Algebra 1: Proportions

1. Bellringer: Solve each equation. 1. | x | = -6 2.  1 + | x  5| = 1 3. 2| x + 1| = 16 4. No Solutions 15 y 30 10 7, 3 5 = 7, -9

3. You have 3 minutes to work on WS from Friday – ask questions if needed.

4. Write and use ratios, rates, and unit rates. Write and solve proportions. Objectives

5. Proportion ? Rate ?

6. In the proportion , the products a • d and b • c are called cross products . You can solve a proportion for a missing value by using the Cross Products property. Cross Products Property In a proportion, cross products are equal. WORDS NUMBERS ALGEBRA 2 • 6 = 3 • 4 If and b ≠ 0 and d ≠ 0 then ad = bc .

7. Example 4: Solving Proportions Solve each proportion. Use cross products. Divide both sides by 3. Use cross products. A. B. Add 6 to both sides. Divide both sides by 2. 3( m ) = 5(9) 3 m = 45 m = 15 6(7) = 2( y – 3) 42 = 2 y – 6 +6 +6 48 = 2 y 24 = y

8. Check It Out! Example 4 Solve each proportion. A. B. Use cross products. Divide both sides by 2. Use cross products. Subtract 12 from both sides. Divide both sides by 4. y = −20 – 12 –12 4 g = 23 g = 5.75 2 y = –40 2( y ) = –5(8) 4( g +3) = 5(7) 4 g +12 = 35

12. Check It Out! Example 2 Cory earns $89.50 in 8 hours. Find the unit rate. The unit rate is $11.19 per hour. -Cory earns $11.19 per hour. 89.5 = 8 x 89.5 x 8 1 = 11.19 = x

13. The ratio of games won to games lost for the Miami Heat basketball team is 3:2. The team has won 18 games. How many games did the team lose? Check It Out! Example 1 The team lost 12 games.

14. Example 2: Finding Unit Rates Raulf Laue of Germany flipped a pancake 416 times in 120 seconds to set the world record. Find the unit rate. Round your answer to the nearest hundredth. The unit rate is about 3.47 flips/s.

15. Check It Out! Example 2 Cory earns $52.50 in 7 hours. Find the unit rate. The unit rate is $7.50. Write a proportion to find an equivalent ratio with a second quantity of 1. Divide on the left side to find x. 7.5 = x

16. Example 5A: Scale Drawings and Scale Models A contractor has a blueprint for a house drawn to the scale 1 in: 3 ft. A wall on the blueprint is 6.5 inches long. How long is the actual wall? x • 1 = 3(6.5) x = 19.5 The actual length of the wall is 19.5 feet. Write the scale as a fraction. Let x be the actual length. Use the cross products to solve. blueprint 1 in. actual 3 ft.

17. Group Quiz: Part 1 1. In a school, the ratio of boys to girls is 4:3. There are 216 boys. How many girls are there? 162 2. Nuts cost $10.75 for 3 pounds. Find the unit rate in dollars per pound. $3.58/lb 3. 4. A scale model of a car is 9 inches long. The scale is 1:18. How many inches long is the car it represents? 16 162 in.

18. Mini-Worksheet Discuss Project