(7) Lesson 1.2 - Complex Fractions and Unit Rates

1. Course 2, Lesson 1-2
Find each unit rate. Round to the nearest hundredth if necessary.
1. $3.99 for 16 ounces 2. 730 miles in 14 hours
3. $28 for 15 goldfish 4. 234 Calories in 3 servings
5. Which is the better unit price: $1.99 for a 3-ounce bottle or $2.49
for a 4-ounce bottle?
6. Cassandra leaves college to go home for the summer. She lives
424 miles away and arrives in 8 hours. Which ratio shows her
rate of travel in simplest form?

2. Course 2, Lesson 1-2
ANSWERS
1. $0.25 per ounce
2. 52.14 miles per hour
3. $1.87 per goldfish
4. 78 Calories per serving
5. $2.49 for a 4-ounce bottle
6. 53:1

3. HOW can you show that
two objects are proportional?
Ratios and Proportional Relationships
Course 2, Lesson 1-2

4. Ratios and Proportional Relationships
Course 2, Lesson 1-2 Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council
of Chief State School Officers. All rights reserved.
• 7.RP.1
Compute unit rates associated with ratios of fractions, including ratios of
lengths, areas and other quantities measured in like or different units.
• 7.NS.3
Solve real-world and mathematical problems involving the four operations
with rational numbers.
Mathematical Practices
1 Make sense of problems and persevere in solving them.
3 Construct viable arguments and critique the reasoning of others.
4 Model with mathematics.
6 Attend to precision.

5. • To simplify a complex fraction
• To find unit rates
Ratios and Proportional Relationships
Course 2, Lesson 1-2

6. Ratios and Proportional Relationships
Course 2, Lesson 1-2
• complex fraction
1
2
2
1
2
3 11
2
1
4

7. 1
Need Another Example?
2 Write the complex fraction as a division problem.
Multiply by the reciprocal of 2, which is .3
4 Simplify.
5
Step-by-Step Example
1. Simplify .
Recall that a fraction can also be written as a division problem.
So, is equal to .

8. Answer
Need Another Example?

9. 1
Need Another Example?
2 Write the complex fraction as a division problem.
Multiply by the reciprocal of , which is .3
4 Simplify.
5
Step-by-Step Example
2.
Write the fraction as a division problem.
So, is equal to 2.

10. Answer
Need Another Example?
20

11. 1
Need Another Example?
2 Write the complex fraction as a division problem.
Write the mixed number as an improper fraction.3
4
Multiply by the reciprocal of , which is .
Simplify.5
6
Step-by-Step Example
3. Josiah can jog 1 miles in hour. Find his average
speed in miles per hour.
Write a rate that compares the number of miles to hours.
So, Josiah jogs at an average speed of 5 miles per hour.

12. Answer
Need Another Example?
Marcus has a bag of cat food that contains
22 cups. If he feeds his cats a total of
cup of food per day, how many days will the bag
last?
30 days

13. 1
Need Another Example?
2 Write the complex fraction as a division problem.
Write the mixed number as an improper fraction.3
4 Multiply by the reciprocal of , which is .
Simplify.5
6
Step-by-Step Example
4. Tia is painting her house. She paints 34 square
feet in hour. At this rate, how many square feet
can she paint each hour?
Write a ratio that compares the amount of square feet to hours.
So, Tia can paint 46 square feet per hour.

14. Answer
Need Another Example?
A construction worker is blacktopping a
driveway. She blacktops 35 square yards
in hour. How many square yards can she
blacktop per hour?
42 square yards per hour

15. Definition of percent1
Need Another Example?
2 Write the complex fraction as a division problem.
Write 33 as an improper fraction.
3
4 Multiply by the reciprocal of 100, which is .
Simplify.5
6
Step-by-Step Example
5. On Javier's soccer team, about 33 % of the
players have scored a goal. Write 33 %
as a fraction in simplest form.
1
1
So, about of Javier's team has scored a goal.

16. Answer
Need Another Example?
Write 6 % as a fraction in simplest form.

17. How did what you learned
today help you answer the
HOW can you show that
two objects are proportional?
Course 2, Lesson 1-2
Ratios and Proportional Relationships

18. How did what you learned
today help you answer the
HOW can you show that
two objects are proportional?
Course 2, Lesson 1-2
Ratios and Proportional Relationships
Sample answers:
• By simplifying a complex fraction to find a unit rate
• By writing a percent as a rate per 100

19. Simplify .
Ratios and Proportional RelationshipsRatios and Proportional Relationships
8
31
5
Course 2, Lesson 1-2