Objectives: To solve proportions and write ratios

Ratio: a comparison of 2 quantities Written as ‘ratio of a to b’ or a: b or Ratios should be written in reduced form Example: 2: 4 should be written as 1:2 If writing a ratio to compare 2 quantities, you need to make sure they are in same units of measure

Example: A scale model of a car is 4 in. long. The actual car is 15 ft. long. What is the ratio of the length of the model to the length of the car?

Example: What is the ratio of the longer side to the shorter side? 2 ft 18 in.

Proportion: a statement that two ratios are equal Can write it as: or a: b = c: d “a is to b as c is to d”

Extended Proportion 3 or more ratios are equal a: b = c: d = e: f 6: 24 = 4:16 = 1:4

Properties of Proportions If you have a proportion, the following are equivelant: 1. ad = bc 2. (cross product property) 3. 4.

Examples: If, which of the following must be true? 1. 8x = 5y

Let’s try some Examples

Cross Product Property: Can be used to solve proportions!!!

Solve each proportion for x. 1.2.

You are making a cake. You need 1 ½ cups of sugar for the recipe. All you have is a tablespoon measuring tool. How many tbsp do you need? (16 tablespoons = 1 cup)

Scale Drawing: Scale compares each length in the drawing to the actual length Drawing length Actual length Example: You are making a map of the US, and your scale indicates 1 in = 35 miles. If Boston and New York City are 220 miles apart, how far apart should you make the two cities on your map?

Warm up 1. Solve for x 2. The diameter of a dinner plate is 1 ft.. In a dollhouse the diameter of a dinner plate is 1 ¼ in.. What is the ratio, using whole numbers, of the diameter of the dollhouse plate to the diameter of the full-size plate? 3. Use the proportion Write 3 different proportions using these same numbers.