Page 47 - Algebra 1

It is important to follow the order of operations at all times, even when working inside symbols of inclusion.
Simplifying Expressions with Brackets
Simplify.
3+5·[(9-3)2 -6]
SOLUTION
Begin inside the innermost symbol of inclusion and work outward.
Example
2
Hint
Use the order of operations:
1. symbols of inclusion; 2. powers and roots;
3. multiply or divide;
4. add or subtract.
3+5·[(9-3)2 -6] =3+5·[62 -6]
= 3 + 5 · [36 - 6]
= 3 + 5 · 30
= 3 + 150 = 153
Simplify inside the parentheses. Evaluate the exponent. Subtract inside the brackets. Multiply.
Add.
To simplify a rational expression such as 4 - 2 , the numerator and denominator must be simplified first.
Simplifying Expressions with Rational Numbers
Simplify. Justify each step.
⎣⎡ 5 · ( 4 + 2 ) 2 ⎦⎤ + _4 · 5 2
SOLUTION
Justify each step using the order of operations or mathematical properties.
6·3 _
Example
3
⎣⎡ 5 · ( 4 + 2 ) 2 ⎦⎤ + _4 · 5 2
= ⎣⎡ 5 · ( 6 ) 2 ⎦⎤ + _4 · 5 2
= ⎣⎡ 5 · 3 6 ⎦⎤ + _4 · 5
Compare Expressions with Symbols of Inclusion
= 1 8 0 + _4 · 5 = 1 8 0 + _2 0
= 190
2 = 180 + 10
2 2
Add inside the parentheses.
Simplify the exponent.
Multiply inside the brackets.
Simplify the numerator.
Simplify the fraction. Add.
Example
4
Compare the expressions. Use <, >, or =. 12+[5(7-5)3 -14] [(9-5)2 +7]-33
32 Saxon Algebra 1