7.1 Ratios and Proportions Objectives: -to write ratios and solve proportions

Ratios  A Ratio is a comparison of two quantities  The ratio of a to b can be expressed in the following ways: (as long as b ≠ 0) 1. a to b 2. a:b 3.

Example: Ratios in the Real World!  Mr. Carucci has an autographed picture of his favorite news anchor, Ron Burgundy. The picture is 8 inches wide and 5 1/3 inches high. Mr. Carucci is going to enlarge the photo to a poster 2 ft. wide by 1 1/3 ft high.  What is the ratio of the width of the photo to the poster? (Remember 1 ft = 12 in)

You try: Ratios  Mr. Falcicchio is building a scale model of his favorite car, a Red Toyota Prius. The model car is 4 inches long. The real car is 10 ft. long. What is the ratio of the length of the model to the actual car? How many times larger is the real car then the model?

Proportion  A proportion is a statement that two ratios are equal.  We can state that:

See if a Proportion is valid…  Multiply both sides by both denominators or by a common denominator.  Eliminate common factors that will divide out to 1  If there is a balanced equation remaining, then they form a proportion

Solving Equations Involving Proportions…  We can use the idea of multiplying both sides of an equation by both denominators to solve proportions.  Some of us may know other methods or “shortcuts” to solve proportions, but be sure to understand why we can use these “shortcuts”.

Examples: Solving equations with proportions

What if there is variables in denominators?

What if there is more than one term in a numerator?

What if there is more than one term in a denominator?

Proportion Practical Examples  If you are mixing paint to paint your house, you need to keep the ratio (of color pigments to white paint) constant to ensure that the color will remain exactly the same.  If city tax rate is $7.75 to every $100 of purchase, then you have to use the same ratio no matter how much your purchase is (because it is the law).

Proportion Word Problems  If 12 gallons of gas cost $26.68, how much will 15 gallons cost?

Proportion Word Problems  Liza has a free throw average of 5 out of 8 attempts. At this rate, how many successful free throws would she be expected to make out of 200 attempts?  If she made 105 free throws how many attempts did she have?  What if she missed 48 free throws… how many did she make?

Try one on your own…  Three times a recipe calls for 5 cups of milk. How many cups of milk will be needed for 12 times the recipe?  How many cups would be needed 1 recipe?

And another…  Two out of three booths sell rag dolls. If there are 27 booths, how many of these sell rag dolls?

And one more…  Tullio reduced the size of a rectangle to a height of 2 in. What is the new width if it was originally 2ft. wide and 1ft. tall?

Scale Drawing  A Scale compares each length in a drawing to the actual length. The lengths used in a scale can be different units.  Examples of scales could be:  1 in. = 100 mi  1 in. = 12 ft.  1 mm = 1 meter

Using a Map  Ms. Okul is planning a camping trip to upstate New York. On a map her route from Lyndhurst was 5.25 inches. The scale on the map said 1 inch = 25 Miles.  How far did she have to travel?  If she left Lyndhurst at 8:30 AM, and drove at an average speed of 75 MPH, what time would she arrive? miles10:15 Am

Using a Blueprint…  Mr. Rasczyk is building a pool in his backyard. The dimensions on the blueprint were 10in by 12in. The scale was 2 in = 5ft.  What was the Dimensions of his real pool?  If the area of the pool was 1/3 of his yard, what is the area of his entire yard?  If his yard is 50 feet wide, how long is it? 25ft x 30ft2250 sq. ft.45 ft.