1. Do Now 10/11/11 In your notebook, consider the following: In your notebook, consider the following: On a bright sunny day, how can you determine the height of a tall object (i.e. flagpole) without physically measuring the object? Create a problem. On a bright sunny day, how can you determine the height of a tall object (i.e. flagpole) without physically measuring the object? Create a problem.

2. Objective find ratios and write and solve proportions find ratios and write and solve proportions solve proportions using cross products solve proportions using cross products

3. RATIO- uses division to compare two quantities a to b a:b ab You can write ratios three different ways: Section 3.5 “Write Ratios and Proportions”

4. Try It Out… SOLUTION VOLLEYBALL A volleyball team plays 14 home matches and 10 away matches. a. Find the ratio of home matches to away matches. = 75 a. home matches away matches 14 10 10 = b. Find the ratio of home matches to all matches. b. home matches all matches all matches 14 14 14 + 10 14 + 10 = = 14 1424 = 712

5. PROPORTION- an equation that states that two ratios are equivalent.

6. Try It Out… 11 11 6x30 = Write original proportion. Multiply each side by 30. 330 6 = x Simplify. 55 = x Divide. 11 11 6x30 = 30 30 x30 Solve the proportion 11 6 =.

7. Proportion Cross Products Property A CROSS PRODUCT is the product of the numerator of one ratio and the denominator of the other ratio in a proportion. If, then Section 3.6 “Solving Proportions Using Cross Products”

8. Write original proportion. 8 15 = x 6 Solve the proportion = 8 x 6 15 Cross products property Simplify. 120 = 6x Divide each side by 6. 20 = x = 8 x 6 15 3 x = 2 x– 6 Cross products property 3(x – 6) = 2 x 3x – 18 = 2x Distributive property Subtract 3x from each side. 18 = x Solve the proportion 3 x = 2 x– 6 Write original proportion.

9. SCALE - the SCALE of a drawing, map, or model relates the dimensions of the drawing, map, or model to the actual dimensions. Write and solve a proportion to find the distance d between Cleveland and Cincinnati if the distance on the map is about 4.2 centimeters. = 4.2 d 1 centimeters 85 kilometers Cross products property d = 357 Simplify. 1 d = 85 4.2

10. The ship model kits sold at a hobby store have a scale of 1 ft : 600 ft. A completed model of the Queen Elizabeth II is 1.6 feet long. Estimate the actual length of the Queen Elizabeth II. The ship model kits sold at a hobby store have a scale of 1 ft : 600 ft. A completed model of the Queen Elizabeth II is 1.6 feet long. Estimate the actual length of the Queen Elizabeth II. Write and solve a proportion to find the length g of the Queen Elizabeth II. =1.6 g 1600 Cross products property g = 960 Simplify. 1 · g = 600 · 1.6 SOLUTION The actual length of the Queen Elizabeth II is about 960 feet.

11. Indirect Measurements You measure the shadow of a telephone pole to be 24 ft. The shadow of a 5ft-tree is 4 ft. How tall is the telephone pole? S H s h