USING THE ORDER OF OPERATIONS
About "Using the order of operations"
Using the order of operations :
Algebraic expressions may have more than one operation or more than one variable. To evaluate these expressions, substitute the given value for each variable and then use the order of operations.
Using the order of operations
Example 1 :
Evaluate the given expression for x = 7.
4(x - 4)
Solution :
Plug 7 for x
4(7 - 4)
Subtract inside the parentheses
4(3)
Multiply
12
Therefore, 4(x - 4) = 12.
Example 2 :
Evaluate the given expression for x = 7.
4x - 4
Solution :
Plug 7 for x
4(7) - 4
Multiply
28 - 4
Subtract
24
Therefore, 4x - 4 = 24.
Example 3 :
Evaluate the given expression for w = 6, x = 5 and y = 3.
w - x + y
Solution :
Plug 6 for w, 5 for x and 3 for y
6 - 5 + 3
Subtract 5 from 6
1 + 3
Add 1 and 3
4
Therefore, w - x + y = 4.
Example 4 :
Evaluate the given expression for x = 9.
x² - x
Solution :
Plug 9 for each x
9² - 9
Evaluate exponents
81 - 9
Subtract
72
Therefore, x² - x = 72.
Example 5 :
Evaluate the given expression for x = 3 and y = 5.
3x + 2y
Answer :
Plug 3 for x and 5 for y
3(3) + 2(5)
Multiply
9 + 10
Add
19
Therefore, 3x + 2y = 19
Example 6 :
Evaluate the given expression for s = 5.
s² + 7s - 2
Answer :
Plug 5 for each s
5² + 7(5) - 2
Evaluate exponents
25 + 7(5) - 2
Multiply 7 and 5
25 + 35 - 2
Add 25 and 35
60 - 2
Subtract 2 from 60
58
Therefore, s² + 7s - 2 = 58
Example 7 :
Evaluate the given expression for m = 5 and n = 2.
m² + 2mn²
Answer :
Plug 5 for m and 2 for n
5² + 2(5)(2)²
Evaluate the exponents
25 + 2(5)(4)
Multiply
25 + 40
Add
65
Example 8 :
Evaluate the given expression for m = 3.
(2m² + 5m - 7) / 2
Answer :
Plug 3 for each m
[2(3)² + 5(3) - 7] / 2
Evaluate the exponents
[2(9) + 5(3) - 7] / 2
Multiply
[18 + 15 - 7] / 2
Add 18 and 15
[33 - 7] / 2
Subtract 7 from 33
26 / 2
Divide
13
Therefore, (2m² + 5m - 7)/2 = 13
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