Simplify each expression. See Examples 2 through 5.EXAMPLE 2  Simplify each expression.a....

Simplify each expression. See Examples 2 through 5.

EXAMPLE 2  Simplify each expression.

a. 6 ÷ 3 + 52

b. 20 ÷ 5 · 4

c.

d. 3 · 42

e.

Solution

a. Evaluate 52 first.

c. First, simplify the numerator and the denominator separately.

d. In this example, only the 4 is squared. The factor of 3 is not part of the base because no grouping symbol includes it as part of the base.

e. The order of operations applies to operations with fractions in exactly the same way as it applies to operations with whole numbers.

EXAMPLE 3   Simplify

Solution The fraction bar serves as a grouping symbol and separates the numerator and denominator. Simplify each separately. Also, the absolute value bars here serve as a grouping symbol. We begin in the numerator by simplifying within the absolute value bars.

EXAMPLE 4   Simplify 3[4 + 2(10 − 1)].

Solution Notice that both parentheses and brackets are used as grouping symbols. Start with the innermost set of grouping symbols.

EXAMPLE 5   Simplify

Solution

5 + 6 · 2