ACTIVITY: Dividing by a Fraction. Work with a partner. Write the division problem and solve it using a model. a. How many two-thirds are in three?

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Cornelius Simon
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1 . Dividing Fractions How can you divide by a fraction? ACTIVITY: Dividing by a Fraction Work with a partner. Write the division problem and solve it using a model. a. How many two-thirds are in three? The division problem is. Remaining piece How many groups of are in? The remaining piece represents of. So, there are groups of in. So, =. COMMON CORE Dividing Fractions In this lesson, you will write reciprocals of numbers. use models to divide fractions. divide fractions by fractions. solve real-life problems. Learning Standard 6.NS. b. How many halves are in five halves? c. How many four-fifths are in eight? d. How many one-thirds are in seven halves? e. How many three-fourths are in five halves? 6 Chapter Fractions and Decimals

2 ACTIVITY: Using Tables to Recognize a Pattern Work with a partner. a. Complete each table. Division Table 6 Multiplication Table 6 Math Practice Analyze Relationships How is multiplying numbers similar to dividing numbers? b. Describe the relationship between the red numbers in the division table and the red numbers in the multiplication table. c. Describe the relationship between the blue numbers in the division table and the blue numbers in the multiplication table. d. STRUCTURE Make a conjecture about how you can use multiplication to divide by a fraction. e. Test your conjecture using the problems in Activity.. IN YOUR OWN WORDS How can you divide by a fraction? Give an example.. How many halves are in a fourth? Explain how you found your answer. Use what you learned about dividing fractions to complete Exercises on page 6. Section. Dividing Fractions 6

$To write the reciprocal of a number, write the number as a fraction. Then invert the fraction.$ $So, the reciprocal of a fraction a b is b, where a and b 0.$ a b b a = This is called the Multiplicative Inverse Property. You will learn more about this property in Chapter.

a b b a = This is called the Multiplicative Inverse Property. You will learn more about this property in Chapter.

$... Dividing Fractions Words To divide a number by a fraction, multiply the number by the reciprocal of the fraction.$

3 . Lesson Lesson Tutorials Key Vocabulary reciprocals, p. 6 Two numbers whose product is are reciprocals. To write the reciprocal of a number, write the number as a fraction. Then invert the fraction. So, the reciprocal of a fraction a b is b, where a and b 0. a Invert Study Tip The product of a nonzero number and its reciprocal is. a b b a = This is called the Multiplicative Inverse Property. You will learn more about this property in Chapter. Study Tip EXAMPLE When any number is multiplied by 0, the product is 0. So, the number 0 does not have a reciprocal. a. b. Writing Reciprocals Original Number Fraction Reciprocal Check c. When you invert a glass, you turn it over. = = = Write the reciprocal of the number. Exercises Dividing Fractions Words To divide a number by a fraction, multiply the number by the reciprocal of the fraction. Numbers Algebra = = a b c d = a b d c = a d, where b, c, and d 0 b c 6 Chapter Fractions and Decimals

4 EXAMPLE Dividing a Fraction by a Fraction Find 6. 6 = 6 = 6 = Multiply by the reciprocal of, which is. Multiply fractions. Divide out the common factor. Simplify. EXAMPLE Dividing a Whole Number by a Fraction A piece of wood is feet long. How many -foot pieces can you cut from the piece of wood? Method : Draw a diagram. Mark each foot on the diagram. Then divide each foot into -foot sections. ft Count the number of -foot pieces of wood. There are four. So, you can cut four -foot pieces from the piece of wood. ft ft Method : Divide by to find the number of -foot pieces. = = = Simplify. Multiply by the reciprocal of, which is. Multiply. Divide out the common factor. So, you can cut four -foot pieces from the piece of wood. Divide. Write the answer in simplest form How many -foot pieces can you cut from a -foot piece of wood? Section. Dividing Fractions 6

5 EXAMPLE Dividing a Fraction by a Whole Number Find. = = = = Write as an improper fraction. Multiply by the reciprocal of, which is. Multiply fractions. Divide out the common factor. Simplify. Divide. Write the answer in simplest form. Exercises EXAMPLE Using Order of Operations Evaluate + 6. Study Tip You can use the LCD,, to add the fractions in Example. + 6 = + = + 6 = + 6 = + 6 = + 6 = + = 6, or Multiply by the reciprocal of, which is. Multiply 6 and. Divide out the common factor. Simplify. Rewrite fractions using a common denominator. Simplify. Exercises Evaluate the expression. Write the answer in simplest form Chapter Fractions and Decimals

6 . Exercises Help with Homework. OPEN-ENDED Write a fraction and its reciprocal.. WHICH ONE DOESN T BELONG? Which of the following does not belong with the other three? Explain your reasoning. 6 MATCHING Match the expression with its value.. A.. B.. 6. C. D. +(-6)= +(-)= +(-)= +(-)= Write the reciprocal of the number Divide. Write the answer in simplest form ERROR ANALYSIS Describe and correct the error in finding the quotient... = = = = = = 0. REASONING How can you use estimation to show that the quotient in Exercise is incorrect? Section. Dividing Fractions 6

$0. APPLE PIE You have of an apple pie. You divide the remaining pie into equal slices. What fraction of the original pie is each slice?$

7 0. APPLE PIE You have of an apple pie. You divide the remaining pie into equal slices. What fraction of the original pie is each slice?. ANIMALS How many times longer is the baby alligator than the baby gecko? ft Determine whether the numbers are reciprocals. If not, write the reciprocal of each number..,., 0 Copy and complete the statement.. 6,. 6, 6 6. =. =. = 6 Without finding the quotient, copy and complete the statement using <, >, or =. Explain your reasoning. ft Evaluate the expression. Write the answer in simplest form ( ). REASONING Use a model to evaluate the quotient 6. Explain.. VIDEO CHATTING You use of your battery for every of an hour that you video chat. You use of your battery video chatting. How long did you video chat? 6 Chapter Fractions and Decimals

$. NUMBER SENSE Explain. When is the reciprocal of a fraction a whole number?. BUDGETS The table shows the portions of a family budget that are spent on several expenses. a. How many times more is the expense for housing than for automobiles?$ Expense Portion of Budget Housing Food Automobiles Recreation 0 6. PROBLEM SOLVING You have 6 pints of glaze. It takes of a pint to glaze a bowl and of a pint to glaze a plate. 6 a.

Expense Portion of Budget Housing Food Automobiles Recreation 0 6. PROBLEM SOLVING You have 6 pints of glaze. It takes of a pint to glaze a bowl and of a pint to glaze a plate. 6 a.

Explain how you found your answer.. A water tank is full. The tank is full when gallons of water are added to the tank. a. How much water can the tank hold? b.

8 . NUMBER SENSE Explain. When is the reciprocal of a fraction a whole number?. BUDGETS The table shows the portions of a family budget that are spent on several expenses. a. How many times more is the expense for housing than for automobiles? b. How many times more is the expense for food than for recreation? c. The expense for automobile fuel is of the 60 total expenses. What fraction of the automobile expense is spent on fuel? Expense Portion of Budget Housing Food Automobiles Recreation 0 6. PROBLEM SOLVING You have 6 pints of glaze. It takes of a pint to glaze a bowl and of a pint to glaze a plate. 6 a. How many bowls could you glaze? How many plates could you glaze? b. You want to glaze bowls, and then use the rest for plates. How many plates can you glaze? How much glaze will be left over? c. How many of each object could you glaze so that there is no glaze left over? Explain how you found your answer.. A water tank is full. The tank is full when gallons of water are added to the tank. a. How much water can the tank hold? b. How much water was originally in the tank? c. How much water is in the tank when it is full? Find the GCF of the numbers. (Section.)., 6., , 0 6.,, MULTIPLE CHOICE How many inches are in yards? (Skills Review Handbook) A B 6 C 66 D Section. Dividing Fractions 6

Point out that when you compare two sets by using fractions, the objects in the sets do not need to be the same size or even the same kind.

$Point out that when you compare two sets by using fractions, the objects in the sets do not need to be the same size or even the same kind.$ Fractions What are some of the ways we use fractions every day? Fractions represent a part of a whole object or unit. (Provide some sets of objects for students to work with to help them understand the