RATIOS and PROPORTIONS Objectives: Set up Proportions Solve Proportions.

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Rates, Ratios, and Proportions

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Presentation transcript:

RATIOS and PROPORTIONS Objectives: Set up Proportions Solve Proportions

RATIOS & PROPORTIONS A ratio is a comparison of two numbers by division. To write ratios, use the word to, a colon, or a fraction bar. EXAMPLE #1: VHHS has 175 teachers to 1062 students. Words: 175 to 1062 Colon: 175:1062 Fraction: 175/1062

FINDING RATIOS Find the ratio of boys to girls in this class. Find the ratio of boys to students in this class. Find the ratio of girls to students in this class.

RATIOS & PROPORTIONS A proportion is a statement that two ratios are equal. Which one is NOT a proportion?

RATIOS & PROPORTIONS A proportion is a statement that two ratios are equal. EXAMPLE#2: Is a proportion? Find the cross products. 30 = 30 TRUE If TRUE, the statement is a proportion.

CROSS PRODUCT PROPERTY The Cross Product property of proportions says: If then. Vocab: a & d are called extremes. b & c are called means. So, the product of the extremes is equal to the product of the means.

RATIOS & PROPORTIONS EXAMPLE#3: Is a proportion? Find the cross products. 20 = 21 FALSE If FALSE, the statement is NOT a proportion.

RATIOS & PROPORTIONS EXAMPLE#4: Solve the proportion: Find the cross products. x Divide both sides by 10.

RATIOS & PROPORTIONS Solve the following proportions:

RATIOS & PROPORTIONS Solve the following proportions:

MAP SCALES Proportions are often used in map scales. When viewing a map, the scale reads “1 inch is to 9 miles”. If your destination is 2.7 inches away on the map, how many miles away is your destination? Set up a proportion of inches to miles:

SCALE DRAWINGS USING PROPORTIONS EXAMPLE#1: ¼ in = 5 ft is a scale for a rock band’s concert stage. A. The scale length of the drum stand is 1 in. What is the actual length of the drum stand? Cross multiply. Divide by.25

SCALE DRAWINGS USING PROPORTIONS EXAMPLE#2: ¼ in = 5 ft is a scale for a rock band’s concert stage. B. The actual length of the stage is 60 ft. What is the scale length of the stage? Cross multiply. Divide by 5

USING PROPORTIONS Mary earns $360 in 4 days. How many days will it take her to earn $450? Assume it will take x days. Setup a proportion and solve for x:

USING PROPORTIONS Five quarts of ice cream were used to make 70 milkshakes. How many quarts of ice cream would be needed for 210 milkshakes?

USING PROPORTIONS A sport utility vehicle can go 350 miles on 25 gallons of gasoline. How far can it go on 33 gallons of gasoline?

USING PROPORTIONS Anna is having a lemonade stand and wants to find out how much to charge for a 6 oz. glass of lemonade. A 12-oz. can of frozen lemonade costs $2.56 and makes 48 oz. of lemonade. What should Anna charge for a 6-oz. glass of lemonade?

Wrap-Up Today we learned: Ratios are a comparison of numbers and are usually expressed as a fraction. Proportions are when two ratios are equal. How to use proportions to model real-life situations. How to solve proportions by cross-multiplying.