In a math equation, what comes first is determined by the order of operations.
Understanding the Order of Operations
The order of operations is a set of rules that dictate the sequence in which mathematical operations should be performed. This ensures that everyone arrives at the same correct answer when solving a complex equation. The most common acronym used to remember this order is PEMDAS (or sometimes BEDMAS).
PEMDAS Explained
| Operation Category | Acronym | Description |
|---|---|---|
| Parentheses | P | Calculations inside parentheses (or brackets) are always performed first. |
| Exponents | E | Operations involving exponents or roots are handled after parentheses. |
| Multiplication | M | Multiplication and division are performed next, from left to right. |
| Division | D | Multiplication and division are performed next, from left to right. |
| Addition | A | Addition and subtraction are carried out last, moving from left to right. |
| Subtraction | S | Addition and subtraction are carried out last, moving from left to right. |
Example
Let's illustrate with an example using the information from our reference, where it was specified: "The order of operations is the order you use to work out math expressions: parentheses, exponents, multiplication, division, addition, subtraction. All expressions should be simplified in this order." Let's consider this expression:
2 x (5 + 3)^2 - 10 / 2
- Parentheses: First we solve the expression within the parentheses:
(5 + 3) = 8.
The expression now looks like this:2 x 8^2 - 10 / 2 - Exponents: Next we evaluate the exponent:
8^2 = 64.
The expression now looks like this:2 x 64 - 10 / 2 - Multiplication and Division: Now we perform multiplication and division, working from left to right:
2 x 64 = 12810 / 2 = 5
The expression now looks like this:128 - 5
- Addition and Subtraction: Finally we do addition and subtraction, working from left to right:
128 - 5 = 123
Therefore, the answer to the equation 2 x (5 + 3)^2 - 10 / 2 is 123.
Key Takeaway
The most important thing to remember is that without a specific order, everyone would solve the same math problem differently. Following the order of operations ensures consistency and accuracy in mathematical calculations.
