CHAPTER. Computing Fractions. Nicholas Parlato Calvert Day School. Computing Fractions 83

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1 CHAPTER Computing Fractions Nicholas Parlato Calvert Day School Computing Fractions

2 . Adding Fractions and Mixed Numbers Objective: to add fractions and mixed numbers Cars use about of the energy consumed by the transportation industry. Buses and trains use. Add and to find the part of the transportation energy used by cars, buses, and trains. Will the sum be greater or less than? Find the LCD. Step Step Step Rename each fraction. :,,, + :,,, + + LCD Cars, buses, and trains use More Examples A C Try Find the LCD. 0 or 0 0 THESE of the transportation energy. Will the sum be greater or less than? Write the sum as a mixed number in simplest form. Will the sum be greater than or less than?. Adding Fractions and Mixed Numbers Add. B. 0 + LCD: or You can use prime factorization to find the LCD

3 Exercises Add. Write each sum in simplest form Evaluate each expression if r, s, t, and v.. r + t. s + t 0. s + v. r + t + v Constructed RESPONSE. Is addition of fractions associative? Write an example to illustrate your answer.. Jade made snack mix. She used pounds of peanuts, pounds of pretzels, and pounds of almonds. How many pounds of snack mix did she make? Test PREP. Ms. Bower needs yd of green fabric and yd of brown fabric to make tree costumes for the spring play. How much fabric does she need in all? a. yd b. yd c. yd d. yd. The length of a rectangle is in. and the width is in. What is the perimeter? a. 0 in. b. in. c. in. d. 0 in.. Adding Fractions and Mixed Numbers

4 . Subtracting Fractions and Mixed Numbers Objective: to subtract fractions and mixed numbers After Sara s birthday party, of her birthday cake was left. The next day Sara ate of the leftover cake. How much cake is left now? Subtract from to find the difference. Step Step Step Find the LCD. :,,, :,,, LCD Rename each fraction. Subtract. Sara has Examples of her cake left. A. 0 B. Estimate 0 0 How does this compare to the estimate? Subtract from. 0 Step Step Step Rename each fraction. Subtract the fractions Subtract the whole numbers Subtracting Fractions and Mixed Numbers

5 Try THESE Subtract. Write each difference in simplest form Exercises Subtract. Write each difference in simplest form Compute. Write each result in simplest form.. a. a b b. a 0 b 0. 0 a b Problem SOLVING. An oil company s stock sold for on Monday and on Tuesday. How many points did the stock drop?. The sum of two numbers is. One addend is. What is the other?. Two drops of paint fell on a ruler. One fell on the -inches mark, and the other fell on the -inches mark. How far apart were the drops?. You have a -foot board. After cutting a -foot piece and a -foot piece, how much of the board remains?. Separate the set below into two sets so that the sums of the fractions in the two sets are equal.,,,, Constructed RESPONSE. Is it possible to add or subtract two fractions with like denominators and get an answer with a different denominator? Explain. If it is possible, give an example.. Subtracting Fractions and Mixed Numbers

6 . Problem-Solving Application: Measurement Objective: to solve problems involving measurement Buildings are insulated to keep them warm in the winter and cool in the summer. The diagram at the right shows a section of the outside wall of a house. Notice that the measurements are given as fractions or mixed numbers. How thick is the entire wall? To find the total thickness, add the measurements. Estimate: Add the measurements. Find the LCD. Rename as necessary and add. :,,, :,, THINK :,,, The wall is inches thick. Does this agree with your estimate? Drywall Insulation Sheathing Siding Try THESE. What is the total thickness of three boards that are in., in., and in. thick?. During the first hour of flight, an airplane uses gallons of fuel. During the second hour, 0 gallons are used. If the tank was full at the start, how much fuel was left in the 0-gallon tank?. Gabriela has yards of material. She uses 0 yards to make curtains and yards for a bedspread. How much material is left?. How many feet of fence are needed to fence in the front yard? Use the diagram to the right.. A rough board in. thick has in. taken off by planing on one side. Find the thickness.. A cabinet ft in. long is built along a wall that measures ft in. What is the length of the remaining space? ft ft ft 0 ft. Problem-Solving Application: Measurement

7 Solve. A green pencil is inches long. A red pencil is inches long. How much longer is the red pencil?. Parking at an airport costs 0 for each half hour or fraction of a half hour. How much does it cost to park 00 minutes? Use the map to solve problems.. How many miles farther is it from Clearfork to the forest reserve than from Clearfork to the oil field?. You are on the road between the oil field and storage tanks, of a mile from the oil field. How far away are the storage tanks? Use the chart to solve problems.. What three parts account for threefourths of the total heat loss?. Rank the parts in order from greatest to least heat loss. Storage Tanks. You are between Clearfork and the forest reserve, miles from the reserve. How many miles are you from the oil field? Ceiling Doors mi Part of House Exterior walls Windows Basement Air leakage Oil Field Clearfork mi mi 0 Fraction of Total Heat Loss 0 Forest Reserve Constructed RESPONSE. Jen walked of a mile on Monday and of a mile on Tuesday. Joe walked of a mile on Monday and of a mile on Tuesday. a. How far did Jen walk? b. How far did Joe walk? c. Who walked farther? Explain. Mid-Chapter REVIEW Add or subtract Problem-Solving Application: Measurement

8 Problem Solving The Secret Formula Professor Wells poured The Secret Formula into a glass until it was onehalf full. Then, he poured The Secret Formula into a second glass until it was one-fourth full. The second glass was twice as large as the first glass. Both glasses were then filled with water. That afternoon, the absent-minded lab assistant mixed the contents of both glasses in a third container. The Secret Formula is what part of the final mixture? Extension Suppose the professor mixes a solution that is The Secret Formula 00 with twice as much solution that is 00 The Secret Formula. What part of the mixture is The Secret Formula? 0 Problem Solving

9 Cumulative Review Solve each equation mentally.. x. t. d. Find the greatest common factor (GCF) of each group of numbers..,.,.,.,, Write each fraction in simplest form Replace each with <, >, or to make a true statement Compute. Write each result in simplest form Solve. n. One loaf of bread is used to make sandwiches. Tom used loaves to make sandwiches for a party. How many sandwiches did he make?. Ben delivers newspapers each day. He earns $0.0 for each newspaper. Does he earn more or less than $0.00 in days?. Judy Carson spent $.0 for gasoline in January, $.0 in February, and $0.0 in March. To the nearest dollar, find the average amount she spent a month.. Marla paid $. for a package of four pens. She also paid $0. tax. How much change did she receive from a five-dollar bill? Cumulative Review

10 . Multiplying Fractions and Mixed Numbers Objective: to multiply fractions and mixed numbers A half-gallon container of rainbow sherbet is made up of equal parts of orange, raspberry, and lime sherbet. Marybeth only likes orange sherbet and wants to know how many gallons of orange sherbet are in a half-gallon of rainbow sherbet. We can multiply fractions to find out how many gallons of orange sherbet are in a half-gallon of rainbow sherbet. We need to find out how much of is. Multiply. A half-gallon container has of a gallon of orange sherbet. Examples When the numerator and denominator have a common factor, you can simplify (cancel) before multiplying by dividing the numerator and denominator by the same factor. Also, make sure to change each mixed number to an improper fraction before multiplying. A. B. 0 The GCF of and is. 0 Divide the numerator and the denominator by. 0 Notice that this answer is 0 in simplest form.,00 C. D.,00 Rename the mixed number , Try THESE Rename each mixed number as an improper fraction Multiplying Fractions and Mixed Numbers

11 Exercises Multiply. Write each product in simplest form , Evaluate each expression if a, b, c, d, and e.. a b. b. a b d. b + a e Problem SOLVING. A theater has 00 seats. Three-fourths of the seats are filled. How many seats are filled?. Sonia s beagle puppy weighs pounds. A full-grown beagle weighs times as much. Estimate the weight of a fullgrown beagle. 0. An animal preserve is of a park. A wooded area is of the animal preserve. What part of the park is wooded?. What is the product of the first terms of the sequence,,,,...?. Farmer Joe s horse pasture is meters long and meters wide. What is the area of Farmer Joe s horse pasture? Constructed RESPONSE 0. The product of two numbers is. One of the factors is. Find the other factor. Explain how you found the other factor.. Multiplying Fractions and Mixed Numbers

12 . Dividing Fractions and Mixed Numbers Objective: to divide fractions and mixed numbers Brad s kitten eats of a can of cat food each day. How many days will five cans last? To solve this problem, you can count the number of halves in. This is the same as dividing by. There are 0 halves, so 0. Five cans will last 0 days. Brad s sister, Patty, solved the problem this way. Since each can will last days, multiply by. Compare the two methods. Brad s Method Patty s Method THINK How many The reciprocal of a fraction is 0 0 halves are in? found by inverting the fraction. The numerator and denominator are interchanged. The numbers and have a special relationship. They are called reciprocals because their product is. To divide by a fraction, multiply by its reciprocal. Examples A. B Rename each mixed number. Try THESE Complete Dividing Fractions and Mixed Numbers

13 Exercises Divide. Write each quotient in simplest form What is the quotient of divided by?. Find the quotient if is divided by. Problem SOLVING. Chloe needs cups of sugar for a cookie recipe. She uses a measuring scoop that holds cup. How many scoops of sugar does she need? 0. Half of a casserole is divided equally among four persons. How much of the original casserole does each person get?. Find the pattern of the following numbers:,,,,,.... Constructed RESPONSE. A pie crust calls for cups of butter. Each stick of butter is cup. If Derek needs to make pie crusts, is sticks of butter enough? Explain. REVIEW Compute Dividing Fractions and Mixed Numbers

14 Chapter Review Choose the letter of the correct term or abbreviation to complete each sentence.. To add fractions with like denominators, add the.. To add fractions with unlike denominators, rename the fractions using the of the denominators.. One way to simplify fractions is to find the of the numerator and denominator.. The statement ( ) ( ) is an example showing addition of fractions is.. One way to with fractions and mixed numbers is to use rounding. a. associative b. commutative c. compute d. denominators e. estimate f. GCF g. LCM h. numerators i. numerators and denominators Add. Write each sum in simplest form. Section Subtract. Write each difference in simplest form. Section Chapter Review

15 Multiply. Write each product in simplest form. Section Name the reciprocal of each number. Section Divide. Write each quotient in simplest form. Section Solve. Sections... Benito has two pieces of ribbon. One piece is feet long, and the other is feet long. Find the total length.. The cost to operate a Boeing -00 for an hour is $,. How much does it cost to operate a Boeing -00 for of an hour?. Logan and his friends ate of a cake, while Sherrie and her friends ate of the cake. Each piece was of the cake. How many pieces were eaten?. Angela runs miles on Monday, miles on Tuesday, and miles on Wednesday. How many miles does she run in all? 0. A golden eagle can fly 0 miles an hour. How far can a golden eagle fly in of an hour? Chapter Review

16 Chapter Test Add or subtract. Write each sum or difference in simplest form Multiply or divide. Write each answer in simplest form Solve Kyung has a -foot board. He cuts off a -foot piece and a -foot piece. How much of the board remains?. A greyhound can run kilometers an hour. How far can the greyhound run in hour?. Bernadette bought two pieces of ribbon. One piece is feet long, and the other is feet long. a. Find the total length of the ribbon. b. If the ribbon cost $.0 a foot, how much did Bernadette pay for the ribbon? 0. A dragonfly flies miles in minutes. How far can the dragonfly fly in minute? Chapter Test

17 Change of Pace Addition with Rulers You can use two rulers to show addition with mixed numbers. Suppose you wish to add and. Place two rulers as shown below. Inches Inches The edge of the yellow ruler lines up with on the blue ruler. Read directly down from on the yellow ruler. The sum of and is on the blue ruler. Use the rulers below to complete exercises. A B Inches Inches. Go to the left edge of the yellow ruler. Find the number on the blue ruler which corresponds to that edge. What is the number?. What number is shown at A on the yellow ruler?. What is the sum of the answers from exercises and? Is it the same number that is shown at A on the blue ruler?. What number is shown at B on the yellow ruler?. What is the sum of the answers from exercises and? Is it the same number as shown at B on the blue ruler? Use two rulers to find each sum Explain how you could use two rulers to show subtraction. Change of Pace

18 Cumulative Test. What is the greatest common factor of and? a. b. c. d. none of the above. a. b. c. d. none of the above. a. b. c. d. none of the above... a. 0. b.. c. 0. d... A license plate number is divisible by and. Which could not be the number? a. 0 b. c. d a. 0. b.. c.. d. 0.. What number is represented at A on the number line? a. b. c. d. A. Which expression is an example of the identity property of addition? a. + + b c d How many hours is Adventure Park open each week? a. b. c. d. Adventure Park Hours Monday Tuesday Friday Saturday Sunday closed :00 P.M. 0:00 P.M. 0:00 A.M. :00 P.M. 0. Out of students in the seventh grade, are girls. Forty-seven students live on a farm. Which question can be answered using this information? a. How many boys live on a farm? b. How many girls do not live on a farm? c. How many students are not girls? d. How many students are not in the seventh grade? 00 Cumulative Test