1. Ratio and Proportions Essential Questions
How do we find and simplify the ratio of two numbers?
How can we use proportions to solve real world problems?

2. Ratios A comparison of two or more numbers that use addition
Usually expressed in lowest terms:
Are expressed without units
Convert to “like” units so they cancel
Ratios with unlike units are called unit rates
such as mpg, mph, etc…
Probability – the ratio of the number of successful outcomes to the number of total incomes

3. Example of ratios
If 7 students in one class have pets and 18 do not, what is the ratio of the number of students who have pets to the total number of students?

4. Example of Ratios
In an art class, 12 students report that drawing is their favorite medium. If there are 18 students in the class, what is the ratio of students who prefer drawing to the total number of students?

5. Comparing Ratios
An orchard has 80 apple trees and 60 peach trees. Analyze the orchard’s mix of fruit trees. Does the orchard have a higher ratio of apple trees to the total number of trees? Or does the orchard have a higher ratio of peach trees to the total number of trees?

6. Proportions An equation that equates 2 ratios.
Solved by setting the product of the means equal to the product of the extremes.
a and d are the extremes, b and c are the means
then
ad = bc

7. Proportions
Use cross-products to solve.

8. Using ratios
Find x if the triangles are similar (sides are proportional to each other) x 45 20 30

9. Using Ratios
Perimeter of a rectangle is 60. Ratio of length to width is 3:2. Find the length and width.
Think of the length as “3x” and the width as “2x.”
3x + 3x + 2x + 2x = 60
10x = 60
x = 6
So the length is 3(6) = 18 and the width is 2(6) = 12.

10. Using Ratios
The measure of the angles in this triangle is the extended ratio of 1:2:3. What are the measures of the angles?
x + 2x + 3x = 180
6x = 180, so x = 30.
1 = 30, 2 = 60, 3 = 90

11. Using Ratios B
If AB:BC is 7:4, find m.
19m + 3
12m A C

12. Factoring Review…..Yikes…..

13. Homework
Worksheet