Finding Proportions using Cross Multiplication

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Presentation transcript:

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 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.

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

How to Solve a Proportion: When solving a proportion you must cross multiply, then find the missing variable. 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. 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. )

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

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 = 3 10 5 8. 9 = T 1 4 9 . 4 = X 7 84 10. 3 = 11 X 20 1. 3 ? 5 6 = 15 2. 5 ? 2 8 = 3 3. 7 ? 21 9 = 27 4. 6 ? 10 8 = 15 5 ? 20 9 = 36