Name Problem Solving Equations with Fractions Essential Question How can you use the strategy solve a simpler problem to solve equations involving fractions? Lesson.7 Expressions and Equations.EE.B.7 MATHEMATICAL PRACTICES MP2, MP, MP7, MP You can change an equation involving a fraction to an equation involving only whole numbers. To do so, multiply both sides of the equation by the denominator of the fraction. Unlock the Problem On canoe trips, people sometimes carry their canoes between bodies of water. Maps for canoeing use a unit of length called a rod to show distances. Victoria and Mick carry their canoe 40 rods. The equation 40 = 11 2 d gives the distance d in yards that they carried the canoe. How many yards did they carry the canoe? Use the graphic organizer to help you solve the problem. Read the Problem What do I need to find? Write a simpler equation. Solve the Problem Image Credits: (C) Radius Images/Alamy Images I need to find What information do I need to use? I need to use. How will I use the information? I can solve a simpler problem by changing the equation to an equation involving only whole numbers. Then I can solve the simpler equation. So, Victoria and Mick carried their canoe _ yards.. Write the equation. Multiply both sides by the denominator. Multiply. Solve the simpler equation. Write the equation. Use the Division Property of Equality. Divide. Math Talk 40 = 2 11 d 11 40 = _ 2 11 d _ = 2d 440 = 2d 440 = 2d _ = d MATHEMATICAL PRACTICES 1 Evaluate How can you check that your answer to the problem is correct? Chapter 457
If an equation contains more than one fraction, you can change it to an equation involving only whole numbers by multiplying both sides of the equation by the product of the denominators of the fractions. Try Another Problem Trevor is making 2_ of a recipe for chicken noodle soup. He adds 1_ 2 cup of chopped celery. The equation 2_ c = 1_ 2 can be used to find the number of cups c of chopped celery in the original recipe. How many cups of chopped celery does the original recipe call for? Use the graphic organizer to help you solve the problem. Read the Problem Solve the Problem What do I need to find? What information do I need to use? How will I use the information? So, the original recipe calls for _ cup of chopped celery. MATHEMATICAL PRACTICE Describe a Method Describe another method that you could use to solve the problem. Math Talk MATHEMATICAL PRACTICES 2 Reasoning How do you know that your answer is reasonable? 45
Name Share and Show MATH BOARD 1. Connor ran kilometers in a relay race. His distance represents 10 of the total distance of the race. The equation 10 d = can be used to find the total distance d of the race in kilometers. What was the total distance of the race? First, write a simpler equation by multiplying both sides by the denominator of the fraction. Unlock the Problem Circle the important information. Use the Properties of Equality when you solve equations. Check your solution by substituting it into the original equation. WRITE Math Show Your Work Next, solve the simpler equation. So, the race is long. 2. SMARTER What if Connor s distance of kilometers represented only 2 10 of the total distance of the race. What would the total distance of the race have been?. The lightest puppy in a litter weighs 9 ounces, which is _ 4 of the weight of the heaviest puppy. The equation _ 4 w = 9 can be used to find the weight w in ounces of the heaviest puppy. How much does the heaviest puppy weigh? 4. Sophia took home 2_ 5 of the pizza that was left over from a party. The amount she took represents 1_ 2 of a whole pizza. The equation 2_ 5 p = 1_ 2 can be used to find the number of pizzas p left over from the party. How many pizzas were left over? 5. A city received _ 4 inch of rain on July 1. This represents 10 of the total amount of rain the city received in July. The equation 10 r = _ 4 can be used to find the amount of rain r in inches the city received in July. How much rain did the city receive in July? Chapter Lesson 7 459
MATHEMATICAL PRACTICES ANALYZE On Your Own. DEEPER Carole ordered 4 dresses for $0 each, a $25 sweater, and a coat. The cost of the items without sales tax was $40. What was the cost of the coat? 7. SMARTER A dog sled race is 25 miles long. The equation 5_ k = 25 can be used to estimate the race s length k in kilometers. Approximately how many hours will it take a dog sled team to finish the race if it travels at an average speed of 0 kilometers per hour?. MATHEMATICAL PRACTICE Explain a Method Explain how you could use the strategy solve a simpler problem to solve the equation _ 4 x = 10. WRITE Math Show Your Work 9. SMARTER In a basket of fruit, 5_ of the pieces of fruit are apples. There are 20 apples f = 20 can be used to find how many pieces of fruit f are in the basket. Use words and numbers to explain how to solve the equation to find how many pieces of fruit are in the basket. in the display. The equation 5_ Image Credits: (r) Thinkstock/Getty Images 40
Name Problem Solving Equations with Fractions Practice and Homework Lesson.7 COMMON CORE STANDARD.EE.B.7 Reason about and solve one-variable equations and inequalities. Read each problem and solve. 1. Stu is 4 feet tall. This height represents _ of his 7 brother s height. The equation _ h = 4 can be used to 7 find the height h, in feet, of Stu s brother. How tall is Stu s brother? 7 _ 7 h = 7 4 h = 2 h_ = 2 _ 2_ h = 4 2_ 4 feet 2. Bryce bought a bag of cashews. He served 7 _ pound of cashews at a party. This amount represents 2 _ of the entire bag. The equation 2 _ n = 7 _ can be used to find the number of pounds n in a full bag. How many pounds of cashews were in the bag that Bryce bought?. In Jaime s math class, 9 students chose soccer as their favorite sport. This amount represents _ of the entire class. The equation _ s = 9 can be used to find the total number of students s in Jaime s class. How many students are in Jaime s math class? 4. WRITE Math Write a math problem for the equation. _ 4 n = 5 _. Then solve a simpler problem to find the solution. Chapter 41
Lesson Check (.EE.B.7) 1. Roger served 5_ pound of crackers, which was 2_ of the entire box. What was the weight of the crackers originally in the box? TEST PREP 2. Bowser ate 4 1_ 2 pounds of dog food. That amount is _ 4 of the entire bag of dog food. How many pounds of dog food were originally in the bag? Spiral Review (.NS.A.1,.RP.A.d,.EE.A.2a,.EE.B.7). What is the quotient 4 2_ 4 1_ 5? 4. Miranda had 4 pounds, ounces of clay. She divided it into 10 equal parts. How heavy was each part? 5. The amount Denise charges to repair computers is $50 an hour plus a $25 service fee. Write an expression to show how much she will charge for h hours of work. 42. Luis has saved $14 for a skateboard that costs $52. He can use the equation 14 + m = 52 to find how much more he needs. How much more does he need? FOR MORE PRACTICE GO TO THE Personal Math Trainer