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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.

+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

If the two products are equal, they form a proportion. When the cross products are not equal, the ratios do not form a proportion.

+Cross multiplication, in a proportion, is the product of one numerator and the other denominator.

Example 1: 3 ? 5 9 = 15

Example 2: 3 ? 11 5 = 20

+How to Solve a Proportion:

For example: 4 = H Steps: 7 84

7×H = 4× 84 1. Write the cross products. 7H = 336 2. Multiply

7 H = 336 7 7 3. To find the value of the variable, undo the multiplication by dividing to both

sides. H = 48 4. Divide 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. )

When solving a proportion you must cross multiply, then find the missing variable.

+Your Example:

Solve the proportion.

2 = 3 4 N

X = 16 3

+Homework:

6. 3 = 11 X 20

7. 4 = 10 9 M

8. Y = 3 10 5

9. 9 = T 1 4

10. 4 = X 7 84

In 1-5, answer yes or no, but you must show your work.

Find the value of the variable by using cross multiplication.

1. 3 ? 5 9 = 15

2. 5 ? 2 8 = 3

3. 7 ? 25 9 = 27

4. 6 ? 10 8 = 15

5. 7 ? 20 9 = 27