1. Finding Proportions using Cross Multiplication
Objective:
We will learn to use cross multiplication to solve a proportion.
We will use cross multiplication to check whether two ratios form a proportion.

2. Property of Cross Products: If two ratios form a proportion, the cross products are equal. When 2 ratios have equal cross products, they form a proportion.
Example 1:
Decide whether each pair of ratios forms a proportion.
You have to multiply the numerator with the denominator of the
other fraction; and vice versa.
105= =105
3×35 = 5 ×21
105 = 105
YES, they form a proportion.
If the two products are equal, they form a proportion.
When the cross products are not equal, the ratios do not form a proportion.

3. Cross multiplication, in a proportion, is the product of one numerator and the other denominator.
Example 1: 3 ? 5
9 = 15
Example 2: ? 12
5 = 20

4. How to Solve a Proportion:
When solving a proportion you must cross multiply, then find the missing variable.
For example: = H Steps:
7×H = 4× Write the cross products.
7H = Multiply
7 H = 336
To find the value of the variable, undo
the multiplication by dividing to both
sides.
H = 48
4. Solve.
5. Write answer.
(You have to think: The opposite of multiplication is division, so I have to divide the number that is with the variable and do the same for both sides of the problem. Then I cancel the opposites, and bring down what I have left. )

5. Your Example: Solve the proportion. 2 = 3 4 N X = 1 6 3

6. Homework: In 1-5, answer yes or no, but you must show your work.
Find the value of the variable by using cross multiplication.
6. 4 = 10 9 M 7. Y = = T = X = 11 X 20
? 5
6 = 15
? 2
8 = 3
? 21
9 = 27
? 10
8 = 15
5 ? 20
9 = 36