(7) Lesson 1.2 - Complex Fractions and Unit Rates

(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

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 percent 1 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 Relationships Ratios and Proportional Relationships Course 2, Lesson 1-2