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Extra info for Algebra in 15 Minutes a Day (Junior Skill Builders)
Replace p with –1: –5(–1) + 9. Remember the order of operations: Multiply before adding. –5(–1) = 5, 5 + 9 = 14. When p = –1, –5p + 9 is equal to 14. Example What is 4(c2 – 7) when c = –3? qxd:JSB 50 12/18/08 11:45 AM Page 50 algebra basics Replace c with –3: 4((–3)2 – 7). (–3)2 – 7 is in parentheses, and since exponents come before subtraction, begin there. (–3)2 = 9, 9 – 7 = 2. Finally, 4(2) = 8. Practice 2 1. What is –9z when z = 9? 2. What is 4u – 3 when u = 7? 3. What is –8 + 2g when g = –5?
Qxd:JSB 12/18/08 11:44 AM S E Page 21 C T I O N 1 algebra basics BEFORE WE CAN use algebra, we need to understand what it is. This section begins by explaining the vocabulary of algebra, so that when you see x in a problem, you will know what it is and why it’s there. Once these deﬁnitions are out of the way, we will review how to perform basic operations (addition, subtraction, multiplication, and division) on real numbers, and then show how these same operations can be performed on algebraic quantities.
2. Parentheses are ﬁrst in the order of operations. 10 + 3 = 13, and the expression becomes –2(13). Multiply: –2(13) = –26. 3. This expression contains an exponent, multiplication, and addition. Exponents come before multiplication and addition, so begin with 32: 32 = 9. The expression is now 9(7) + 1. Multiplication comes before addition, so multiply next: 9(7) = 63, and the expression becomes 63 + 1. Finally, add: 63 + 1 = 64. 4. There are two sets of parentheses in this expression, so work on each of them separately.