Multiply Fractions. Divide a square in half. Then divide it in thirds. Shade a rectangle that is _ 1 -unit wide and

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1 Multi-Part Lesson - A PART B C D Main Idea Multiply fractions using models. NGSSS MA..A.. Explain and justify procedures for multiplying and dividing fractions and decimals. glencoe.com In Lesson -D, you used decimal models to multiply decimals. You can use a similar model to multiply fractions. BACKYARDS One half of Mr. Lytle s backyard is a garden. One third of his garden is covered with flowers. What fraction of Mr. Lytle s backyard is covered with flowers? What do you need to find? what fraction of Mr. Lytle s backyard is covered with flowers - by -unit rectangle. To find, find the area of a Divide a square in half. Then divide it in thirds. Shade a rectangle that is -unit wide and -unit long. One sixth of the square is shaded. So, of Mr. Lytle s backyard is covered with flowers. and Apply Find each product using a model Chapter Multiply and Divide Fractions

2 BAKING Mia is baking brownies. She covers of the brownies with icing. Of the brownies with icing, she covers of them with sprinkles. What fraction of Mia s brownies are covered with icing and sprinkles? What do you need to find? the fraction of Mia s brownies that are covered with icing and sprinkles To find, find of. Divide a square into thirds. Then divide it in fifths. Shade a rectangle that is -unit wide and -unit long. Six out of parts are shaded. Since =, of the brownies are covered with both icing and sprinkles. and Apply Find each product using a model. Then write in simplest form.... the Results 7. Draw a model to show that = 0. Then explain how the model shows that 0 simplifies to 9.. Explain the relationship between the numerators of the problem and the numerator of the product. What do you notice about the denominators of the problem and the denominator of the product? 9. MAKE A CONJECTURE Write a rule you can use to multiply fractions. Lesson - 0

3 Multi-Part Lesson - PART A B C D Main Idea Multiply fractions. NGSSS MA..A.. Multiply and divide fractions and decimals efficiently. MA..A.. Solve realworld problems involving multiplication and division of fractions and decimals. Also addresses MA..A... glencoe.com REPTILES A chameleon s body is about the length of its tongue. A certain chameleon has a tongue that is foot long. The shaded rectangle represents of or.. Refer to the model. What fraction represents?. What is the relationship between the numerators and denominators of the factors and the numerator and denominator of the product? Body is of. Tongue is foot. Words Multiply the numerators and multiply the denominator. Examples Numbers Algebra = a c b d = a c, where b and d are not 0. b d Find. = Multiply the numerators. Multiply the denominators. = Simplify. a. b. c. 0 Chapter Multiply and Divide Fractions

4 Factor two or more numbers that are multiplied together to form a product; Example:,,, and are all factors of If the numerators and the denominators have a common factor, you can simplify before you multiply. Find = = Simplify Before Multiplying. Estimate = Divide both the numerator and the denominator by. Simplify. Compare to the estimate. d. 9 e. 9 0 f. 0 LAWN MOWING Frank had of the lawn left to mow. On Saturday, he mowed of what was left. What fraction of the entire lawn did Frank mow on Saturday? = = Divide both the numerator and denominator by. Simplify. So, Frank mowed of the lawn on Saturday. g. SUB SANDWICHES Rick has of a footlong sub left from yesterday. He ate of the leftover sandwich as a snack. What fraction of the entire sandwich did he eat as a snack? Examples and (pp. 0 0) Example (p. 0) MONEY Juanita spent of her allowance at the mall. Of the money spent at the mall, was spent on new earphones. What part of her allowance did Juanita spend on earphones? Lesson - 0

5 = Step-by-Step Solutions begin on page R. Extra Practice begins on page EP. Examples and (pp. 0 0) Example (p. 0) SPORTS The bleachers at a football game are 7 full, and of the fans in the bleachers are rooting for the home team. What fraction of the bleachers are filled with home-team fans? Justify your procedure. Real-World Link Clydesdales can stand as tall as 0 hands and weigh as much as,000 pounds. B. ELECTIONS The table shows the fraction of the votes that each candidate received. If 0 students voted, how many students voted for each candidate?. HORSES The height of a horse is often measured in hands, which is the distance across an adult s palm. A pony measures Fraction Candidate of Votes Nyemi Luke 0 Natalie 0 hands. If a hand is equal to foot, about how tall is the pony?. INVENTORY A paint store has gallons of paint in storage, of which are for outdoor use. The others are for indoor use. If each gallon costs $, what is the total cost of the indoor paint in storage?. PIZZA Tico ate of a pizza. If there were slices of pizza, how many slices did Tico eat? Multiply PHYSICAL EDUCATION Mr. Williams P.E. class lasts for 7 hour. a. How many minutes are spent warming up and cooling down? b. How many minutes are not spent on instruction? Explain. 7 Part of -hour Class playing game instruction warm-up and cool-down 0 0 Chapter Multiply and Divide Fractions

6 0. WATER PARK Alberto rode of the water rides at a water park. His sister, Reina, rode half of the rides that Alberto rode. What fraction of the water rides did Reina not ride? Support your answer with a model.. RECIPES Lee is making oatmeal chocolate chip cookies and the recipe calls for cup of chocolate chips. If she wants to make of the recipe, what fraction of a cup of chocolate chips will she need? Justify your procedure.. MULTIPLE REPRESENTATIONS Use the bar diagram. $00 a. WORDS Write a real-world problem represented by the bar diagram.? b. MODELS Draw an area model to represent the situation. c. WORDS Explain how you would solve your problem. BULLETIN BOARD Homeroom 0 and Homeroom 0 share a hallway bulletin board. If Homeroom 0 uses of their half to display artwork, what fraction of the bulletin board is used to display Homeroom 0 s artwork?. MUSIC About of an orchestra is made up of string instruments. If of the string instruments are cellos, what fraction of the orchestra is made up of cellos? Counterexample A counterexample is an example that shows why a statement is false.. REASONING State whether each statement is true or false. If the C statement is false, provide a counterexample. a. The product of two fractions that are each between 0 and is also between 0 and. b. The product of a mixed number between and and a fraction between 0 and is less than. c. The product of two mixed numbers that are each between and is between and.. NUMBER SENSE If the product of two positive fractions a and b is, find three pairs of possible values for a and b. 7. CHALLENGE Is the product of two positive fractions that are each less than also less than? Explain.. b d Justify why a c is equal to a. b c d e e Lesson - 07

7 NGSSS Practice MA..A.., MA..A.., MA..A.. 9. In a recent survey, of pet owners stated that they allow their pet to go outside. Of these, allow their pet outside without supervision. Which expression gives the fraction of the pet owners surveyed that allow their pet outside without supervision? A. + C. B. - D. 0. EXTENDED RESPONSE Four fifths of Terrence s text messages are to his friends. One half of those messages are to his friend Bianca. Part A Draw a model to represent the situation. Part B What fraction of Terrence s text messages are to Bianca? Part C Explain how you solved the problem.. Scott is taking a dance class twice a week for weeks. How many hours altogether will Scott have spent in dance class at the end of the weeks? F. hours H. hours G. hours I. hours Erin s Dance Studio - hour classes. SATELLITES A main satellite sends a signal to each of two smaller satellites. If each of those two satellites sends a signal to each other and a signal back to the main satellite, determine the number of signals sent. (Lesson -E) (Lesson -D)... MEASUREMENT A game board measures 9 inches by inches. Estimate the area of the game board. (Lesson -B) GASOLINE Benita spent $.0 to fill up her gas tank. If she pumped 9 gallons of gasoline, is about $, $.0, or $ a more reasonable estimate for the cost of each gallon of gasoline? (Lesson -C). DECORATING Selena is considering new carpeting for her living room. How many square feet of carpet will Selena need? (Lesson -E). ft. ft 0 Chapter Multiply and Divide Fractions

8 Multi-Part Lesson - PART A B C D Main Idea Multiply whole numbers by mixed numbers. Explain and justify the process of multiplying whole numbers and mixed numbers. NGSSS MA..A.. Explain and justify procedures for multiplying and dividing fractions and decimals. glencoe.com Multiply Whole Numbers by Mixed Numbers MUSIC Genevieve is designing an insert to put into a CD case. She measured the case and it is inches by inches. What is the area of the case? What do you need to find? the area of a CD case Use an area model. Shade a rectangle units that is units wide and units long. units Find the total number of shaded units. units half-units or whole units The area of the case is 7 square inches. half-unit and Apply Find each product using models. Justify your procedure.... Lesson - 09

9 Multi-Part Lesson - PART A B C D Main Idea Multiply mixed numbers. NGSSS MA..A.. Multiply and divide fractions and decimals efficiently. MA..A.. Solve realworld problems involving multiplication and division of fractions and decimals. Also addresses MA..A.. and MA..A... glencoe.com Multiply Mixed Numbers ANATOMY The Atlantic Giant Squid has an eyeball that is about times as large as the average human eyeball. If the average human eyeball is inches across, how large is the Atlantic Giant Squid s eyeball?. Write a multiplication expression that shows the size of the Atlantic Giant Squid s eyeball.. Use repeated addition to find.. Write the multiplication expression from Exercise using improper fractions.. Multiply the improper fractions from Exercise. How large is the Atlantic Giant Squid s eyeball? Multiply Mixed Numbers To multiply mixed numbers, write the mixed numbers as improper fractions and then multiply as with fractions. Multiply a Fraction and a Mixed Number Find. Estimate Use compatible numbers. = = 7 = 7 = 7 Write as 7. Multiply. Simplify. Compare to the estimate. a. b. c. 0 Chapter Multiply and Divide Fractions

10 Real-World Link The Hoover Dam, located on the Arizona-Nevada border, contains enough concrete to pave a highway, feet wide, from San Francisco to New York City. Find 7 7. = 0 Multiply Mixed Numbers = 0 = = Write 7 as. Write 0 as. Divide the numerator and denominator by and by. Multiply. Simplify. million cubic yards of concrete. The Grand Coulee Dam, in Washington state, contains times as much concrete. How much concrete does it contain? DAMS The Hoover Dam contains Estimate = = 9 = 9 = = or Simplify. Write the mixed numbers as improper fractions. Divide 9 and by their GCF,. Then divide and by their GCF,. Multiply the numerators and multiply the denominators. There are million cubic yards of concrete in the Grand Coulee Dam. Check for Reasonableness = d. MEASUREMENT Mr. Wilkins is laying bricks to make a rectangular patio. The area he is covering with bricks is feet by 9 feet. What is the area of the patio? Examples and (pp. 0 ) Example (p. ) COOKING A waffle recipe calls for cups of flour. If Chun wants to make times the recipe, how much flour does he need? Lesson -

11 Examples and (pp. 0 ) = Step-by-Step Solutions begin on page R. Extra Practice begins on page EP Example (p. ) 0. MEASUREMENT A reproduction of Claude Monet s Water-Lilies has dimensions inches by inches. Find the area of the painting. FISH A carp can travel at a speed of 7 miles per hour. At this rate, how 0 far can a carp travel in hours? B RUNNING Use the formula d = rt to find the distance d a long-distance runner can run at a rate r of 9 miles per hour for time t of hours. 7. ASTRONOMY Earth is about million miles from the Sun. Use the table shown. Planet a. How far is Venus from the Sun? b. How far is Mars from the Sun? c. How far is Jupiter from the Sun? d. How far is Saturn from the Sun?. FIND THE DATA Refer to the Data File on pages. Choose some data and write a real-world problem in which you would multiply mixed numbers. Then solve your problem. ALGEBRA Evaluate each expression if a =, b = 9. ab 0. c Approximate Number of Times as Far from the Sun as Earth Venus Mars Jupiter Saturn 9, and c =. bc. a Chapter Multiply and Divide Fractions

12 C. OPEN ENDED Name two positive mixed numbers, each greater than and less than, with a product greater than and less than.. CHALLENGE Analyze each product in First the table. Factor a. Why is the first product less than? b. Why is the second product equal to? c. Why is the third product greater than?. NUMBER SENSE Without multiplying, determine whether the product is located on the number line at point A, B, or C. Explain your reasoning. Second Factor Product = = = 9 0. Summarize how to multiply mixed numbers. NGSSS Practice MA..A.., MA..A.., MA..A.. 7. Which number when multiplied by gives a product between and? A. 0 C. B. D.. GRIDDED RESPONSE Ben is taking guitar classes three times a week for weeks. Each class will last hours. How many hours will Ben have spent in guitar classes in weeks? (Lesson -B) TREES The Palmers are planting trees along each side of their -foot-long driveway. There is feet between each tree, and the trees are planted directly across from each other. How many trees do they need? (Lesson -E) Find each sum or difference. Write in simplest form. (Lesson 0-) Lesson -

13 CHAPTER Mid-Chapter Check Estimate each product. (Lesson -B) CLOTHES A new shirt costs $.99. If the shirt is on sale for off its price, about how much would you save? (Lesson -B) (Lesson -D) MEASUREMENT Find the area of the magnet shown. (Lesson -D) (Lesson -B) NGSSS PRACTICE A recipe calls for cups of flour. If you triple the recipe, how much flour is needed? (Lesson -D) A. 7 c B. 7 c C. c D. c. DOG FOOD A cup of dog food weighs 7 ounces. A K9 dog eats cups of dog food a day. How many ounces of dog food does the dog eat each day? (Lesson -D) 9. NGSSS PRACTICE What is the area of the picture and frame shown? (Lesson -D) 7 in. 7 in. in.. WEATHER In a recent year, the weather was sunny of the days. Assuming there are days in a year, how many days were not sunny? (Lesson -D). FOOD Rosemaria wants to cut her sub into thirds. Find the length of each piece. (Lesson -B) ft F. 7 square inches G. square inches H. square inches I. 77 square inches 0. CONSTRUCTION Corey needs boards that are 7 inches long. a. How many feet of boards should he buy? Explain. b. If you can only buy -foot boards, how many should he buy? Explain. (Lesson -D) in. Chapter Multiply and Divide Fractions