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Chapter 2 Integers 2-11 Ordering Operations with Integers You should already know about this: Review Notes - When solving combinations of addition and subtraction operations on three or more terms, do the operations from left to right.
Example: - 2 + 5 – 7 + 8 = 7 – 7 + 8
- 7 – 7 + 8 = 0 + 8
- 0 + 8 = 8
| - When solving combinations of multiplication and division operations on three or more terms, do the operations from left to right.
Example: - 2 x 12 ÷ 4 x 8 = 24 ÷ 4 x 8
- 24 ÷ 4 x 8 = 6 x 8
- 6 x 8 = 48
| | But what about instances where you have combinations of addition, subtraction, multiplication, and division n the same expression? Solve from left to right? Not exactly. Then what about expressions that are enclosed in parentheses? What about terms with exponents? There are very specific rules for solving all these combinations of math operations--these rules are called order of operation, or order of precedence. Solving Combinations of Addition, Subtraction, Multiplication, and Division Procedure When solving combinations of addition, subtraction, multiplication, and division in the same expression: - Do the multiplication and division first, from left to right.
- Do the addition and subraction last, from left to right.
| Examples 1. Simplify 4 + 2 x 6 The Problem: 4 + 2 x 6 = ? The Procedure - Multiply first: 4 + 2 x 6 = 4 + 12
- Add last: 4 + 12 = 16
The Solution: 4 + 2 x 6 = 16 Notice that the solution is NOT 4 + 2 x 6 = 36. | 2. Simplify 6 + 18 ÷ 6 The Problem: 6 + 18 ÷ 6 = ? The Procedure - Divide first: 6 + 18 ÷ 6 = 6 + 3
- Add last: 6 + 3 = 9
The Solution: 6 + 18 ÷ 6 = 9 Notice that the solution is NOT 6 + 18 ÷ 6 = 4 | | | 1. Simplify 4 + 3 x 6 – 4 + 8 x 2 The Problem: 4 + 3 x 6 – 4 + 8 x 2 = ? The Procedure - Multiply first, from left to right:
- 4 + 3 x 6 – 4 + 8 x 2 = 4 + 18 – 4 + 16
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- Add/subtract last, from left to right:
- 4 + 18 – 4 + 16 = 22 – 4 + 16
22 – 4 + 16 = 18 + 16
18 + 16 = 34 The Solution:4 + 3 x 6 – 4 + 8 x 2 = 34 | | Parentheses Exponents Multiplcation, Division (left-to-right) Addition, Subtraction (left-to-right)
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