Topic 10. Adding and Subtracting Mixed numbers. Name. Test Date

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1 Topic 0 Adding and Subtracting Mixed numbers Name Test Date

2 Topic 0 Vocabulary Cards proper fraction proper fraction A fraction less than ; its numerator is less than its denominator. mixed number Fold here mixed number A number that combines a whole number and a fraction improper fraction improper fraction A fraction in which the numerator is greater than or equal to its denominator Topic 0 of

3 . A store places out-of-season clothes on sale. The sales price is _ of the original price. Which expression describes the new sales price? A x 2 _ B x _ C x _ D _ x 2. Shelley read 0 pages of a book on Monday. On Tuesday, she read twice as many pages as she read on Monday. On Wednesday, she read twice as many pages as she read on Tuesday. How many pages did she read in all? A B C 0 pages 0 pages 70 pages D 00 pages. Cara lives 0 7 mi from school. One morning, she walks _ 5 mi towards school and meets her friend, Aaron. How many miles from school are they? A _ 5 mi B _ 2 mi C _ 5 mi D 5 mi Daily Common Core Review 0-. Find _ _. Simplify your answer if possible. 5. What is the measure of /A? A B 0. Draw a number line from 0 to 2. Write _, _ and.25 on the number line. 7. Write the rule for the table as an algebraic expression. In x 2 5 Out y C D 0 7

4 Estimating Sums and Differences of Mixed Numbers Round to the nearest whole number. Practice 0-. _ Estimate each sum or difference. 5. _ + 2 5_. 5 _ _ _. _ + 2 2_ Robert and May are competing in a track meet. The table at the right shows the results of their events. 9. Robert says his better jump was about ft longer than May s better jump. Is he correct? Participant Robert Event Long jump Softball throw Results/Distance. 5 ft _ 2 ft 2 _ 5 ft May Long jump Softball throw. 2_ ft 2. _ ft 7 7_ ft 0. Use the table above. If the school record for the softball throw is 7 ft, about how much farther must Robert throw the ball to match the record? A 5 ft B ft C ft D 20 ft. Consider the sum of _ 5 + _. Round each fraction and estimate the sum. Add the two fractions using a common denominator and then round the result. Which estimate is closer to the actual answer? P 0

5 Quick Check 0-. Which fraction rounds to 5? A 5 2_ B 5 _ 2 C 5 9 D Estimate _ _. A B 2 C 5 D. Taylor has _ yd of crepe paper. He uses 5_ yd to make party decorations. Estimate how many yards of crepe paper he has left. A yd B 2 yd C yd D 2 yd. Writing to Explain Describe three ways to estimate sums by answering the questions below. Then estimate each sum. Label 2, 5_, 5_, and 2 _ on the number line. Explain how to use the number line to estimate 5_ 2 _. How could you estimate 5_ 2 _ without using the number line? Explain how to use benchmark fractions to estimate 2 5_. 0 _ 2 _ _ 2 Q 0

6 . It takes pounds of grapes to make pound of raisins. How many pounds of grapes would you need to make,000 pounds of raisins? A,000 pounds B,000 pounds C 9,000 pounds D 2,000 pounds 2. What number represents n in the diagram below? 5,00 Daily Common Core Review 0-2. What is the least common denominator of 9 5 and _ 2? 5. Jen needs to save $0 for a new camping tent. She is able to save $5 each week. How many weeks will Jen need to save to reach her goal? Draw a picture and write an equation to solve the problem. Explain how you found your answer. n n n n n n n n A 7 B 0 C 700 D 00. What equation is modeled with this number line? A = 2 9 B 7 5 = C = 7 7 D = 7 9 D 0 2

7 Modeling Addition and Subtraction of Mixed Numbers For and 2, use each model to find each sum or difference. Practice Use fraction strips to find each sum or difference. Simplify, if possible Jerome s rain gauge showed 9 centimeters (cm) at the end of last month. 0 At the end of this month, the rain gauge showed 5 centimeters. How many more centimeters of rain fell this month? A 29 2 cm B 5 cm C 2 cm D cm. You are adding _ _ using fraction strips. Explain how you rename the fraction part of the problem. 0 P 0 2

8 Quick Check 0-2 For through, use fraction strips to find each sum or difference.. What is the sum of 7 + 5? A 0 B 0 2 C 2 D 5. Lou used cups of oats and _ cups of raisins in a recipe. How many more cups of oats did Lou use than raisins? A more cups B more cups C 2 D 5 2 more cups more cups 2. What is the difference of 5 _ 5 2 _ 5? A 2 5 B 2 2 C 5 D 5. Writing to Explain Use the models of mixed numbers below to answer a and b. a Write a mixed number for each model. b Explain how you can use the models to find how much greater one mixed number is than the other. Q 0 2

9 . Find the difference. Simplify, if possible A _ 9 B 2 2 C D After Ronaldo s Fourth of July party, _ 2 of his cake is left. How much cake will be left after his cousin Max eats another _? Simplify your answer if possible. A 5_ B _ 2 C _ D 2 Daily Common Core Review 0-. A day pass at a theme park costs $ for children and $2.50 for adults. How much would it cost to get day passes for adult and 2 children? 5. Eric uses _ 5 yards of material to make a shirt. Which is _ 5 written as an improper fraction? A B 29 C 5 D. Noreen bought two shirts for $ each and two pairs of shoes for $ a pair. How much did she pay in all? A $ B $ C $9 D $2 D 0

10 Adding Mixed Numbers Practice 0- In through, find each sum. Simplify, if possible. Estimate for reasonableness Write two mixed numbers that have a sum of.. What is the total measure of an average man s brain and heart in kilograms (kg)? Vital Organ Measures Average woman s brain 0 kg 2 5 lb Average man s brain 2 kg lb 5 Average human heart kg lb 9. What is the total weight of an average woman s brain and heart in pounds (lb)? 0. What is the sum of the measures of an average man s brain and an average woman s brain in kilograms?. Which is a good comparison of the estimated sum and the actual sum of 7 _ ? A Estimated < actual C Actual > estimated B Actual = estimated D Estimated > actual 2. Can the sum of two mixed numbers be equal to 2? Explain why or why not. P 0

11 . What is the sum of _ 5 and 2 _? A 7 B 9 20 C 7 0 D 7 20 Quick Check 0-2. Find the sum of _ 5 _. A 5 2 B 5 2 C D 5. Mr. Romano walks 7 miles from his home to the train station. 0 Then he takes the train 9 _ 5 miles to work. How many total miles does Mr. Romano travel to get to work? A 5 B 5 C 0 D 0 5. Writing to Explain A recipe calls for bread flour and whole-wheat flour. What is the total amount of flour used in the recipe? Express your answer as a mixed number in simplest form. Show your work. bread flour whole-wheat flour milk water sugar yeast Recipe cups 2 cups cup 2 cups cups 2 tablespoons Q 0

12 . What number is missing from the pattern? 2.0.0? A 2.05 B.05 C.05 D Neil spends _ hours washing the car and 2 _ 5 hours mowing and weeding the yard. How many total hours does he spend on his chores? Simplify your answer if possible. A _ B 5_ C _ D _ 7 Daily Common Core Review 0-. Mr. DeWitt carved a wooden boat for his granddaughter. He began with a piece of wood that was 20. centimeters long. The boat is.7 centimeters long. How many centimeters did Mr. DeWitt carve off the length of the wood when he made the boat? 5. The distance between Miami and Naples is 07 miles. The distance between Miami and Jacksonville is about three times this distance. Landon estimates that the distance between Miami and Jacksonville is about 00 miles. Is Landon s estimate reasonable? Why or why not?. Which of the fractions is equal to _ 5? A 20 B 25 C 2 20 D 5 D 0

13 Subtracting Mixed Numbers For through 0, find each difference. Simplify, if possible Practice The table shows the length and width of several kinds of bird eggs.. How much longer is the Canada goose egg than the raven egg? 2. How much wider is the turtledove egg than the robin egg? Egg Sizes in Inches (in.) Bird Length Width Canada goose Robin Turtledove. Which is the difference of 2 5 _? A 2 7 B 2 9 C D 9. Explain why it is necessary to rename _ if you subtract _ from it Raven P 0

14 . What is the difference of 5 5? A 2 5 B 5 C D 5 5 Quick Check 0-2. Find the difference of 9 5. A B 5 C 2 D 5. Some of the largest insects are beetles. The Titanus beetle can measure 7 centimeters in length and the Giant Weta 0 beetle can measure _ centimeters in length. How much 2 longer is the Titanus than the Giant Weta? A 25 5 centimeters B 9 5 centimeters C 2 centimeters D 5 centimeters. Writing to Explain Jessie is building a doghouse. For one side of the roof, she needs a board that is 7 _ feet long. She has a board that measures 9 feet. How much of the length 2 does she need to cut from the board? Show your work and simplify the fraction. 7 feet Q 0

15 . Which mixed number is represented by the shaded parts of the model? Daily Common Core Review 0-5. Hector s father is times as old as Hector and twice as old as Carlos. If Carlos is 2 years old, how many years old is Hector? A 2 2 B 2 C D 2 5. Explain the difference between an acute angle and an obtuse angle. In your explanation, give sample measures for each type of angle. 2. Which of these is the correct order of operations for evaluating the expression + 2 2? A Add, evaluate the term with an exponent, then multiply B Add, multiply, then evaluate the term with an exponent C Evaluate the term with an exponent, add, then multiply D Evaluate the term with an exponent, multiply, then add. The Sunshine Skyway Bridge, which crosses Tampa Bay, Florida, is the world s longest cablestayed bridge. It is,5.92 meters long. What place is the 9 in this number? A Hundreds B Tenths C Hundredths D Thousandths D 0 5

16 More Adding and Subtracting Mixed Numbers In through, simplify each expression. Practice ( ) 5. ( 5 9 ) ( ). ( ) ( ). ( ) + 2. ( ) ( ). Which shows three mixed numbers that have sum of 0? A C B D What is a reasonable estimate for the sum of ?. Veronica is buying cubed cheese from Mr. Sand s deli. She asks for pounds. When Mr. Sand places some cheese in a container and weighs it, the scale shows pounds. The container weighs pound. How many more pounds of cheese would Mr. Sand need to add to the scale to get the amount that Veronica asked for? Explain how you solved the problem. P 0 5

17 . Which is the sum of 2 2? A 0 B 0 2 C D Quick Check Which is the difference of 25 2? A B 2 C 2 D 2. What is (9 5 ) 5? A B 5 C D 7. Writing to Explain Emma made a rectangular picture frame with a height of 25 5 inches. The frame is 5 2 inches wide. What is the height of the picture Emma placed in the picture frame? Explain how you found your answer. 2 5 in. h 5 25 in. 2 5 in. Q 0 5

18 . Workers at the Color-Right Marker Factory pack 2 markers in each box. If the factory makes 7 markers, how many full boxes of markers can the workers pack? A 50 B 5 C 57 D 2 2. Perimeter is the distance around a figure. What is the perimeter of this figure?. feet 2.75 feet Daily Common Core Review 0-. The table below shows the heights of four friends. Friends Heights Name Kay Leo Jay Ina Height (feet) 5 _ 5 _ 2 _ 7 Which lists the friends in order from shortest to tallest? A Jay, Ina, Leo, Kay B Kay, Leo, Jay, Ina C Leo, Jay, Kay, Ina D Ina, Jay, Kay, Leo. How many degrees does a right angle measure? 2 A.05 feet B. feet C 9.5 feet D 2. feet 5. Rita finds the quotient of 5 7 to be 2 R0. Explain why her answer is not correct. Then find the correct answer. D 0

19 Problem Solving: Draw a Picture and Write an Equation Draw a picture and write an equation. Then solve. Practice 0-. Mr. Flanders drives _ 2 miles to school and _ 2 miles home each day. He also drives an extra 2 _ 2 7 miles to go to the gym. How many miles does he drive in one day? 2. Alison is making a -inch necklace. The first _ inches are filled with red beads and _ inches are filled with blue beads. The rest has white beads. How many inches are filled with white beads?. Stewart draws a triangle, and each side is 2 _ inches long. Judith draws a square, and each side is _ 5 inches long. Which figure has the greater perimeter, the triangle or the square?. Cristoff practices playing his guitar for _ hours each weekday. He practices 2 this amount of time plus an additional _ hours on Sundays. Let x = the 2 number of hours Cristoff practices on Sundays. Draw a picture and write an equation and solve to find the number of hours he practices on Sundays. 5. Which of these fractions, when added to 2 _, will give you a sum greater than six? A 2 B 5 2 C 7 2 D. Dennis says that _ 2, 2 _, and _ are all equivalent. Is he correct? Draw a picture and explain your answer. P 0

20 . Todd biked miles to his friend s 0 house. Then he biked _ 2 miles to the store and _ miles home. 5 Which equation can you use to find out how far Todd biked? A ( 5 0 ) 2 d B d C 5 ( 2 0 ) 5 d D d Quick Check 0-2. Students in a physical education class are running a total of 7 miles this week. Shayla has 2 run _ 2 miles. Which equation can you use to find out how much farther Shayla needs to run? A r B r C 2 5 r D r. Writing to Explain Silas is shipping two gifts to his grandmother. The box and stuffing weigh _ 7 of a pound and one gift weighs 2 _ pounds. The entire package weighs a total of 2 pounds. How many pounds does the other gift weigh? 2 Let n 5 the number of pounds the second gift weighs. Draw a picture and write an equation to solve. Q 0

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