Multiply the dividend by the reciprocal of the divisor.

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$Domain Lesson 6 Complex Fractions Common Core Standards: 7.RP., 7.RP. Getting the Idea To divide fractions, first find the reciprocal of the divisor.$

1 Domain Lesson 6 Complex Fractions Common Core Standards: 7.RP., 7.RP. Getting the Idea To divide fractions, first find the reciprocal of the divisor. Then multiply the dividend by the reciprocal of the divisor. Reciprocals are two numbers whose product is. You can find the reciprocal of a fraction or whole number by switching the numerator and the denominator. For example, and 8 are reciprocals because Example Divide. Multiply the dividend by the reciprocal of the divisor. Step Rewrite as a multiplication problem, using the reciprocal of the divisor. The reciprocal of is. Multiply is in simplest form A complex fraction is a fraction in which the numerator and/or denominator contains a fraction. Recall that a fraction represents a quotient. The quotient is the numerator divided by the denominator (where the denominator is not equal to 0). For example,. The division expression in Example can be written as a complex fraction: and the denominator is. The complex fraction and the division expression are equivalent:. The numerator of the complex fraction is You can express a percentage as a complex fraction and vice versa.. 8

2 Example Express.% as a complex fraction. Step Step Use the definition of percent to write the complex fraction. Convert the percent to a fraction. Percent means per hundred. Divide the percentage by 00 and drop the percent sign...% _ Convert the decimal to an improper fraction. Since 0.,. 00. ( ) 7 Write the complex fraction. Write the improper fraction over % written as a complex fraction is 7. Simplifying a complex fraction is the same as dividing its numerator by its denominator. Example Simplify. Step Step Multiply the numerator by the reciprocal of the denominator. Rewrite as a multiplication problem using the reciprocal of the denominator. The reciprocal of is. Multiply. Write the answer in simplest form. 9

3 To divide mixed numbers, first rewrite the mixed numbers as improper fractions. Then follow the rules for dividing fractions. Example Jamie divided pounds of apples into baskets that hold pounds each. How many baskets did she use? Step Step Step Rewrite the mixed numbers as improper fractions. Then divide. Write an expression to represent the problem. Find. Rewrite the mixed numbers as improper fractions. ( ) ( ) 7 7 Rewrite as a multiplication problem using the reciprocal of the divisor. The reciprocal of 7 is Simplify the factors and multiply. 7 Step Simplify. Jamie used baskets. Any whole number can be expressed as a fraction. For example,. So, the reciprocal of a whole number divisor is a unit fraction. For example, the reciprocal of is. Example Divide. 6 8 Rewrite the whole number as a fraction. Then find the reciprocal. 60 Domain : The Number System

4 Lesson 6: Complex Fractions Step Step Step Rewrite 6 as an improper fraction. Write the reciprocal of (6 8) 8 8 The reciprocal of is. Rewrite as a multiplication problem and solve Multiply. 8 8 Simplify the product. 6 8 Coached Example Mr. Camara cuts a -foot wooden board into pieces that are each feet long. How many pieces of wood does he have? Let w represent the number of pieces of wood. Write a number sentence to represent this problem. _ Rewrite as an improper fraction. Rewrite as an improper fraction. Rewrite the number sentence using improper fractions. To divide fractions, multiply the dividend by the of the divisor. The reciprocal of the divisor is _. Rewrite as a multiplication problem using the reciprocal of the divisor. Multiply. Simplify the product. Mr. Camara has _ pieces of wood. 6

5 Lesson Practice Choose the correct answer.. Divide. 8 A. B. _ 8 C. _ D.. Mrs. Chapman made vests for cast members of the school play. She used _ yard of material for each vest. She used 6 yards in all. How many vests did she make? A. B. C. 6 D. 8. Which complex fraction is equivalent to 8.%? A. 8 B. 8 C. 6 0 D. 8. Kelly had a ribbon that was _ feet long. Each piece she cut was _ feet long. How many pieces of ribbon did she cut? A. B. C. 8 D.. Divide A. 7 6 B. 7 8 C. 8 D. _ 7 6. Divide. 0 A. B. C. D. 6 Domain : The Number System

6 Lesson 6: Complex Fractions 7. What is the value of the following expression? A. B. 6 C. 9 D. 8. Which quotient is less than? A. _ 8 _ B. 7 0 _ C. _ _ D. 7 _ 8 7 _ 9 9. In math class, Ms. Kuramoto wrote the following complex fraction on the board: 6 _ 9 A. Rewrite the complex fraction as a division expression.. _ 6 B. Show the complex fraction _ simplest form. Show your work. in 9 0. Look at each equation. Is the equation true? Select Yes or No. A. _ _ 9 6 Yes No B Yes No C. Yes No _ D. _ 7 9 _ _ 7 Yes No 6

7 . Select True or False for each equation. A. 9 6 True False B. _ True False C. 9 0 _ 6 0 True False D. _ 7 _ 8 7 True False. Which complex fraction is equivalent to 9.%? Circle all that apply. A. 9 0 B. 7 C. 7 D. 9 _ E F. 9 0,000. Emanuel had _ gallons of paint. He used _ gallon of paint for each room. Circle the number of rooms that Emanuel painted. Emanuel painted 6 rooms. 6 Domain : The Number System

8 Lesson 6: Complex Fractions. Simplify each complex fraction. Write each complex fraction in the correct box. 6 Equal to Equal to. Use numbers from the box to complete each equation _ 8 0 _ _ _ 6

Section 2.3 Rational Numbers. A rational number is a number that may be written in the form a b. for any integer a and any nonzero integer b.

Section 2.3 Rational Numbers. A rational number is a number that may be written in the form a b. for any integer a and any nonzero integer b. Section 2.3 Rational Numbers A rational number is a number that may be written in the form a b for any integer a and any nonzero integer b. Why is division by zero undefined? For example, we know that