Using Cross Products

Lesson 6-4

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.

Example: Do the ratios form a proportion? Check using cross products.

412

, 39

12 x 3 = 369 x 4 = 36

These two ratios DO form a proportion because their cross products are the same.

Example 2

58

, 23

8 x 2 = 163 x 5 = 15

No, these two ratios DO NOT form a proportion, because their cross products are different.

Solving a Proportion Using Cross Products

• Use the cross products to create an equation.

• Solve the equation for the variable using the inverse operation.

Example: Solve the Proportion

k17

=2068

Start with the variable.

=68k 17(20)

Simplify.

68k = 340

Now we have an equation. To get the k by itself, divide both sides by 68.

68 68

k = 5

Homework Time