8-36th grade math

Solving Proportions Using

Cross Products

Objective

• To solve proportions using cross products

• Why? To know how to find the missing number in a proportion- especially when the ratios are not easily ‘convertible.’

California State Standards NS 1.3 : Use proportions to solve problems …

Use cross-multiplication as a method for solving such problems, understanding it as the multiplication of both sides of an equation by a multiplicative inverse.

NS 1.2 : Interpret and use ratios in different contexts … to show the relative size of two quantities, using appropriate notations (x/y, x to y, x : y)

AF 1.1 : Write and solve one-step linear equations in one variable.

Vocabulary• Cross products– In a proportion, the product of a numerator of one

ratio with the denominator of the other ratio. bc (b x c)• a = c b d ad (a x d)

– This is similar to solving an equation with fractions.• a = c b d• a (b) = c (b) = bc (b x c) b (a) d (a) = ad (a x d)

How to Solve Proportions Using Cross Products1)Multiply the numerator

and the denominator of two known numbers

2) Divide by the last used number.

3) Check your answer for reasonableness. You could also recheck the final proportion by dividing the fractions.

7 = n1.2 3

7 x 3 = 2121 ÷ 1.2 = 17.5

7 = 17.51.2 3

7 ≈ 5.81.2

17.5 ≈ 5.8 3

Try It!1) 6 = 8 9 n

2) 9 = n 15 10

3) 8.5 = n 3.2 8

4) 2.6 = 4 n 4.8

1) n = 12

2) n = 6

3) n = 21.25

4) n = 3.12

Try Some More!Proportional?5) 4 , 6 10 15

6) 6 , 9 9 12

7) 6 , 9 8 12

8) 6 , 9 10 15

5) Yes (60)

6) No (72, 81)

7) Yes (72)

8) Yes (90)

Objective Review

• To solve proportions using cross products

• Why? You now know how to find the missing number in a proportion- especially when the ratios are not easily ‘convertible.’

• You can use cross products to solve for the unknown value in a proportion.

Independent Practice

• Complete problems 10-18

• Copy original problem first.

• Show all work!

• If time, complete Mixed Review: 19-25

• If still more time, work on Accelerated Math.