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Technical Mathematics, Sixth Edition by Michael A. Calter Ph.D., Paul A. Calter

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1.6. Combined Operations

1.6.1. Order of Operations

If the expression to be evaluated does not contain parentheses, perform the operations in the following order:

  1. Powers and roots, in any order.

  2. Multiplications and divisions, from left to right.

  3. Additions and subtractions, from left to right.

Our first group of calculations will be with integers only, and later we will do some problems that require rounding. We first show a problem containing both addition and multiplication.

Example 60:

Evaluate 7 + 3 × 4.

Solution: The multiplication is done before the addition.

7 + 3 × 4 = 7 + 12 = 19

Next we do a calculation having both a power and multiplication.

TI-83/84 screen for Example 60.

Example 61:

Evaluate 5 × 32.

Solution: We raise to the power before multiplying:

5 × 32 = 5 × 9 = 45

TI-83/84 screen for Example 61.

1.6.2. Parentheses

When an expression contains parentheses, first evaluate the expression within the parentheses and then the entire expression.

Example 62:

Evaluate (7 + 3) × 4.

Solution:

(7 + 3) × 4 = 10 × 4 = 40

TI-83/84 screen for Example 62.

If the sum or difference of two or more numbers is to be raised to a power, those numbers must be enclosed in parentheses. ...

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