Topic 9. Adding & Subtracting Fractions. Name. Test Date

Topic 9 Adding & Subtracting Fractions Name Test Date

A veterinarian weighed four cats. Use the data shown in the table for 1 through. Cat Weights of Cats x Weight (pounds) Bob 8.25 Fluffy 8 _ 4 Miss Kitty 8.5 Tiger 8 1. Which cat s weight does point X name? Daily Common Core Review 9-1 4. Plot 0.29 on the number line below. 0 0.1 0.2 0. 0.4 0.5 0.6 0.7 0.8 0.9 1 5. The table shows the number of miles a taxi drives and the cost of the taxi ride. Distance (miles) 8 10 16 22 Cost $4 $5 $8? Describe how to find the cost of a 22-mile taxi ride? 8 9 A Bob B Fluffy C Miss Kitty D Tiger 6. Write a whole number greater than 99,999,999 and less than 100,000,100. 2. Which cat s weight in the table above is closest to 9 pounds? A Bob B Fluffy C Miss Kitty D Tiger. What is the difference between Bob s weight and Miss Kitty s weight? A 0.20 pounds B 0.25 pounds C 0.5 pounds D 0.75 pounds D 9 1

Problem Solving: Writing to Explain Estimate the fractional part of the shaded portions below. Explain how you decided. Practice 9-1 1. 2.. Draw a square and shade about _ 1 of it. How did 8 you decide how much to shade? 4. Draw two rectangles that are different sizes. Shade about 1 _ 2 of each. Are the shaded parts the same amount? Explain. 5. Look at a picture of the American flag. Approximately what part of the flag is blue? Explain. P 9 1

1. About how much of the pizza is covered with pepperoni? Quick Check 9-1 2. Claire is painting a wall in her room white. About how much of the wall has she painted? A about 9 10 B about _ 5 6 C about _ 8 D about _ 2 A about _ 8 B about _ 4 C about _ 7 8 D about 9 10. Writing to Explain Estimate the part of the garden that is planted with tomatoes. Explain how you decided. pumpkins lettuce tomatoes cucumbers Q 9 1

1. Bukka has 986 paperback books. He wants to put these books on storage shelves. Each shelf can hold 50 paperback books. How many shelves will Bukka need to hold all of the books? A 20 shelves B 19 shelves C 18 shelves D 10 shelves Daily Common Core Review 9-2 4. What is the missing y-value in the table below? x 2 4 6 8 10 y 24 48 72 96? 5. Carter drew this number line to illustrate the sum of two fractions. He forgot to label the fractions. 2. The U.S. Census Bureau estimated that the population of St. Petersburg, Florida, in 2006 was 248,098. What is this number in expanded notation? A 200,000 + 40,000 + 8 B 200,000 + 40,000 + 8,000 + 900 + 8 C 200,000 + 40,000 + 8,000 + 90 + 8 D 248,000 + 90 + 8 0 What fraction equation did he draw? Explain how you know what number to use for the denominator. 1. Which is the correct product of n 7 if n = $0.25 A $.25 B $2.75 C $1.75 D $2.25 D 9 2

Estimating Sums and Differences of Fractions In 1 through 8, tell if each fraction is closest to 0, _ 1, or 1. You may 2 use a number line to help. Practice 9-2 1. 1 9 2. 5 9. 11 4. 6 20 10 5. 6 6. 5 7 12 7. 8. 12 4 15 In 9 through 16, estimate each sum or difference by replacing each fraction with 0, _ 1, or 1. 2 9. 7 12 + 4 10. 1 5 12 + 2 4 11. 4 9 1 6 12. 2 6 + 8 9 1. 1 6 1 8 14. 2 5 7 15. 7 8 7 16. 5 9 12 + 2 5 17. Which is the best estimate for the difference of 9 16 4 _ 9? A 1 1 = 0 C 1 1 2 = 1 2 B 1 2 1 2 = 0 D 0 0 = 0 18. Which fraction can NOT be replaced with _ 1 when estimating? 2 A 10 12 C 4 10 B 2 6 D 1 24 19. Mia estimated _ 5 8 + _ 1 9 by replacing _ 5 8 with 1 and _ 1 with 0. Her 9 estimated sum was 1 + 0 = 1. Explain why Mia s estimate is NOT accurate. P 9 2

1. Which fraction can be replaced with _ 1 when estimating with 2 fractions? A 1 8 B 2 9 C 2 D 10 12. Which is the BEST estimate for the sum of 5 12 + _ 2 5? A 0 + 0 = 0 B 1 2 + 0 = 1 2 C 1 + 1 = 2 D 1 2 + 1 2 = 1 Quick Check 9-2 2. Which fraction can be replaced with 0 when estimating with fractions? A 1 5 B 4 C 8 20 D 4 9 4. Which is the BEST estimate for the difference of _ 7 8 _ 4 9? A 1 1 = 0 B 1 2 1 2 = 0 C 1 1 2 = 1 2 D 0 0 = 0 5. Writing to Explain Keri says that you can replace a fraction with 0, _ 1, or 1 by looking at the denominator first. If the numerator 2 is half or close to half the value of the denominator, replace with _ 1 2. If the numerator is closer to the value of the denominator, replace with 1. Is Keri correct? Use the number line and _ 5 as an example 8 to help you explain your reasoning. 0 1 1 2 Q 9 2

1. Find the lowest common multiple of 5 and 8. A 16 B 20 C 24 D 40 Daily Common Core Review 9-4. Casey s watch beeps every 15 minutes. Her brother s watch beeps every 10 minutes. The last time both watches beeped was at 5:0 p.m. What time will it be the next time both watches beep at the same time? Explain how you know. 2. Which decimal is equal to 1 _ 4? A 1.75 B 1.4 C 1.4 D 1.25. Use the diagram below. 400 x x x x x x x x What is the value of x? D 9

Adding Fractions with Unlike Denominators Find each sum. Simplify if necessary. Practice 9-1. 2 9 + 1 2. 1 + 7 21. 2 + 1 5 4. 1 4 + 2 5. 1 12 + 4 6 6. 1 2 + 2 5 7. 1 + 5 6 12 8. 4 6 + 1 9. 1 5 + 1 8 10. 4 + 1 11. 6 9 12 + 1 12. 4 8 + 1 2 Jeremy collected nickels for one week. He is making stacks of his nickels to determine how many he has. The thickness of one nickel is 1 16 inch. 1. How tall is a stack of 16 nickels? 14. What is the combined height of nickels, 2 nickels, and 1 nickel? 15. What is the sum of 5 0 + 4 6? A 5 6 B 7 9 C 2 D 9 12 16. How do you rename _ 2 so you can add it to 11? What is the sum? 5 25 P 9

1. What is the sum of 1 5 and 4? A 5 9 B 9 10 C 18 20 D 19 20 2. Find the sum of 1 6 + 1 2. A 1 B 1 4 C 2 D 4 Quick Check 9-. A piece of glass is _ 1 inch thick, and a second piece of glass 4 is 7 inch thick. What is the combined thickness of the two 16 pieces of glass? A 11 16 inch B 15 16 inch C 1 16 inches D 1 4 inches 4. Writing to Explain Anna bought a package of one dozen eggs at the store. She used _ 1 of them to make cookies, and 4 her brother used _ 1 of them to make pancakes for the family. Add the fractions to calculate the number of eggs used and then determine how many eggs were left. Show your work. Q 9

1. Find the sum. Simplify if possible. 2 5 + 6 A 5 11 B 9 10 C 27 0 D 2 2. The circumference of the moon, measured at its equator, is 10,921 kilometers. What digit is in the thousands place? A 9 B 2 C 1 D 0 Daily Common Core Review 9-4. As of 2008, the record for the longest rabbit ear span ever measured was 1.125 inches. Toby s pet rabbit has an ear span of 12.505 inches. How much longer, in inches, is the record measurement than the ear span of Toby s pet rabbit? 4. Use compatible numbers to estimate the quotient of,780 9. What compatible numbers did you use? Is your estimate an underestimate or overestimate? Explain why. D 9 4

Subtracting Fractions with Unlike Denominators Find the difference. Simplify if necessary. Practice 9-4 1. 10 12 1 2. 9 4 10 5. 7 8 2 6 4. 7 12 1 4 5. 4 5 1 6. 2 1 6 7. 4 8 1 8. 4 4 10 1 5 9. 9 9 2 10. 9 15 1 11. 4 12 1 12. 14 6 20 5 1. The pet shop owner told Jean to fill her new fish tank _ 4 full with water. Jean filled it 9 full. What fraction of the tank does 12 Jean still need to fill? 14. Paul s dad made a turkey potpie for dinner on Wednesday. The family ate _ 4 of the pie. On Thursday after school, Paul 8 ate 2 of the pie for a snack. What fraction of the pie remained? 16 15. Gracie read 150 pages of a book. The book is 227 pages long. Which equation shows the amount she still needs to read to finish the story? A 150 n = 227 C n 150 = 227 B 227 + 150 = n D n + 150 = 227 16. Why do fractions need to have a common denominator before you add or subtract them? P 9 4

1. What is the difference of 4 5 1 4? A 2 B 9 10 C 11 20 D 19 20 2. Find the difference of 2 1 6. A 5 9 B 1 2 C 1 4 D 1 Quick Check 9-4. A _ 1 yard of ribbon is needed for a craft project. How much 2 ribbon will remain from a piece that measures _ 7 8 yard? A 16 yard B 1 4 yard C 1 6 yard D 8 yard 4. Writing to Explain You have a cake that was cut into 18 pieces. At the end of your party, one half of the cake was left. Then your friend took 5 pieces home for her family. What fraction of the cake do you still have? Simplify if necessary. Show your work. Q 9 4

1. A bank charges 5.25672% annual percentage rate on a home mortgage. What is this number rounded to the nearest tenth? A 5.2 B 5.25 C 5. D 6 Daily Common Core Review 9-5 4. Draw a picture to show 4_ 7 as a part of a set. 5. Evaluate the expression for m 5 2. 5m 1 2(m + 8) + 2. What fraction of the rectangle is shaded? 6. Carla checked 8 books out of the library. This was more than Lee checked out. How many books did Lee check out of the library? Write an equation to solve the problem, then write the answer. A 2_ 8 B 4_ 8 C _ 6 D 5_ 8. How would you get the variable alone in the equation 4y 5? A Divide both sides of the equation by 4 B Add 4 to both sides of the equation C Multiply both sides of the equation by 4 D Subtract from both sides of the equation 7. Jim s book club offers 1 free book for every 4 books he buys. How many books would Jim have to buy to get 6 free books? Books bought Free books 4 8 12 16 20 1 2 4 5 6 D 9 5

More Adding and Subtracting Fractions Find each sum or difference. Simplify your answer. Practice 9-5 1. 5_ 6 1 4 12 5 2. 4_ 5 2 1 10 5. 5 1 2_ 12 5 4. 9 1 _ 5 5 5. 6 2 1_ 5 6. 19 2 2_ 7 5 20 7. 2_ 5 1 5 20 5 8. 8_ 10. Number Sense Is 7_ 8 or 11 10 16 4 2 5 9 12 5 9. 7_ 21 8 1 11 2 5_ 24 closer to 1? How did you decide? 6 5 Emma has a small garden. Emma s garden is 1_ 5 beans, 1_ peas, and 8 1_ corn. The rest is planted with flowers. 2 11. What fraction of Emma s garden is planted with vegetables? 12. Are there more flowers or peas in Emma s garden? 1. To solve the subtraction sentence 17 2 2_ 10 5 5?, which common denominator is the best choice? A 10 B 15 C 20 D 50 14. Writing to Explain To find the sum of 4_ and 7, Mario rewrites the fractions 9 12 as 8 and 21. His answer is 29. Is Mario right? If not, show his error and correct it. 6 6 6 P 9 5

Quick Check 9-5 1. Find 1_ 1 1_ 4 6. A 1_ 2 B 5 C 1_ D 1_ 5 2. Find 2_ 2 5_ 8. A 24 1 B 1_ C 11 24 D _. The picnic area in a park is on the trail that connects the parking lot with the lake. The picnic area is 2_ 5 mi from the parking lot and 1_ mi from the lake. How long is the trail? A 1_ 5 mi B 1_ 2 mi C 11 mi D 4_ 5 mi 15 4. Writing to Explain A gallery used this floor plan to display art. What fraction names each display area? hint: Each numerator is 1 and the smallest sections show 1 Write one question about the floor plan that can be answered by writing an addition sentence and one question that can be answered by writing a subtraction sentence. Answer your questions. 12 8 5 24. Paintings Cloth Materials Glass Metal Metal Special Exhibits Paintings Sculpture Special Exhibits Sculpture Glass Cloth Materials Q 9 5

1. How many pairs of parallel sides are in a parallelogram? Daily Common Core Review 9-6. How many lines of symmetry can be found in the figure below? A 1 B 2 C D 4 2. The area of the state of Florida is 5,927 square miles. What is this number rounded to the nearest thousand? A 50,000 B 5,000 C 5,900 D 54,000 4. Every weekday, Tasha walks _ 8 mile to school. After school, she walks _ 2 mile to her grandparents 8 house. Then she takes the same route home. Does Tasha walk more than one mile each day? Explain how you know. D 9 6

More Adding and Subtracting Fractions In 1 through 12, simplify each expression. Practice 9-6 1. 4 6 + 2 9 2. 2 7 + 1. 8 2 12 + 1 6 4. 8 + 1 6 5. 1 12 + 7 6. 4 9 18 + 2 9 7. 1 + 1 8. 5 4 15 + 5 9. 1 2 ( 1 8 + 1 8 ) 10. 4 + ( 1 4 1 6 ) 11. ( 1 + 2 20 ) 2 20 12. ( 2 5 + 1 5 ) 10 1. A plumber is fitting a water pipe that is _ foot long on to a water 4 pipe that is 2 foot long. How long 12 will the finished pipe be? A 11 foot 12 C 2 12 foot B 8 foot 16 D 1 foot 14. Joel made some muffins. He gave _ 1 of the muffins to a 4 neighbor. He took _ of the muffins 8 to school. What fraction of the muffins is left? A 4 12 C 5 12 B 8 D 8 8 15. Carl has three lengths of cable, _ 5 6 yard long, _ 1 yard long, 4 and _ 2 yard long. He needs at least 1 yard of cable. a Which two pieces together make a length at least 1 yard and closest to 1 yard? b If Carl uses the two shortest pieces, how much more cable would he need? c After Carl has used 1 yard of cable, how much cable will he have left? Explain how you found your answer. P 9 6

Quick Check 9-6 1. What is the sum of 1 _ + 1 _ + 1 _ 8? A 14 B 11 C 19 24 D 6 8 2. What is the difference of 7 _ 8 1 _? A 6 5 B 8 11 C 6 8 D 1 24. A recipe for crumb cake says to mix _ cup of brown sugar 8 and _ 1 cup of white sugar. From this sugar mixture, set aside _ 1 cup for the crumb topping. The remaining sugar 4 mixture is used to make the cake. What amount of the sugar mixture is used to make the cake? A 11 24 cup B 1 2 cup C 7 12 cup D 17 24 cup 4. Writing to Explain Owen and Bella shared a granola bar. Bella ate _ 1 4 of the granola bar. Owen ate _ 1 of the bar. a Explain how to find the fraction of the granola bar that Owen and Bella ate. b Explain how to find the fraction of the granola bar that is left. Q 9 6

1. A deli is open 5 days a week for 5 hours each day. One week the deli served 925 customers. If the same number of customers were served each hour, how many were served each hour? Daily Common Core Review 9-7 4. Mr. Rosenthal is getting ready to make gumbo, a type of soup. He buys some shrimp for $7.95, an onion for $0.26, and a bunch of celery for $1.0. How much does he spend on ingredients? A 185 B 125 C 7 D 16 2. Which number completes the equation below? 5. What is the missing number in this equation? Explain how you know. 2 (10 ) = ( 10) What property does the equation illustrate? (2 4 1) + 21 = + 14 + 5 A 6 B 7 C 14 D 5. Choose a fraction to make the inequality true. 5 > A 4 5 B 6 C 4 6 D 5 6 D 9 7

Problem Solving: Draw a Picture and Write an Equation Draw a picture and write an equation to solve. Practice 9-7 1. Jamie bought _ 5 pound of wheat flour. He also bought _ 8 1 pound of white flour. 4 How much flour did he buy? 2. Katie is _ of the way to Brianna s house. Larry is 7 of the way to Brianna s 5 10 house. How much closer to Brianna s house is Larry?. Nina practiced the trumpet for _ 1 hour. Santiago practiced the trumpet for 6 _ 2 hour. How much longer did Santiago practice than Nina? 4. Ned caught _ 1 pound of fish. Sarah caught 5 pound of fish. Jessa caught 12 _ 1 pound of fish. Which bar diagram shows how to find how many pounds 6 of fish they caught in all? A B x pounds in all 2 6 2 6 x pounds in all 1 6 C D 12 x pounds in all 5 12 x pounds in all 6 12 1 5 12 1 6 1 12 5 12 1 12 5. In solving a fraction equation, John added the numerators of several fractions with unlike denominators. What should John have done first? P 9 7

Quick Check 9-7 For 1 and 2, you may draw a picture and write an equation to help. 1. Betty mixed _ 1 6 pound of peanuts with _ 1 pound of raisins. How much mix did Betty have in all? A 1 4 pound C 1 2 pound B 1 pound D 1 pound 2. Jill did aerobics for _ 5 hour and then lifted weights for _ 1 hour. How much exercise did Jill get? A 14 15 hour C 2 5 hour B 4 5 hour D 1 5 hour. Justin used _ pound of broccoli to make a stir-fry and 9 4 10 pound of broccoli to make cheddar and broccoli soup. Which picture can be used to find how much broccoli Justin used in all? A 9 10 4 x C x 9 10? B x 4 9 10 D 4 9 10 x 4. Writing to Explain Matt jogged _ 1 2 of a mile. Thomas jogged _ 5 of a mile. How 8 much farther did Thomas jog? Draw a picture and write an equation to solve. Q 9 7