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Solving Proportions . Lesson 2-7. Warm Up:

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### Solving Proportions

Lesson 2-7

You are making beaded necklaces using a pattern in which 2 large red beads are followed by 3 small blue beads. Each set of 5 beads adds 1 ¼ inches to the length of the necklace. How many of each color bead will you need for a 20-in. necklace. Explain your answer.

ratios

A __________________ is an equation that states two ___________ are equal.

A. What is the solution to the proportion ?

___________________________ Write the equation

___________________________

___________________________ Cross-multiply

___________________________ Divide

___________________________ Simplify

5●x = 7 ●4

5x = 28

x = 5.6

These examples are reviews of problems similar to ones you have solved in earlier grades.

3●3 = 5 ● y

5●x= 9 ● 15

9 = 5y

5x= 135

5y = 9

x= 27

____________________________ ____________________________

____________________________

y = 1.8

In example B, the symmetric property was used to rewrite the problem with the variables on the left side of the equation.

In both example B and C, the first two steps could have been combined into one step.

6n = 5(2n + 4)

6n = 10n + 20

Simplify using the distributive property.

6n – 10n = 10n –10n + 20

“Move” the “10n” by subtracting it from both sides.

– 4n = 20

Simplify.

Divide each side by -4 so that only 1n remains.

n = -5

Simplify

4w = 2w + 6

Cross- multiply.

Simplify using the distributive property

4w – 2w= 2w – 2w+ 6

Move “2w” by subtracting from each side.

2w= 6

Simplify

Divide each side by 2 – the coefficient of w

w= 3

Simplify

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