Since there are no parentheses or exponents, division is our first step (the D in PEMDAS).
5 – 3 + 6 ÷ 2 = 5 – 3 + 3
Next, simplify the first addition/subtraction operation.
5 – 3 + 3 = 2 + 3
Finally, simplify the last addition/subtraction operation.
2 + 3 = 5
All done!
Now try to do the problem in your head from left to right. The answer would then be 4, which is obviously not correct. See? Order matters!
Example 2
What is 5(6 + 9 ÷ 3 – 1)2 ?
First, simplify the parentheses. Since there are many operations in the
parentheses, follow the order of operations inside them, too. In this
problem, division comes first.
5(6 + 9 ÷ 3 – 1)2 = 5(6 + 3 – 1)2
Next, simplify the addition and subtraction from left to right.
5(6 + 3 – 1)2 = 5(9 – 1)2 = 5(8)2
Now, tackle the exponents.
5(8)2 = 5(64)
Finally, multiply.
5(64) = 320
Awesome. We're done!
Example 3
Simplify .
In this problem, treat the numerator and denominator like they're in
separate parentheses, and the fraction bar as a division sign. You
could rewrite this problem as: . Now simplify each set of parentheses using the correct order of operations.
=
=
Finally, divide.
=
Yahoo!
Example 4
Simplify [3(6 – 4)]2.
Here, we have two sets of parentheses: the regular ones and the brackets. Simplify the innermost set first.
.
. Now simplify each set of parentheses using the correct order of operations.
