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PRE-ALGEBRA Lesson 5-4 Warm-Up Use the cards 1, 4, 2, and 3 to find each sum in exercises 1 – 4. Each card can only be used once. Use the cards 6, 2, 5, and 8 to find each sum in exercises 1 – 4. Each card can only be used once. PRE-ALGEBRA Multiplying and Dividing Fractions (5-4) How do you multiply fractions? To multiply fractions together, multiply the numerators and denominators together separately. If the numerator and denominator have common factors, you can simplify them before multiplying. Example: Multiply the numerators and denominators together separately. Since 2 and 8 have a GCF, 2, simplify by dividing by 2 Multiply the numerator. Multiply the denominatos. How do you model the multiplication of fractions? PRE-ALGEBRA Multiplying and Dividing Fractions LESSON 5-4 Additional Examples Find 2 • 5 . 3 2 5 2•5 • = 3 7 3•7 = 10 21 7 Multiply the numerators. Multiply the denominators. Simplify. PRE-ALGEBRA Multiplying and Dividing Fractions LESSON 5-4 Additional Examples a. Find 3 • 2 . 4 3 3 2 3 12 • = • 4 3 24 13 1 = 1 2 Divide the common factors. Multiply. 5 3w • . w 17 5 • 3w = 5 • 3w 1 w 17 17 1w b. Find = 15 17 Divide the common factors. Multiply. PRE-ALGEBRA Multiplying and Dividing Fractions LESSON 5-4 Additional Examples 1 1 Keesha’s desktop is a rectangle 3 2 ft long and 1 ft 2 wide. What is the area of her desktop? A =3 1 1 •1 2 2 Area of a rectangle = length • width. 1 1 7 3 and 1 as improper fractions, and . 2 2 2 2 =7• 3 Write 3 21 4 Multiply. 2 = 2 1 = 54 Write as a mixed number. The area of Keesha’s desk is 5 1 ft2. 4 PRE-ALGEBRA Multiplying and Dividing Fractions (5-4) What are “reciprocals”? Reciprocals: two numbers whose product is 1 – The reciprocal of a is b , b a since a • b = 1. b a How do you find the reciprocal of a number? To find the reciprocal of a number, simply switch the numerator and denominator around. In the case of a whole number, make it a fraction by putting it over 1 first (so, the reciprocal of a whole number will always be 1 over the number) Example: What is the reciprocal of 9? = 9 1 Make the whole number into a fraction by 9 = 1 1 9 Turn the fraction over so that the numerator 1 Check : 1 • 9 = 1 = 1 1 91 1 Check using rule of reciprocals (a number times putting it over 1. and denominatorare switched its reciprocal equals 1) PRE-ALGEBRA Multiplying and Dividing Fractions (5-4) How do you divide by a fraction? To divide by a fraction, multiply by its reciprocal. c a Rule: a = • d b b ad , where b, c, and d do not equal 0. bc d = c Example: What is the 1 1 ? 2 8 How do you model the division of fractions? 1 1 = 1 • 8 2 8 2 1 To divide by a fraction, multiply by its 1 • 8 = 1•8 1 2 2•1 = 8 =4 2 Multiply the numerators and denominators reciprocal separately. The fraction bar means divide, so divide the numebrator into the denominator to simplify. 1 4 2 = 8 , so there are 4 one-eighth parts in onehalf. PRE-ALGEBRA Multiplying and Dividing Fractions LESSON 5-4 Additional Examples 3 7 a. Find ÷ . 5 10 3 7 3 10 ÷ = • 5 10 5 7 Multiply by the reciprocal of the divisor. 2 3 10 = • 7 15 Divide the common factors. = 6 Simplify. 7 PRE-ALGEBRA Multiplying and Dividing Fractions LESSON 5-4 Additional Examples (continued) b. Find 27 ÷ 9 . 8q 4q 27 ÷ 9 = 27 • 4q 4q 9 8q 8q 3 1 Multiply by the reciprocal of the divisor. 1 27 = • 4q 91 2 8q 1 Divide the common factors. = 3 Simplify. 2 = 11 2 Write as a mixed number. PRE-ALGEBRA Multiplying and Dividing Fractions LESSON 5-4 Additional Examples (continued) c. Find 4 1 ÷ (–3 3 ). 2 8 4 1 ÷ (–3 3 ) = 9 ÷ (– 27 ) 2 8 2 8 9 8 • (– ) 2 27 = Change to improper fractions. Multiply by – 8 27 , the reciprocal of – . 27 8 4 1 9 8 = • – 273 12 4 3 = – , or –1 Divide the common factors. 1 3 Simplify. PRE-ALGEBRA Multiplying and Dividing Fractions LESSON 5-4 Lesson Quiz Simplify each expression. 1. – 3 7 • 8 12 – 7 3z 5z ÷ 4 7 21 1 , or 1 20 20 32 12g 2. 5 3. 25 • 2g 4. 5 5 ÷ 1 11 8 16 6 1 , or 1 5 5 10 1 , or 3 3 3 PRE-ALGEBRA