 10x
180 = 10x
18 = x
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?
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.