1. Using Cross Products
Chapter 3

2. Cross Products
When you have a proportion (two equal ratios), then you have equivalent cross products.
Find the cross product by multiplying the denominator of each ratio by the numerator of the other ratio.

3. Example: Do the ratios form a proportion? Check using cross products.4 3 , 12 9
These two ratios DO form a proportion because their cross products are the same.
12 x 3 = 36
9 x 4 = 36

4. Example 2 5 2 , 8 3
No, these two ratios DO NOT form a proportion, because their cross products are different.
8 x 2 = 16
3 x 5 = 15

5. Solving a Proportion Using Cross Products
Use the cross products to create an equation.
Solve the equation for the variable using the inverse operation.

6. Example: Solve the Proportion
Start with the variable. 20 k = 17 68
Simplify.
Now we have an equation. To get the k by itself, divide both sides by 68.
68k
17(20) =
68k =
340 68 68 k = 5

7. Homework Time