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Operations Study Guide: GED Math (page 3)

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Order of Operations

The basic operations of real numbers include addition, subtraction, multiplication, division, and exponentiation. Often, in expressions, there are grouping symbols—usually shown as parentheses—which are used to make a mathematical statement clear. In math, there is a predefined order in which you perform operations. This is an agreed-upon order that must be used. For the five basic operations, the order is:

• First, perform all operations enclosed in parentheses.
• Second, evaluate all exponents. (See Chapter 5 for a discussion of exponents.)
• Third, perform any multiplication and division, in order, working from left to right.
• Finally, evaluate any addition and subtraction, in order, working from left to right.

Examples
1. 8 + 15 × 3
2. There are no parentheses or exponents, so evaluate multiplication first: 15 × 3 = 45. Now perform the addition: 8 + 45 = 53.

3. 7 + 24 ÷ 6 × 10
4. There are no parentheses or exponents, so evaluate multiplication and division from left to right. First, do the division: 24 ÷ 6 = 4. Next, perform multiplication: 4 × 10 = 40. Finally, perform addition: 7 + 40 = 47.

5. (36 + 64) ÷ (18 – 20)
6. First, evaluate the parentheses, from left to right: (36 + 64) = 100 and (18 – 20) = –2. Now, do the division: 100 ÷ –2 = –50.

Practice problems for these concepts can be found at:

Numbers and Operations Practice Problems: GED Math

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