3-5 Write Ratios & Proportions Objective: Students will create and solve equations in one variable. Standards: A.REI.3 , A.CED.1 , A.REI.1

Vocabulary Ratio: Uses division to compare two quantities. You can write the ratio of two quantities a and b, where b is not equal to zero, in three ways: a to b a : b a b Each ratio is read “the ratio of a to b” Ratios should be written in simplest (reduced) form.

Vocabulary Proportion: An equation that states that two ratios are equivalent. a = c where b ≠ 0, d ≠ 0 b d

Example 1 = = = = = ninth graders tenth graders 18 14 9 7 At a carwash fund raiser, 18 ninth grade students and 14 tenth grade students worked the first shift. Find the ratio of ninth graders to tenth graders. Find the ratio of ninth graders to all students. ninth graders tenth graders 18 14 9 7 = = ninth graders all students 18 18 +14 18 32 9 16 = = =

Example 2 h = 68 Solve the proportion: h 17 h 17 12 = 3 12 = 3 12 = 3 h 17 12 = 3 h 17 Cross Multiply. Divide both sides by 3. 3h = 204 3 3 h = 68

Example 3 x = 5 Solve the proportion: 28 56 28 56 10 = 4x 10 = 4x 28 56 10 = 4x 28 56 Cross Multiply. Divide both sides by 112. 112x = 560 112 112 x = 5

Example 4 = = mi hr mi hr 5.5 2 x 7 2 7 x = 19.25 or 19 ¼ miles 2 2 A backpacker in the Sierras hikes 5.5 miles in 2 hours. If the hiking rate remains the same, how far will the backpacker hike in 7 hours? Write and solve a proportion to find the answer. mi hr mi hr 5.5 2 x 7 = = 5.5 = x 2 7 Cross Multiply Divide both sides by 2. 2 2 2x = 38.5 x = 19.25 or 19 ¼ miles

Homework Section 3-5 Pg. 165 – 166 5-14, 23- 25, 32-38even, 45,50,51, Solve and Prove: 62-66 even