October 08, 2015
4-3: Proportions
Outcome: to test whether ratios form a proportion by using equivalent ratios and cross
products.
A proportion is an equation stating that two ratios are equal. One method of testing
whether ratios form a proportion is to write both ratios in simplest form, then see if they are
equal.
Writing Ratios in Simplest Form
1. Surveys For each class, write the ratio of the number of students who saw a movie to the
total number of students. Do the ratios form a proportion?
Did you see a movie this weekend?
Class
Yes
Total Number
A
10
24
B
25
60
Your Turn ...
Do 10 and 40 form a proportion?
12
56
October 08, 2015
Key Concept: PROPORTION!!!
Ratios that are equal form a proportion!
6 = 9
8 12
*You can use the properties of equality to
discover another way to determine
whether ratios form a proportion.
*The products 6 12 and 9 8 are called cross
products. For the two ratios, the cross
products are the two products found by
multiplying the denominator of each ratio by
the numerator of the other ratio.
You can use the Cross-Products Property to determine whether ratios form a proportion.
Do the ratios in each pair form a proportion?
a. 5/9 and 30/54
b. 7/8 and 55/65
Your Turn ...
c. 3/8 and 6/16
d. 6/9 and 4/6
October 08, 2015
4-4: Solving Proportions
Outcome: to solve proportions using unit rates, mental math, and cross products
Using Unit Rates
You know the price of six oranges, but you want to buy eight. You can solve a proportion to find
the total cost of the quantity that you want to buy.
You can use unit rates to solve a proportion. First, find the unit rate. Then, multiply to solve the
problem.
6 for $2.34
Use the information to find the cost in dollars of eight oranges.
October 08, 2015
Your Turn ...
1. Postcards cost $2.45 for 5 cards. How much will 13 cards cost?
2. Swimming goggles cost $84.36 for 12. At this rate, how much will new goggles cost for
17 members of the swim team?
Solving Using Mental Math
Solve each proportion using mental math.
a. z = 21
12 36
b. 8 = n
10 40
Your turn ...
c. 3 = b
8
24
d. m = 16
5
40
October 08, 2015
Solving Using Cross Products
Many proportions cannot be solved with mental math. In these situations, you can use cross
products to solve a proportion.
1. Solve 25 = 15
38
x
using cross products.
Your Turn ...
a. 12 = x
15
21
b. 16 = d
30 51
c. 20 = 110
35
m