1-6 Multiplying and Dividing Real Numbers Hubarth Algebra

Make a Conjecture a. b What can we now determine from the patterns? Positive times a positive = positive Positive times a negative = negative Negative times a positive = negative Negative times a negative = positive

Simplify each expression. a. –3(–11) –3(–11) = 33 The product of two negative numbers is positive. b. –6 ( ) 3434 The product of a positive number and a negative number is negative. –6 ( ) = – Ex 1 Multiplying Numbers

Evaluate 5rs for r = –18 and s = –5. 5rs = 5(–18)(–5)Substitute –18 for r and –5 for s. = –90(–5)5(–18) results in a negative number, –90. = 450–90(–5) results in a positive number, 450. Ex 2 Evaluating Expressions

Use the order of operations to simplify each expression. a. –2 4 = –16Simplify. = 81Simplify. b. (–3) 4 Write as repeated multiplication.–( ) = Write as repeated multiplication.(–3)(–3)(–3)(–3) = Ex 3 Simplify Exponential Expressions

Simplify each expression. a.70 ÷ (–5) b.–54 ÷ (–9) The quotient of a positive number and a negative number is negative. = –14 The quotient of a negative number and a negative number is positive. = 6 Ex 4 Dividing Numbers

Evaluate – – 4z 2 for x = 4, y = –2, and z = –4. = – 4(16)Simplify the power. –4 –2 = 2 – 64Divide and multiply. = –62Subtract. – – 4z 2 = – 4(–4) 2 Substitute 4 for x, –2 for y, and –4 for z. xyxy –4 –2 Ex 5 Evaluating Expressions

Evaluate for p = and r = –. = –2Simplify. prpr = p ÷ rRewrite the equation. prpr = ÷ Substitute for p and – for r ( – ) = Multiply by –, the reciprocal of – ( – ) Ex 6 Division Using the Reciprocal

Practice 2. Evaluate each expression for c= -8 and d= -7 a. –(cd)b. (-2)(-3)(cd)