1. Ratios 4 Possible Ways to Write a Ratio #1
A ratio is a comparison of two whole numbers in the same unit.
4 Possible Ways to Write a Ratio
5 girls to 7 boys
You solve a ratio by simplifying the fraction.

2. #2
EQUIVALENT RATIOS
To determine if two ratios are equivalent simplify each ratio by dividing.
Since ,
the ratios are equivalent. 1 5 = 3 15
and 9 45 3 15 =
÷ 3 1 5 9 45 =
÷ 9 1 5
The GIANT ONE is used to simplify ratios.

3. The ratio of bikes to skateboards is 5:3, 5 to 3, or
#3 Ratios in Simplest Form
To find the simplest form divide the numerator and denominator by the GCF.
Write the ratio 15 bikes to 9 skateboards in simplest form.
bikes
skateboards 15 9
Write the ratio as a fraction. =
15 ÷ 3
9 ÷ 3 5 3
Simplify. = = 5 3
The ratio of bikes to skateboards is 5:3, 5 to 3, or

4. Ratio vs. Rate #4 A comparison of two whole numbers in the same units.
A comparison of a number to one in different units.
Always written as a single
number on a per unit basis.
Always written as two numbers.
Never write the units.
Always write the units.
Reduce to simplify.
Divide to simplify.

5. # Unit Rate
Unit Rate is a comparison of a number to one in different units.
It is written as a fraction.
You divide to simplify and always include units in your answer.
1) 120 students in 4 classrooms
2) 29 grams per cubic centimeter
Unit Rate is a rate that is reduced to 1 unit

6. Unit Price #6 Unit price is the same as unit rate, but
you divide the $ by the number of items.
Example: For a dozen roses it costs $ What is the unit price?

7. #7 Proportion 1) Write the original proportion. 2) Cross multiply.
3) Divide both sides by 6 to isolate the variable, then simplify.

8. #8 WRITE A PROPORTION
A PROPORTION is an equation that shows two ratios are equivalent.
If it takes 6 cups of flour to make 54 cookies,
how many cookies can be made with 10 cups?
cups 6 10
Let x = the number of cookies =
cookies 54 x 6x =
540
x = 90 cookies

9. Common Measurements Length Time 60 sec. = 1 min. Volume 8 oz. = 1 cup#9
Length
12 inch. = 1 ft
36 inch. = 1 yd.
3 ft. = 1 yd.
5280 ft. = 1 mile
Time sec. = 1 min.
60 min. = 1 hr.
24 hrs. = 1 day
7 days = 1 week
365 days = 1 year
52 weeks = 1 year
Volume oz. = 1 cup
16 oz. = 1 pint
2 pints = 1 quart
4 quarts = 1 gallon
Weight ounces= 1 pound
2000 pounds = 1 ton

10. Conversion Factor #10 Change to minutes Change to inches
A conversion factor is a ratio of two quantities that are equal but use different units. To convert units you must multiply by a common measurement.
Change to minutes
Common Measurement
Change to inches
Common Measurement

11. #11 Dimensional Analysis
Dimensional Analysis is used to convert units. You must express both quantities in the same unit!
Change 10 feet to inches
Change 3 hours to minutes
Change 21 days to weeks

12. #12 Rate Converting Units Your heart beats 70 beats/min. How many
beats per hour is this?
Start
Finish
Rate

13. Rewriting With The Same Units
#13
Rewriting With The Same Units
You want to build a house that is 10 feet high, and you want the model to be 6 inches high. What is the ratio?
You need to express both quantities in the same unit!
Change feet to inches

14. #14 25 x 5 10 Similar Figures = corresponding angles have
Two figures are SIMILAR if they have the same shape
but not necessarily the same size. 25 x 5 = X 10
In similar figures the lengths
of the corresponding sides
are proportional and the
corresponding angles have
equal measures.

15. Corresponding Corresponding means “it goes with” #15 <B and<X
<A and <W
<B and<X
<C and <Y
<D and <Z X W A B D C Z Y
Corresponding Angles
Corresponding Sides

16. #16 Indirect Measurement
Similar figures and proportions can be used
to find an unknown length. This is called
Indirect Measurement. 10 4 x 2