1 2 full. You drink. of the water. How much of the bottle of water do you drink? 1 2? Numbers: 2 3. length, divide it into 3 equal sections.

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1 . Multiplying Fractions What does it mean to multiply fractions? ACTIVITY: Multiplying Fractions Work with a partner. A bottle of water is full. You drink of the water. How much of the bottle of water do you drink? THINK ABOUT THE QUESTION: To help you think about this question, rewrite the question. Words: What is of? Numbers: =? Here is one way to get the answer. 0 Draw a length of. Because you want to find of the length, divide it into equal sections.??? Now, you need to think of a way to divide into equal parts. Rewrite as a fraction whose numerator is divisible by. Because the length is divided into equal sections, multiply the numerator and denominator by. 0 Dividing Fractions In this lesson, you will use models to multiply fractions. multiply fractions by fractions. In this form, you see that can be divided into equal parts of. Each part is of the bottle of water, and you drank two of them. Written as multiplication, you have = =. 0 So, you drank of the bottle of water. Chapter Fractions and Decimals

2 ACTIVITY: Multiplying Fractions Work with a partner. A park has a playground that is of its width and of its length. What fraction of the park is covered by the playground? Fold a piece of paper horizontally into fourths and shade three of the fourths to represent. Fold the paper vertically into fihs and shade of the paper another color. Count the total number of squares. This number is the denominator. The numerator is the number of squares shaded with both colors. = =. So, of the park is covered by the playground. Inductive Reasoning Work with a partner. Complete the table by using a model or folding paper. Exercise Verbal Expression Answer. of Math Practice Consider Similar Problems What are the similarities in constructing the models for each problem? What are the differences?..... of. IN YOUR OWN WORDS What does it mean to multiply fractions? 0. STRUCTURE Write a general rule for multiplying fractions. Use what you learned about multiplying fractions to complete Exercises on page. Section. Multiplying Fractions

3 . Lesson Lesson Tutorials Multiplying Fractions Words Multiply the numerators and multiply the denominators. Numbers Algebra = = a b c d = a c, where b, d 0 b d EXAMPLE Multiplying Fractions Find. = = Multiply the numerators. Multiply the denominators. Study Tip EXAMPLE When the numerator of one fraction is the same as the denominator of another fraction, you can use mental math to multiply. For example, = because you can divide out the common factor. Multiplying Fractions with Common Factors Find. Estimate = = = = Multiply the numerators. Multiply the denominators. Divide out common factors. The product is. Reasonable? Exercises Chapter Fractions and Decimals

4 EXAMPLE Real-Life Application You have of a bag of flour. You use of the flour to make empanada dough. How much of the entire bag do you use to make the dough? Method : Use a model. Six of the squares have both types of shading. So, you use = of the entire bag. Method : To find of, multiply. = = So, you use of the entire bag. Multiply the numerators and the denominators. Divide out common factors.. WHAT IF? In Example, you use of the flour to make the dough. How much of the entire bag do you use to make the dough? Multiplying Mixed Numbers Write each mixed number as an improper fraction. Then multiply as you would with fractions. EXAMPLE Multiplying a Fraction and a Mixed Number Find. Estimate = = = Write as the improper fraction. Multiply the numerators and the denominators. =, or The product is. Reasonable? Section. Multiplying Fractions

5 EXAMPLE Multiplying Mixed Numbers Find. Estimate = = = =, or Write and as improper fractions. Multiply fractions. Divide out the common factor. The product is. Reasonable? Exercises EXAMPLE Real-Life Application A city is resurfacing a basketball court. Find the area of the court. Estimate = A = w Write the formula for the area of a rectangle. m = Substitute for and for w. = Write and as improper fractions. m = Multiply fractions. Divide out common factors. = So, the area of the court is square meters. Reasonable? 0. Find the area of a rectangular air hockey table that is feet by feet. Chapter Fractions and Decimals

6 . Exercises Help with Homework. WRITING Explain how to multiply two fractions.. REASONING Name the missing denominator. =. OPEN-ENDED Write two mixed numbers between and that have a product between and. +(-)= +(-)= +(-)= +(-)= ERROR ANALYSIS Describe and correct the error in finding the product. 0 = 0 0 = 0 = 0 =. AQUARIUM In an aquarium, of the fish are surgeonfish. Of these, are yellow tangs. What fraction of all fish in the aquarium are yellow tangs?. JUMP ROPE You exercise for of an hour. You jump rope for of that time. What fraction of the hour do you spend jumping rope? Without finding the product, copy and complete the statement using <, >, or =. Explain your reasoning.. ( 0 ). ( ). ( ) Section. Multiplying Fractions

7 ERROR ANALYSIS Describe and correct the error in finding the product... = 0 0 ( = ( ) + ) = + = 0. VITAMIN C A vitamin C tablet contains of a gram of vitamin C. You take tablets every day. How many grams of vitamin C do you take every day?. SCHOOL BANNER You make a banner for a football rally. a. What is the area of the banner? GO PANTHERS! b. You add a -foot border on each side. What is the new area of the banner?. NUMBER SENSE Without calculating, is less than or greater than? Is the product less than or greater than? Explain your reasoning ().. () ().. PICTURES Three pictures hang side by side on a wall. What is the total area of the wall that the pictures cover? () ( ) 0 in in. n.. OPEN-ENDED Find a fraction that, when multiplied by, is less than. 0 Chapter ms_green pe_00.indd in. 0 in. 0 in. Fractions and Decimals // :: PM

8 . DISTANCES You are in a bike race. When you get to the first checkpoint, you are of the distance to the second checkpoint. When you get to the second checkpoint, you are of the distance to the finish. What is the distance from the start to the first checkpoint? Start Checkpoint Checkpoint Finish 0 miles. NUMBER SENSE Is the product of two positive mixed numbers ever less than? Explain.. MODELING You plan to add a fountain to your garden. a. Draw a diagram of the fountain in the garden. Label the dimensions. b. Describe two methods for finding the area of the garden that surrounds the fountain. c. Find the area. Which method did you use, and why?. COOKING The cooking time for a ham is of an hour for each pound. a. How long should you cook a ham that weighs pounds? b. Dinner time is : p.m. What time should you start cooking the ham?. PETS You ask 0 people about their pets. The results show that of the people own a dog. Of the people who own a dog, of them also own a cat. a. What fraction of the people own a dog and a cat? b. How many people own a dog but not a cat? Explain. Find the prime factorization of the number. (Section.) MULTIPLE CHOICE A science experiment calls for cup of baking powder. You have cup of baking powder. How much more baking powder do you need? (Section.) A cup B cup C cup Section. ms_green pe_00.indd D cups Multiplying Fractions // ::0 PM

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