1. Warm up Lesson 3.1 Solve the following equations: 1. -5(3z + 7) = -8z 2. 3y + 12 = -(6 – 2y) 3. 8a = -4(5a + 7) 4. 10(3b – 1) = -2(b - 3) 1. -5 = z 2. y = -18 3. a = -1 4. b = ½

2. Lesson 3.1 Ratios and Proportions Strand 3 Concept 4 P.O. 2/ Strand 1 Concept 2 P.O. 2

3. What is a Ratio? A ratio compares two quantities. You get 8 correct out of 10 on a quiz # correct to total # possible This is a ratio! You can write a ratio 3 ways: a) 8 to 10 (in words) b) 8:10 (with a colon) c) 8 (as a fraction) 10

4. Writing Ratios as Fractions… (your favorite!)

5. Writing Ratios as Fractions 1)Women owned about 350 of every 1000 law firms in the US. 350 (women owned firms) 1000 (total firms) 2)The McLaren car could go 240 miles per hour. 240 (miles) 1 (hour)

6. You Try These: 3)Sam makes $5.00 per hour babysitting. $5.00 1 hour 4) Cereal is on sale: 4 boxes for $6.00 4 boxes $6.00 5) On a trip we went 450 miles in 7 ½ hours. 450 miles 7.5 hours

7. Proportions: A proportion is two ratios set equal to each other. In a proportion, cross products are equal.

8. More on Proportions: When working with ratios and proportions it is important to note that to check to see if two ratios form a proportion, their cross-products MUST be equal! Example: Do the following ratios form a proportion? Yes because the cross products are both 56! No because one cross product is 33 and the other is 45 33 ≠ 45

9. To solve a proportion: Follow these easy Steps: 1.Cross multiply 2.Solve the one-step equation for the variable. 3(21) = 4(x) 63 = 4x 63 = 4X 4 4 X = 63/4

10. Your Turn… 6) 7) 8) x = 5a = 12 y = 5

11. But those are too easy…so let’s challenge ourselves! 9) 10) 11) x = -2a = 13 y = -5 Whenever you have an expression in your proportion, (like x + 2) don’t forget to distribute when you multiply!

12. Summary: Explain how to solve a proportion. Homework: Worksheet 3.1