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TIP: If there is more than one operation inside a set of parentheses, use the order of operations to tell you which operation to perform first. In the expression (5 + 4(3)) – 2, addition and multiplication are both inside parentheses. Because multiplication comes before addition in the order of operations, we begin by multiplying 4 and 3. qxd:JSB 12/18/08 11:45 AM Page 49 single-variable expressions 49 Practice 1 Evaluate each expression. 1. 5 – 6 ÷ 2 2. –2(10 + 3) 3. 32(7) + 1 4. (–5 + 12)(21 – 13) 5.
Add: 5 + 30 = 35. Replace x with 1: 12(4 – 1) Subtraction is in parentheses, so subtract before multiplying: (4 – 1) = 3 The expression becomes 12(3). Multiply: 12(3) = 36. Replace q with –6: (–6)2 + 15 Exponents come before addition in the order of operations, so handle the exponent ﬁrst: (–6)2 = 36 The expression becomes 36 + 15. Add: 36 + 15 = 51. Replace m with 4: –8(4)2 Exponents come before multiplication, so handle the exponent ﬁrst: 42 = 16 The expression becomes –8(16). Multiply: –8(16) = –128.
11x3y5) ÷ (11y5z2) = 5. (–42m2n–2o5) ÷ (6mn2) = ANSWERS Practice 1 1. Both factors are positive, so your answer is positive: (5)(6) = 30. 2. One factor is positive and one is negative, so your answer is negative: (–4)(9) = –36. 3. One number is positive and one is negative, so your answer is negative: (24) ÷ (–6) = –4. 4. Both numbers are negative, so your answer is positive: (–32) ÷ (–8) = 4. qxd:JSB 44 12/18/08 11:45 AM Page 44 algebra basics Practice 2 1. Multiply the coefﬁcients: (–7)(4) = –28.