Adding Fractions and Mixed Numbers: Like Denominators

Transcription

1 Adding Fractions and Mixed Numbers: Like Denominators R - If fractions have the same denominator, you can add them by adding the numerators. Find. Add the numerators:. Use the common denominator. Simplify, if possible. Find. Step Step Step Add the Add the whole Simplify the sum, fractions. numbers. if possible. Simplify Add. Write each answer in simplest form Scott Foresman, Gr. () Use with Chapter, Lesson.

2 Adding Fractions and Mixed Numbers: Like Denominators Add. Write each answer in simplest form H Test Prep Circle the correct letter for each answer.. Albert s family ordered an -slice pizza for dinner. Albert ate slices for dinner. The next day, Albert ate more slices for lunch. What fraction of the pizza did Albert eat? A B C D. Breakwater School has two newspapers, The Bugle and The Bulletin. The Bugle comes out on Tuesday and Friday. The Bulletin comes out on Thursday. On what fraction of the school week does a paper come out at Breakwater? (Hint: There is no school on Saturday or Sunday.) F G H J Scott Foresman, Gr. (0) Use with Chapter, Lesson.

3 Subtracting Fractions and Mixed Numbers: Like Denominators R - If fractions have the same denominator, you can subtract them by subtracting the numerators. Find. Subtract the numerators:. Use the common denominator. Simplify, if possible. When you subtract mixed numbers, you may have to rename the numbers. Rename to show more ninths. 0 Now, find. Step Step Step, so you will need to Subtract the fractions. Then Simplify, rename to show more ninths. subtract the whole numbers. if possible Find each missing numerator.. =. =. = 0 0 Subtract. Write each answer in simplest form..... Scott Foresman, Gr. () Use with Chapter, Lesson.

4 Subtracting Fractions and Mixed Numbers: Like Denominators Subtract. Write each answer in simplest form. H Jenna had of a dozen eggs in the refrigerator. She used of a dozen eggs for a recipe. How many eggs were left after she used the eggs for her recipe? Test Prep Circle the correct letter for each answer.. After a class picnic, Mitchica wrapped up leftover pizzas. For dinner, she and her brother ate pizza. How many pizzas were left after their dinner? A B C D. Alma s bakery made dozen blueberry muffins. They spread frosting on dozen. How many muffins were not frosted? F dozen G dozen H dozen J dozen Scott Foresman, Gr. () Use with Chapter, Lesson.

5 Problem-Solving Skill Too Much or Too Little Information R - Here is an example of a problem with too much information. Jim is years old. He lives in a -story house on th Street. He has hamsters. How old will Jim be next year? To answer the question, you need to know how old Jim is now. Jim is years old. Next year he will be 0 years old. All the other information is not needed. Here is an example of a problem with too little information. Sheila is years old. She lives at West Street with her older sister Pam. How much older is Pam than Sheila? To answer the question, you need to know how old Pam is. The problem doesn t say. Greg mowed lawns last week and earned a total of $. This Monday he mowed and earned $. On the same day, Greg got a new customer and this will improve the amount of money he earns. Greg wants to compare the amount of money he earns this week with what he earned last week.. What information is needed to compare the amount of money Greg earns? a. The amount of money Greg earned last week. b. The amount of money Greg will earn this week. c. The amount of money Greg earned on Monday.. What information is not needed to compare the amount of money earned? a. The amount Greg earned mowing lawns last week. b. Greg mowed lawns last week. c. The amount of money Greg mowing lawns this week.. The new customer will pay Greg $0 to mow his yard. Which inequality shows the correct comparison of wages Greg earned last week with the wages he will earn this week? a. $ $ b. $ $ c. $ $ Scott Foresman, Gr. () Use with Chapter, Lesson.

6 Problem-Solving Skill Too Much or Too Little Information H - Here is a recipe for cole slaw. The ingredients cost about $.00. You can prepare and mix the vegetables in minutes, then you must refrigerate the finished cole slaw for to hours before serving. Recipe Cole Slaw cups shredded cabbage shredded carrots cup shredded red cabbage cup sour cream cup mayonnaise tablespoon vinegar teaspoon sugar cup French dressing. Which fact is needed to find how much sour cream to put in the recipe? a. Refrigerate the finished cole slaw to hours before serving. b. Use cup sour cream. c. Use cup mayonnaise.. Which of the following information is missing? a. the amount of shredded carrots b. the amount of sugar c. how long to refrigerate the finished cole slaw. Which fact is not necessary to make the cole slaw? a. It costs about $.00 to make. b. It uses cup shredded red cabbage. c. It uses cup French dressing.. Suppose you want to double the recipe. Which number sentence represents how much sour cream you would need? a. b. c.. Can you tell how many people the recipe serves? Explain.. Suppose you begin preparing the cole slaw at :00 P.M.. Is there enough information to decide if it will be ready to serve by :00 P.M.? Explain. Scott Foresman, Gr. () Use with Chapter, Lesson.

7 Estimating Sums and Differences of Mixed Numbers R - To estimate sums and differences of mixed numbers, round each number to the nearest whole number. If the fraction is greater than or equal to, round up to the nearest whole number. Otherwise round down. Round: > so round to < so round to Estimate each sum or difference. so round to so round to < so round to > so round to Estimate each sum or difference Scott Foresman, Gr. () Use with Chapter, Lesson.

8 Estimating Sums and Differences of Mixed Numbers H - Estimate each sum or difference Decide if you need an estimate or an exact answer. Tell why.. Eli is making his own fruit soda. He uses cups of fruit juice. He blends this with cups of fizzy soda water. Estimate the amount of fruit soda this will make.. Celeste is baking bread. The recipe calls for cups of flour. Celeste has cups of white flour and cups of whole wheat flour. Estimate the amount of flour she has for the recipe.. Will Celeste have enough flour for the recipe? Explain. Test Prep Circle the correct letter for each answer.. is A about B less than C about D equal to. is F equal to G about H greater than J equal to Scott Foresman, Gr. () Use with Chapter, Lesson.

9 Adding Fractions: Unlike Denominators R - To add fractions with unlike denominators, you need to find the least common denominator (LCD). Find Step Step +. Find the LCD. Multiples of :,, The LCD is the least common multiple of and. Multiples of :,,, Write the equivalent fractions using the LCD. Step Add. Simplify the sum, if possible. ( ( ( ( ) ) ) ) Add. Simplify each sum, if possible Scott Foresman, Gr. () Use with Chapter, Lesson.

10 Adding Fractions: Unlike Denominators Add. Simplify each sum, if possible. H Heidi likes to create different fruit juice combinations. In a large glass, she pours cup of pineapple juice, cup of pear juice, cup of apple juice, and cup of lime juice. How much juice is in the glass?. Heidi decided to switch to other juices. In another large glass, she pours cup of tomato juice, cup carrot juice, cup of beet juice, and cup of lemon juice. How much juice is in the glass?. Next Heidi mixed cup of raspberry juice, cup cranberry juice, cup grape juice, and cup peach juice. How much juice is in the glass? Test Prep Circle the correct letter for each answer.. C A B D. is: F less than. H greater than. G equal to. J less than. Scott Foresman, Gr. () Use with Chapter, Lesson.

11 Subtracting Fractions: Unlike Denominators R - To subtract fractions with unlike denominators, you need to find the least common denominator (LCD). Find. Step Step Find the LCD. Multiples of :,,, Multiples of :,, Write the equivalent ( ( ) ) fractions using the LCD. ( ( ) ) Step Subtract. Simplify the difference, if possible. 0 0 Subtract. Simplify, if possible Scott Foresman, Gr. () Use with Chapter, Lesson.

12 Subtracting Fractions: Unlike Denominators Subtract. Simplify each difference, if possible..... H Ramon and his sister Gabi are coloring a stack of posters to advertise their school s talent show. In one afternoon, Ramon colored of the posters, while Gabi colored of the posters. How much more of the posters has Gabi colored?. Gabi bought a box of crayons to color in the posters. Ramon was using of the crayons, and Gabi was using of the crayons. What fraction of the crayons are still in the box? Test Prep Circle the correct letter for each answer.. What is the difference of and? A B C D. What is the difference of and? F G H J Scott Foresman, Gr. () Use with Chapter, Lesson.

13 Adding Mixed Numbers R - Find. Step Step Step Find the LCD. Multiples of :,,, Multiples of :,, Write the equivalent fractions using the LCD. Add. Simplify the sum, if possible. Estimate to check:. Find the sum and simplify, if possible. Check by estimating Scott Foresman, Gr. () Use with Chapter, Lesson.

14 Adding Mixed Numbers Find the sum and simplify, if possible. H It takes Susan hours to prepare a soup recipe, and hours to prepare a bread recipe. How much time does Susan spend preparing both recipes? Test Prep Circle the correct letter for each answer.. Darlene is making up fruit baskets for the senior citizen s home. She s using pound of apples, pound oranges, pound of dates, and pound of walnuts in each basket. How much will each basket weigh? A pounds C pounds B pounds D pounds. Caleb s meat loaf recipe calls for pounds ground beef, pounds ground veal, and pounds of ground turkey. How many pounds of meat are in the meat loaf? F pounds H pounds G pounds J pounds Scott Foresman, Gr. () Use with Chapter, Lesson.

15 Subtracting Mixed Numbers R - Find. Step Write equivalent fractions with the LCD. Step 0 Because, you will have to rename to show more twenty-fourths Step Subtract the fractions and the whole numbers. Simplify the difference, if possible. Estimate to check:. 0 Find each difference and simplify, if possible. Check by estimating Scott Foresman, Gr. (0) Use with Chapter, Lesson.

16 Subtracting Mixed Numbers H - Find each difference and simplify, if possible Two cooks are in the kitchen of the Splendid Soup Shop this afternoon. Antonio has been working for hours. Nanetta has been at work for hours. How many more hours has Antonio worked than Nanetta?. Before breakfast started, the cooks in the Sunview Hotel had dozen eggs. So far they have used dozen eggs to make breakfast for their customers. How many dozen eggs are left? Test Prep Circle the correct letter for each answer.. A B C 0 D 0. F G H J Scott Foresman, Gr. () Use with Chapter, Lesson.

17 Problem-Solving Strategy Solve a Simpler Problem R - Robin is stacking boxes of sugar cubes in the stable at the horse farm where she works. There are labels on the top and front side of each box. If Robin stacks the boxes high with boxes in each level, how many labels can she see? Understand Plan You need to find the number of labels that can be seen if the boxes are stacked in a array. You can solve a simpler problem. Think about how many labels could be seen if the boxes are stacked in a array, then in a array, then in a array. Look for a pattern and use it to solve the problem for a array. Solve In a array, labels show. In a array, labels show. In a array, labels show. L L L L L L L L L L L L L L L L L L L L L L L L L L L Each time more labels can be seen. So Robin can see labels in the array. Look Back Did you count only the number of labels that show? Use a simpler problem to help you solve each problem.. The stable stocks different kinds of horse foods. Robin feeds the horses two kinds of food each day. In how many ways can Robin choose different kinds of foods from the foods stocked in the stable?. Robin is setting up six rows of horses for a horse show. There is horse in the first row. There are horses in the nd row, horses in the third row, and so on. How many horses are there in the show?. There were horses at the stable when Robin began working there. At the end of her first year, more horses had been added. At the end of the nd year, there were more horses than the year before. At the end of the next year there were more horses than the year before. If this pattern continues, how many horses will there be at the end of the th year? Scott Foresman, Gr. () Use with Chapter, Lesson.

18 Problem-Solving Strategy Solve a Simpler Problem H - Use a simpler problem to help you solve each problem.. There are rows of vegetables at a farm stand. In the first row, there are vegetables. In the second row there are vegetables. In the next row there are vegetables, and so on. How many vegetables are in the rows?. Sandra can make different types of fruit drinks. She drinks two types of fruit drinks each day. In how many ways can she choose different fruit drinks from the she can make?. The vegetable stand owner is setting up a display. He needs to cut a rope into pieces to complete his display. How many cuts does he need to make?. Boxes of raspberries are labeled on each of the four sides of a box. How many labels can you see if boxes are lined up next to one another?. Thomas planted a peach tree. It grew branches during the first year. It then grows new branches every year. How many branches will it have after it has been growing for years?. In a picnic area there are small tables like the one shown at the right. Ten of these tables are placed end to end to make one long table. How many people can sit at this long table?. Jeffrey bought bags of dried fruit for every days he will be on vacation. If he will be on vacation for days, how many bags of dried fruit did he buy? Scott Foresman, Gr. () Use with Chapter, Lesson.

19 Multiplying by a Fraction R -0 To multiply a fraction by a fraction, multiply the numerators and then the denominators. Simplify the product if necessary. To find of, multiply. Multiply the numerators. Then multiply the denominators. Simplify the product, if necessary. To find of, write as a fraction,. Multiply the numerators. Then multiply the denominators. 0 Simplify the product, if necessary. 0 A reciprocal of a fraction is found by reversing the numerator and the denominator. The reciprocal of n is n. Remember: The product of a number and its reciprocal is. Multiply. Simplify the product, if possible.. ( ( ). ) ( ) ( ) =. ( ( ) = = ). = ( ( = ) ) Scott Foresman, Gr. () Use with Chapter, Lesson 0.

20 Multiplying by a Fraction H -0 Multiply. Simplify the product, if possible There are students in Ms. Ruiz s fifth grade class. If of them bring lunch to school, how many of the students bring lunch?. There are students in a cooking class. of the students have never taken a cooking class. How many students have never taken a cooking class? Test Prep Circle the correct letter for each answer.. In a cooking class of students, of the students enjoy making deserts. How many students do not enjoy making deserts? A C B D. Ms. Ruiz baked muffins. She brought them to school for the bake sale. Within the first hour, of the muffins were sold. How many muffins were not yet sold? F H G J 0 Scott Foresman, Gr. () Use with Chapter, Lesson 0.

21 Dividing Fractions R - To divide by a fraction, multiply by the reciprocal of the fraction. Example To find, multiply by the reciprocal of.. Example To find, multiply by the reciprocal of.. Multiply the numerators, then multiply the denominators. Multiply the numerators, then multiply the denominators. Simplify the product. The product is already simplified. Divide. Simplify the quotient if possible =.. Scott Foresman, Gr. () Use with Chapter, Lesson.

22 Dividing Fractions Divide. Simplify the quotient, if possible. H Mental Math How many portions can be cut from large sandwiches if each portion is of a sandwich?. Math Reasoning What fraction of a pound is ounces? Explain how you can use division by a fraction to figure out how many ounce pieces of beef are in pounds. Test Prep Circle the correct letter for each answer.. Which of the following has a quotient different from the others? A C 0 B D. Which of the following has a quotient different from the others? F H G J Scott Foresman, Gr. (0) Use with Chapter, Lesson.

23 Multiplying and Dividing Mixed Numbers R - To multiply or divide mixed numbers, you need to rewrite each mixed number as an improper fraction. Example Find. Write the numbers as improper fractions. Example Find. ( ( ) ) Multiply. Simplify. 0 Write the numbers as improper fractions. 0 Multiply by the reciprocal of the divisor. ( ) ( 0) 0 0 Simplify. Multiply or divide. Simplify, if possible Scott Foresman, Gr. () Use with Chapter, Lesson.

24 Multiplying and Dividing Mixed Numbers H - Multiply or divide. Simplify, if possible Laurence bicycled 0 miles in hours. What was his average speed?. Laurence brought pounds of trail mix for the ride. He shared it equally with friends. Was each friend s share greater than or less than pound? Explain.. The entire bike ride lasted hours. It drizzled rain for of the ride. How long did the cyclists ride in the rain? Test Prep Circle the correct letter for each answer.. Which of the following has the same product or quotient as? A B C D. Which of the following has the same product or quotient as? F G H J Scott Foresman, Gr. () Use with Chapter, Lesson.

25 Problem-Solving Application Finding Fraction Patterns R - You can solve a problem by finding a pattern. The band director is arranging musicians in rows. The first row is as wide as the bandstand. The second row is as wide as the bandstand. The third row is as wide as the bandstand. How wide will the sixth row be? Understand Plan You need to find out how wide the sixth row will be. You know how wide the first three rows are. You can look for a pattern of how the fractions change with each row. Then you can continue the pattern for three more rows. Solve Row : Row : Row : Continue the pattern. Row : Row : Row : Look Back So, Row will be as wide as the bandstand. Check the pattern. Do the fractions increase or decrease in a way that makes sense? Look at a pattern to solve these problems. The musicians will sit on steps that decrease in height from top to bottom. The first steps will decrease by the following fractions:,,.. What number is the same in all the fractions?. What numbers change as the fractions decrease?. Is the pattern in the numerator or denominator of the fractions? Explain.. By what fractions will the height of the next two steps decrease? Scott Foresman, Gr. () Use with Chapter, Lesson.

26 Problem-Solving Application Finding Fraction Patterns H - Look for a pattern to solve these problems.. Some circus clowns arrange themselves so that the second clown is the height of first clown, the third clown is the height of the first clown, and so on. What fraction of the height of the first clown is the height of the fifth clown? the sixth clown?. The set crew is hanging photographs of various sizes around the stage. The second photo is the height of the first, the third photo is the height of the second, the fourth photo is the height of the third. What size will the sixth photo be?. The height of a series of boxes used in a clown act will decrease by the following fractions: 0, 0,. By what fractions will the height of the boxes 0 decrease over the next two boxes?. One clown juggles balls that decrease by the following fractions of the first ball:,,. What are the next three fractions in the pattern? 0. The clowns wear oversize wigs, each larger than the next. The first clown s wig is cm long, the next clown s wig is cm long, and the third clown s wig is cm long. If the pattern remains the same, what is the length of the hair on the next three clowns wigs?. Clowns can get covered with pie. One clown has 0 of his costume covered. The second clown has 0 of his costume covered. The third clown has 0 of his costume covered. How much of the fifth clown s costume will be covered? Scott Foresman, Gr. () Use with Chapter, Lesson.

27 Evaluating Expressions with Fractions R - Evaluating expressions with fractions is similar to evaluating expressions with decimals or whole numbers. Example Evaluate x when x. x Example Evaluate x when x. x 0 Example Evaluate x when x. x 0 Example Evaluate x when x. x Evaluate each expression for x, x, and x. x. x. x. x Evaluate each expression for x, x, and x.. x. x. x. x Scott Foresman, Gr. () Use with Chapter, Lesson.

28 Evaluating Expressions with Fractions H - Evaluate n and n for each given value of n.. n. n. n Evaluate n and n for each given value of n.. n. n. n. Terrell s coin collection is pennies and quarters. If the number of coins in the collection is c, write an expression that describes the number of pennies. Write a second expression to describe the number of quarters. a. If Terrell has 0 coins in his collection, how many are pennies? How many are quarters? b. Write an expression to describe what fraction Terrell s total collection is neither pennies nor quarters? Explain. c. There are half as many nickels as there are quarters in the collection. What fraction of the collection are nickels? Explain. Test Prep Circle the correct letter for each answer.. Which expression is the correct translation for x is of? A x B x C x D x. Which expression is the correct translation for the difference between and a number x? F x G x H x J x Scott Foresman, Gr. () Use with Chapter, Lesson.