Lesson 7.2.2 A ratio is the comparison of two quantities by division. We also, learned about proportions. A proportion states that 2 ratios are equal. We learned that you can use cross multiplication to determine if 2 ratios are equal to each other. We also solved proportions that had a variable. Why learn? Proportions can be used to find missing numbers in a real world math problem. Later on in the third nine weeks we will see how proportions can be used to solve problems involving scale models and similar figures. Engineers use scale models to build high tech aircraft. If two figures are similar (same shape, but different size), a proportion can be used to find a missing side length on one of the shapes.

What do proportions have to do with food, distance, measurements, etc.?

Solving proportions with complex fractions Lesson 7.2.2: Solving proportions with complex fractions https://www.youtube.com/watch?v=Vrc_Z0a_nkY

Guided practice: dividing fractions YOU TRY #1 Lesson 7.2.2 GUIDED PRACTICE #1 3 5 3 4 1 2 5 6 9 10 1 1 5 Guided practice: dividing fractions Step 1: set up as a division problem Step 2: write the reciprocal of the second fraction (KCF) Step 3: solve as a multiplication problem.

= = 7 4 6 x 3 x 𝑥=20 𝑥=63 GUIDED PRACTICE #2 YOU TRY #2 3 5 7 4 = = 6 x 3 x 𝑥=20 𝑥=63 Guided practice Step 1: set up the proportion Step 2: cross multiply Step 3: Divide Step 4: Check answer.

= = x 6 9 4 x 6 𝑥=81 𝑥=42 YOU TRY #3 GUIDED PRACTICE #3 2 3 = 9 4 4 7 = x 6 𝑥=42 𝑥=81 Guided practice Step 1: set up the proportion Step 2: cross multiply Step 3: Divide Step 4: Check answer.

= = 3 x 6 x 𝑥=4 1 2 𝑥=7.5 YOU TRY #4 GUIDED PRACTICE #4 1 4 5 8 1 2 3 8 = = 3 x 6 x 𝑥=4 1 2 𝑥=7.5 Guided practice Step 1: set up the proportion Step 2: cross multiply Step 3: Divide Step 4: Check answer.

= = 2 x x 3 2 𝑥=3 1 3 𝑥=1 2 13 YOU TRY #5 GUIDED PRACTICE #5 5 7 2 3 2 x x = = 3 6 7 1 8 5 2 𝑥=3 1 3 𝑥=1 2 13 Guided practice Step 1: set up the proportion Step 2: cross multiply Step 3: Divide Step 4: Check answer.

Lesson 7.2.2 : Proportions with Complex Fractions For each problem below, do the following: • Set up a proportion by writing the original rate (including labels) as a ratio (in fraction form), and show that it is equal to the new rate, filling in the part of that rate that you know so far. • Show any calculations needed to find the missing value.

𝑥=8 19 28 𝑚𝑖 𝑥=1 1 3 cup GUIDED PRACTICE #6 YOU TRY #6 Jerry can run 3 3 8 miles in 1 1 6 of an hour. How far can he run in 3 hours? Sarah uses 1 3 4 cup of sugar and 2 1 3 cups of flour. If she uses 1 cup of Sugar, how much flour will she need? 𝑥=8 19 28 𝑚𝑖 𝑥=1 1 3 cup

𝑥=1.125 𝑥=328 mi 𝑥= 1 1 8 /𝑠𝑒𝑟𝑣𝑖𝑛𝑔 GUIDED PRACTICE #7 YOU TRY #7 Susan’s car will travel 246 miles on 3 4 of tank of gas. How far can she drive on a full tank of gas? Sharon made a large pot of spaghetti. 18 servings is 20 1 4 cups of spaghetti. How much is one serving? 𝑥=1.125 𝑥=328 mi 𝑥= 1 1 8 /𝑠𝑒𝑟𝑣𝑖𝑛𝑔

𝑥=3 in 𝑥=1 5 21 in GUIDED PRACTICE #8 YOU TRY #8 Pedro grew 4 1 3 inches during a 3 1 2 month growth spurt. If his growth spurt continued at the same rate how much did he grow in one month? During one winter snowstorm in Denver, Colorado, Jesse noted that 16 inches of snow fell in 5 1 3 hours. What was the rate of snowfall in one hour? 𝑥=3 in 𝑥=1 5 21 in

𝑥=4 15 29 mi 𝑥=6 cups GUIDED PRACTICE #9 YOU TRY #9 Brianna’s Chocolate Chip Cookie Recipe will make about 3 dozen chocolate chip cookies. The recipe calls for 2 1 4 cups of flour and 3 8 Cups of baking soda. If Brianna was to adjust the recipe to include 1 cup Of baking soda, how many cups of flour would she need to use? Mackenzie ran the Olympic marathon of 26 1 5 miles in a time of 5 4 5 hours. How Far did she run in 1 hour? 𝑥=4 15 29 mi 𝑥=6 cups

PRACTICE #1 PRACTICE #2 7 5 1 3 20 3 3 2 21 100 2 9

PRACTICE #3 PRACTICE #4 4 1 2 5 7 9 3 3 8 6 3 7 1 1 3

𝑥=296𝑚𝑖 𝑥= 3 8 Tbs. PRACTICE # 5 PRACTICE #6 If Mark uses 3 3 4 tablespoon of coffee to make10 cups of coffee, how much would he need to make on cup of coffee? Tiana’s car traveled 111 miles on 3 8 of a tank of gas. How far will she be able to go on a full tank of gas? 𝑥=296𝑚𝑖 𝑥= 3 8 Tbs.

𝑥= 9 10 cup 𝑥= 1 2 pizza PRACTICE #7 PRACTICE #8 The drama club ordered 15 pizzas for the cast party. If the 25 members ate 12 1 2 pizzas out of the 15. How much pizza did each cast member eat? Ben’s 6 bird feeders hold 5 2 5 cups of bird feed. How much will one bird feed hold? 𝑥= 9 10 cup 𝑥= 1 2 pizza

𝑥=2 1 6 𝑏𝑎𝑡𝑐ℎ𝑒𝑠 𝑥=2 8 15 cups PRACTICE #9 PRACTICE #10 Hudson made 2 1 2 portions of slime. He used 6 1 3 cups of glue. How much glue would it take to make one portion of slime? A cookie factory made 6 1 2 batches of cookies in 3 hours. How many batches can they make in 1 hour? 𝑥=2 1 6 𝑏𝑎𝑡𝑐ℎ𝑒𝑠 𝑥=2 8 15 cups

𝑥=1 4 5 cup PRACTICE #11 PRACTICE #12 A suggested planting rate for wildflower seeds is 1 2 pound per 1 8 acre. What is the unit rate in pounds per acre? Hadley is cooking a second dinner. This time the recipe calls for 3 5 cups of flour for every 1 3 cups of sugar. How much flour is required for every cup of sugar? 𝑥=4 𝑙𝑏𝑠/𝑎𝑐𝑟𝑒 𝑥=1 4 5 cup