1.Obj. 34 Ratio and Proportion The student is able to (I can): Write and simplify ratios Use proportions to solve problems

2. ratioA comparison of two numbers by division. The ratio of two numbers a and b, where b does not equal 0 (b 0) can be written as a to b a:b a b Example: The ratio comparing 1 and 2 can 1 be written 1 to 2, 1 : 2, or . 2 Note: To compare more than two numbers, use dot notation. Ex. 3 : 7 : 9 3. proportionAn equation stating that two ratios are equal. Two sets of numbers are proportional if they use the same ratio.a c Example: = or a : b = c : d b d Cross Products Property a c In a proportion, if = , and b and d 0, b d then ad = bc 4. Solving Problems with Ratios If a problem contains a ratio of numbers, set up a proportion and cross-multiply. Example: The student-faculty ratio at a college is 15: 1. If there are 500 faculty, how many students are there? students 15 x : = faculty 1 500 x = (15)(500) = 7500 students 5. If a problem contains a ratio comparing more than two numbers, let x be the common factor and set up an equation to solve for x. Once we know x, we can find the original quantities. 6. ExampleThe ratio of the side lengths of a triangle is 2 : 3 : 5, and its perimeter is 80 ft. What are the lengths of each side? Let the side lengths be 2x, 3x, and 5x. 2x + 3x + 5x = 80 10x = 80 x=8 This means that the sides measure 2(8) = 16 ft. 3(8) = 24 ft. 5(8) = 40 ft. 7. ExamplesSolve each proportion:3 x 1. 8 = 32 8x = 96x = 124 2 2. x = 5 2x = 20x = 10x x2 = 3. 6 3 3x = 6(x 2) 3x = 6x 12 3x = 12x=4 8. Examples4. The ratio of the angles of a triangle is 2: 2: 5. What is the measure of each angle? 2x + 2x + 5x = 180 9x = 180 x = 20 2(20) = 40 2(20) = 40 5(20) = 100 9. Examples5. A 60 meter steel pole is cut into two parts in the ratio of 11 to 4. How much longer is the longer part than the shorter? 11x + 4x = 60 15x = 60 x=4 11(4) = 44 m 4(4) = 16 m The longer part is 28 m longer than the shorter part. 10. Examples (PAP only)6. Find the ratio of x to y if a) 2x = 3y 2x 3y = 2y 2y x 3 = y 2 b) 6 ( y + 3 ) = 2 ( x + 9 ) 6y + 18 = 2x + 18 6y = 2x x 6 = =3 y 2