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Chapter 2 – Properties of Real Numbers 2.7 – Division of Real Numbers 2.7 – Division of Real Numbers Today we will learn how to: Divide real numbers Use division to simplify algebraic expressions 2.7 – Division of Real Numbers Suppose you owe a friend $50.00. You and your friend decide to come up with a payment schedule. You decide on 4 equal monthly payments. We can determine the monthly payment using division of real numbers. 2.7 – Division of Real Numbers Every real number (except zero) has a RECIPROCAL The product of a number and its reciprocal is 1 Example: 2 · ½ = 1 This property is referred to as the inverse property of multiplication. 2.7 – Division of Real Numbers The reciprocal of a is 1 , when a ≠ 0 a Example: -8 and 1 8 a b The reciprocal of is , when a ≠ 0 and b ≠ 0 b a 2 and 5 Example: 5 2 2.7 – Division of Real Numbers Zero is the only real number that has no reciprocal. There is no number that when multiplied by zero gives a product of 1. Because zero does not have a reciprocal, you cannot divide by zero. 2.7 – Division of Real Numbers You can use a reciprocal to write a division as a product. DIVISION RULE To divide a number a by a nonzero number b, multiply a by the reciprocal of b. 1 a b a b 2.7 – Division of Real Numbers Example 1 1. 15 (5) 5 2. 45 6 1 2 3 3. 3 1 4. 2 3 2.7 – Division of Real Numbers THE SIGN OF A QUOTIENT The quotient of two numbers with the same sign is positive -a -b = a/b -20 (-4) = 5 The quotient of two numbers with opposite signs is negative -a b = - a/b -20 4 = -5 2.7 – Division of Real Numbers Example 2 Simplify the expression 9 27 x 3 2.7 – Division of Real Numbers Example 3 A mountain climber descends 300 feet in 50 minutes. What is her velocity? 2.7 – Division of Real Numbers HOMEWORK Page 111 #24 – 31, 32 – 46 even, 48 – 51, 62 – 63