1. 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.

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

3. Solving proportions with complex fractions
Lesson 7.2.2:
Solving proportions with complex fractions

4. Guided practice: dividing fractions
YOU TRY # 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.

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

6. = = 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.

7. = = 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 = = x x 𝑥=
𝑥=7.5
Guided practice
Step 1: set up the proportion
Step 2: cross multiply
Step 3: Divide
Step 4: Check answer.

8. = = 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=
Guided practice
Step 1: set up the proportion
Step 2: cross multiply
Step 3: Divide
Step 4: Check answer.

9. 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.

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

11. 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 cups of spaghetti.
How much is one serving?
𝑥=1.125
𝑥=328 mi
𝑥= /𝑠𝑒𝑟𝑣𝑖𝑛𝑔

12. 𝑥=3 in 𝑥=1 5 21 in GUIDED PRACTICE #8 YOU TRY #8
Pedro grew inches during a
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 hours. What was the rate of snowfall in one hour?
𝑥=3 in
𝑥= in

13. 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 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 miles in a time of hours. How Far did she run in 1 hour?
𝑥= mi
𝑥=6 cups

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

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

17. 𝑥=296𝑚𝑖 𝑥= 3 8 Tbs. PRACTICE # 5 PRACTICE #6
If Mark uses 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= Tbs.

18. 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 pizzas out of the 15. How much pizza did each cast member eat?
Ben’s 6 bird feeders hold cups
of bird feed. How much will one
bird feed hold?
𝑥= cup
𝑥= pizza

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

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