1. Chapter 5 Ratios, Rates, Proportions

2. Ratios A ratio is a comparison of two quantities by division
There are three ways to write a ratio:
Using the word “to”
5 to 24
Using a colon “:”
5 : 24
Using a fraction 5 24
Two ratios that name the same number are equal ratios

3. Warm-Up Write each fraction in simplest form. 1. 3/9 2. 15/25 3. 45/54
1. 3/ / /54
4. 14/ / /204

4. Ratios cont’d
Ex. Two students report the ratio of the number of girls in a class to the total number of students. One student says the ratio is 18/30. The other says the ratio is 9/15. The two ratios are equal.
Ex. Find two ratios equal to 12 15
12 x 2 = ÷ 3 = 4
15 x ÷

5. Ratios cont’d To write a ratio as a decimal, divide
Ex. 5 to 12, 5 : 12, 5 12
= 0.416…
To write a ratio in simplest form, divide the numerator and the denominator by the GCF
Ex ÷ 3 = 4
15 ÷

6. Unit Rates A unit rate is the rate for one given quantity
*unit price is the same as unit rate(just deals with money)
Ex. Determine the unit rate if a car travels 120 miles in 2 hours.
***Hint***-you want to know how many miles the car travels in “1” hour
*** the unit rate is 60 miles/1 hour or 60 miles/hour

7. Example(s) of Unit Rates/Prices
1.) 40miles/gal 4.) $1.59/lb
2.) 5yds/min 5.) $24.99/dozen
miles/hour 6.) $3.19/gal

8. Proportions
A proportion is an equation stating that two ratios are equal
For two ratios, the cross products are found by multiplying the denominator of each ratio by the numerator of the other ratio
***Hint***-to solve proportions “cross multiply” or “orbit”
***after you “orbit” you have a one-step equation

9. Scale Drawings(Models) & Maps
A scale drawing(***scale model is similar to the actual object it represents) is an enlarged or reduced drawing of an object that is similar to the actual object
A scale is the ratio that compares a length in a drawing to the corresponding length in the actual object
Example: If a 30-mile road is 1 inch long on a
map, you can write the scale of the map in
these three ways
1 inch : 30 miles 1 inch / 30 miles 1 inch = 30 miles

10. Scale Drawings(Models) & Maps
To find either the actual or drawing size(s), use the following proportion to solve.
Drawing = Drawing
Actual Actual

11. Example(s):
The scale of a model building is 1 in : 40 ft. Suppose the height of the model is 3 in. What is the actual height of the building?

12. Example(s):
The scale of a map is 1 in. : 15 mi. How many actual miles does each of the following measurements represents?
1.) 3 ¼ 2.) 2 ½

13. Example(s):
Suppose you want to make a map with a scale 1 in. : 4 mi. How many inches does each of the following actual distances represent?
1.) 22 mi. 2.) 39 mi.