1. Homework – Worksheet Do Now 5/27/14 Japan’s Bullet Train is one of the world’s fastest trains. It has a top speed of 186 miles per hour! What was the train’s unit rate for the trip below?

2. What is a proportion? • Two ratios, set equal to each other. • Used to solve for a missing piece of the proportion. • Ex: 3x 4 = 9 • Solving Proportions: http://www.youtube.com/watch?v=Uv_hPQfJE4g

3. Solving Proportions • Alex makes granola to take for a healthy snack at school. Six cups of rolled oats are needed to make 9 cups of granola. If he wants to make only 5 cups of granola, how many cups of rolled oats should he use? • Set up a proportion for the problem. 6 c oats = ___x____ 9 c granola 5 c granola

4. “Cross Multiplication” 6 c oats= ___x_____ 9 c granola5 c granola 6 * 5 = 9x 30 = 9x 30/9 = x 3 1/3 = x He needs 3 1/3 cups of rolled oats.

5. How does this work? • There are many reasons, here’s one: • Remember the trick for comparing fractions? Just cross multiply and compare the numerators. • If the numerators are the same, the fractions are equal. For proportions, we assume they are equal ratios and then solve for the missing number.

6. More Examples Solve using cross multiplication: 6 = x 6*12 = 8x 8 12 72 = 8x 9 = x 4 = 5 4*36 = 5m m36 144 = 5m 28.8 = m

7. Number Sense • If a car travels 48 miles per hour, about how many miles does it travel in 5 hours? • Layla can read 24 pages in 30 minutes. How can you mentally calculate the number of pages she can read in 45 minutes? • How can you tell without solving that n is greater than 100? 45 = n 20 50

8. Practice • Classwork: 13-3 • Homework: 13-4