1. 4.1 Ratios
Ratio: uses division to compare two numbers. Numbers are usually the same unit of measurement. Do not convert to a decimal or a mixed fraction, denominator not equal to 0.
Read as “the ratio of a to b.”
Written as “a to b”, a:b or a/b
6M 6R 6W
Boys
Girls
What is the ratio of girls to boys in 6M?
What is the ratio of 6R to 6W in our math class?
In our math class, what is the ratio of 6M students to all students?

2. 4.2 Rates
Rate: is a ratio that compare two quantities measured in different units, which is usually expressed as a Unit Rate.
Unit Rate: is a rate whose denominator is 1. Write the rate as a fraction and then divide the numerator and denominator by the denominator.
Show the units of measure.
Word after “per” is in the denominator.
If it drove 150 miles to Washington, DC in 2 hours, what was my speed? (in miles per hour)
If I drove 90 miles to New York in 1 hour and 40 minutes, what was my speed? (in miles per hour)

3. 4.3 Identifying and Writing Proportions
Equivalent ratio: name the same comparison
Proportion: an equation that states that two ratios are equivalent.
Same Denominator
We can use equivalent ratios (fractions) to solve proportions where one number is unknown.
Are 3/5 and 12/20 equivalent ratios?
Common Denominator is 20.
3/5 × 4/4 = 12/20 They are equivalent.
Are 1/3 and 17/48 equivalent ratios?
Common denominator is 48.
1/3 × 16/16 = 16/48. They are not equivalent.

4. 4.4 Solving Proportions
There are at least three ways to solve a proportion: equivalent fractions and cross products, algebra
What is an equivalent fraction to ¾ = x/132 ?
Equivalent Fractions
¾ = x/132 What times 4 is 132? (33)
¾ · 33/33 = 99/132
Cross Products
3 · 132 = 4 · x → 396 = 4x → 396 ÷ 4 = 99
Algebra: What operation is happening?
¾ · 132 = ¾ · 132/1 = 396/4 = 99

5. 4.7 Dimensional Analysis
Unit conversion factor is a fraction where the numerator and denominator represent the same quantity in different units. We can use these fractions as proportions to convert measurement.
Customary Metric
Measurement Measurement
5,280 feet/1 mile 1,000 meters/1 kilometer
12 inches/1 foot 100 cm/1 meter
16 ounces/1 pound 1,000 grams/1 kilogram
2000 pounds/1 ton 1,000 milligrams/1 gram
8 fluid ounces/1 cup 1,000 liters/1 kiloliter
2 pints/1 quart 100 centiliters/1 liter

6. 4.7 Dimensional Analysis Other measurements
12 months/1 ______ 7 ____/1 _______ 60_______/1 hour
3,600 _____/1 ______ 52 ______/_______ 24 _____/1 _____
4 ____/1 gallon
12 ______/ 1 foot 1,760 _____/1 mile
Approximate conversions
1.609 km/1 mi mi/1 km
L/1 qt qt/1 L
2.54 cm/1 inch in/1 cm
0.914 m/1 yd yd/1 m
.454 kg/1 pound 2.2 lb/1 kg

7. 4.8 Similar Figures and Proportions
Similar figures have the same shape, but not necessarily the same size. The symbol “~” means “is similar to.” Similar figures may be reflections or flips of each other
Corresponding angles and sides of two or more similar polygons are in the same relative position.
Similar figures must have:
Equal corresponding angles
Corresponding sides with the same proportional lengths
You can use proportions to figure out the dimensions of similar figures.

8. 4.9 Using Similar Figures
Indirect measurement is a method for using proportions to find an unknown length or distance in similar figures.
Examples: surveyors, golf range finders, GPS

9. 4.9 Using Similar Figures Location Length of A Length of B Slide 12 cm

10. 4.10 Scale Drawings and Scale Models
Scale Drawing: proportional two-dimensional drawing of an object.
Scale Model: proportional three-dimensional model of an object
Scale Factor: the dimensions of the drawing or model to the actual, expressed as Model/Actual
Examples: blueprints, maps, toys, sculptures
EARTH Actual Globe Scale
Diameter 7,920 miles 12 inches 1/41,817,600
Actual Map Scale
Circumference 24,901 miles 48 inches 1/32,869,320

11. 4.10 Scale Drawings and Scale Models
Diameter
Model (Globe): 1 foot
Actual 7,926 miles × 5,280 feet/mile = 41,817,600
Scale
Model/Actual: 1/41,817,600
Circumference
Model (World Map): 48 inches
Actual: 24,901 mi × 5,280 feet/mile × 12 inches/foot = 1,577,727,360 inches
Model/Actual: 48/1,577,727,360 = 1/32,869,320

12. 4.10 Scale Drawings and Scale Models
Clothespin actual: 7.3 cm
Clothespin sculpture (model): 14 m
Scale: