1. S OLVING P ROPORTIONS Lesson 2-7

2. Warm Up: 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.

3. A __________________ is an equation that states two ___________ are equal. proportionratios A. What is the solution to the proportion ? ___________________________Write the equation ___________________________ ___________________________Cross-multiply ___________________________ Divide ___________________________Simplify 5●x = 7 ●4 5x = 28 x = 5.6

4. 3●3 = 5 ● y 9 = 5y 5y = 9 ____________________________ y = 1.8 5●x= 9 ● 15 5x= 135 x= 27 These examples are reviews of problems similar to ones you have solved in earlier grades. 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.

5. Cross - multiply 6n = 5(2n + 4) Simplify using the distributive property. 6n = 10n + 20 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

6. 4w = 2(w + 3) Cross- multiply. 4w = 2w + 6 Simplify using the distributive property 4w – 2 w = 2w – 2 w + 6 Move “2w” by subtracting from each side. Simplify 2 w = 6 Divide each side by 2 – the coefficient of w w = 3 Simplify

7. Try each of the problems below.