Ratios and Proportions

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Presentation transcript:

Ratios and Proportions Lesson 3-6 Ratios and Proportions

Objectives Determine whether two ratios form a proportion Solve proportions

Vocabulary Ratio – a comparison of two numbers by division Proportion – an equation stating that two ratios are equal Extremes – the large and small numbers in a proportion Means – the middle numbers in a proportion Rate – ration of two measurements with different units of measure Scale – ratio or rate using in modeling

Four Step Problem Solving Plan Step 1: Explore the Problem Identify what information is given (the facts) Identify what you are asked to find (the question) Step 2: Plan the Solution Find an equation the represents the problem Let a variable represent what you are looking for Step 3: Solve the Problem Plug into your equation and solve for the variable Step 4: Examine the Solution Does your answer make sense? Does it fit the facts in the problem?

Example 1 Determine whether the ratios and form a proportion. Answer: The ratios are equal. Therefore, they form a proportion.

Example 2 Use cross products to determine whether the pair of ratios below forms a proportion. Write the equation. Find the cross products. Simplify. Answer: The cross products are not equal, so the ratios do not form a proportion.

Example 3 Answer: Solve the proportion . Original equation Find the cross products. Simplify. Divide each side by 8. Answer: Simplify.

Example 4 Bicycling The gear on a bicycle is 8:5. This means that for every eight turns of the pedals, the wheel turns five times. Suppose the bicycle wheel turns about 2435 times during a trip. How many times would you have to turn the pedals during the trip? Explore Let p represent the number of times needed to crank the pedals. Plan Write a proportion for the problem. turns of the pedals wheel turns

Example 4 cont Solve Original proportion Find the cross products. Simplify. Divide each side by 5. Answer: 3896 = p Simplify.

Example 5 The scale on a map of the United States is 1 and 3/8 inches = 750 miles. The distance, on the map, between Los Angeles and Washington, D.C., is about 3 and 7/8 inches. What is the distance in miles between the two locations? changing fractions 1 3/8 in. 3 7/8 in ------------ = ------------- 750 miles d miles 11/8 in. 31/8 in ------------ = ------------- 750 miles d miles map scale cross multiplication multiply by inverse 11/8 d = 31/8 (750) d = (8/11) (31/8) (750) cancel 8’s out d = (31/11) (750) = 2,113.64 miles Answer: The distance in miles between Los Angeles and Washington, D.C., is about 2,114 miles.

Summary & Homework Summary: Homework: A ratio is a comparison of two numbers by division A proportion is an equation stating that two ratios are equal A proportion can be solved by finding the cross products Remember the distributive property! Homework: pg 158: 12-32 even