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7-1 RATIO AND PROPORTION Answers to Warm Ups 1. 3 5 2. 2 1 3. 3:20 4. 2:15 5. 2 to 1 RATIO: A COMPARISON OF 2 NUMBERS a b a:b a to b Must be in same units 12 in = 1 ft 5280 ft = 1 mi 100 cm = 1 m 10 mm = 1 cm 1000 mm = 1 m EXAMPLE: SIMPLIFY THE RATIO 2 FT: 30 IN Method 1 * Feet 2 ft: 2.5 ft 20 : 25 4:5 Method 2 * Inches 24 in: 30 in 4:5 TRY ON OWN 1) 1 m: 52 cm 2) 10 mm: 3.2 cm 3) 1.25 ft: 3 in Answers: 1) 25:13 2) 5:16 3) 5:1 EXAMPLE: LET X = 2 AND Y = 3 6x2 to 12xy 6(2)2 to 12(2)3 6(4) to 12(6) 24 to 72 4 to 12 1 to 3 TRY ON OWN: X = 2 AND Y = 3 1) 2) 3) yx x xy y x2 y x y 1 Answers: 1) 1 2 2) 2 1 3) 3 2 EXAMPLE: SIMPLIFY 2 6x 12 xy *Divide Whole Numbers *Subtract Exponents x 2y TRY ON OWN: SIMPLIFY 1) 2) 3) yx x xy y x2 y x y 1 Answers: 1) In Simplest Form 2) 3) x 1 xy y 1 EXAMPLE The ratio of the angles of a triangle are 4:4:7. Find the measure of each angle. *Usually we reduce by dividing. Now we will work backwards by multiplying 4x + 4x + 7x = 180 15x = 180 x = 12 4x = 4(12) = 48 4x = 4(12) = 48 7x = 7(12) = 84 TRY ON OWN 1) 2) The ratio of the measures of 2 complementary angles is 1:2. Find the measure of each angle. The measures of the angles of a pentagon are in the ratio 1:2:3:6:15. Find the measure of each angle. Answers: 1) 30,60 2) 20,40,60,120,300 HOMEWORK Pg 243 #1-31