Page 33 - Algebra 1

Simplifying Expressions with Exponents
Simplify each expression. Justify each step.
a. 43 +9÷3-2·(3)2
SOLUTION Write the expression. Then use the order of operations to simplify.
Example
2
43 +9÷3-2·(3)2 = 64 + 9 ÷ 3 - 2 · 9 = 64 + 3 - 18
= 49_
Simplify exponents.
Multiply and divide from left to right. Add and subtract from left to right.
Hint
Remember to use the order of operations inside parentheses as well.
b.
(2 · 3 - 2)2 2
S_OLUTION Write the expression. Then use the order of operations to simplify. (2 · 3 - 2)2
= =
_2
(6 - 2)2
2 _(4)2
2
Multiply inside the parentheses. Subtract inside the parentheses.
Simplify the exponent. Divide.
= 16 _
2 = 8
Example
3
Comparing Expressions
Compare the expression_s. Use < , > , or = . (1.5+3)÷9+33 (18+8) -8÷4
2
Use the order of operations to simplify t_he two expressions.
(1.5 + 3) ÷ 9 + 33 (18 + 8) - 8 ÷ 4 2
= (4.5) ÷ 9 + 33
= 4.5 ÷ 9 + 27 = 0.5 + 27
= 27.5
Since 27.5 > 11, (1.5 + 3) ÷ 9 + 33
SOLUTION
_
= 26 - 8 ÷ 4
2
= 13 - 8 ÷ 4
Hint
Remember to compare the original expressions in the inequality.
= 13 - 2 = 11
> _(18 + 8) - 8 ÷ 4. 2
18 Saxon Algebra 1