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EXAMPLE 1 Writing a Ratio Skiing A ski resort has 15 easy, 25 intermediate, 7 difficult, and 11 expert-only trails. Write the ratio “intermediate trails : easy trails” in three ways. intermediate trails easy trails = 25 15 = 5 3 Write as a fraction and simplify. ANSWER The ratio can be written as, 5 : 3, or 5 to 3. 5 3

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EXAMPLE 2 Finding an Equivalent Rate Weather Lightning strikes about 100 times per second around the world. About how many times does lightning strike per minute around the world? SOLUTION Because 60 seconds = 1 minute, 60 sec is equivalent to 1. 1 min 100 times 1 sec Multiply by a fraction that is equivalent to 1. = 6000 times 1 min Simplify. 100 times 1 sec = 60 sec 1 min ANSWER Lightning strikes about 6000 times per minute around the world.

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EXAMPLE 3 Finding a Unit Rate Write –24 feet per 5 seconds as a unit rate. –24 ft 5 sec = – 24 5 5 Divide numerator and denominator by 5 to get a denominator of 1 unit. = –4.8 1 Simplify. ANSWER The unit rate is –4.8 feet per second. Check: Round –4.8 feet per second to –5 feet per second. The product –5 5 = –25, which is about –24, so the answer is reasonable.

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GUIDED PRACTICE for Examples 1, 2 and 3 1. expert only trails easy trails = 15 11 Write as a fraction and simplify. difficult trails 2. easy trails = 7 15 Write as a fraction and simplify. The ratio can be written as, 15 : 7, or 15 to 7. ANSWER 15 7 11 15 ANSWER The ratio can be written as, 11 : 15, or 11 to 15. Use the information in Example 1 to write the ratio in three ways.

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GUIDED PRACTICE for Examples 1, 2 and 3 3. A water pump moves 2 gallons of water per second. How many gallons of water are pumped per minute? Write your answer as a rate. Pumping Water ANSWER 120 gallons of water are pumped per minute

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GUIDED PRACTICE for Examples 1, 2 and 3 6 games 4. 114 points = 114 6 6 = 19 1 ANSWER The unit rate is 19 points per game. 5. 5 months 365 people = 73 1 ANSWER The unit rate is 73 people per month. = 365 5 5

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GUIDED PRACTICE for Examples 1, 2 and 3 6. 10 gallons 329 miles ANSWER The unit rate is 32.9 miles per gallon. 7. 14 sec –49 m = –49 14 14 ANSWER The unit rate is –3.5m per sec. = –3.5 m 1 sec = 329 10 10 = 32.9 1

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EXAMPLE 2 Multiply rational expressions involving polynomials Find the product 3x 2 + 3x 4x 2 – 24x + 36 x 2 – 4x + 3 x 2 – x Multiply numerators and denominators.

EXAMPLE 2 Multiply rational expressions involving polynomials Find the product 3x 2 + 3x 4x 2 – 24x + 36 x 2 – 4x + 3 x 2 – x Multiply numerators and denominators.

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