How do you use the order of operations (PEMDAS) in mathematics?

Order of Operations, also known as PEMDAS (Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction), is a set of rules that dictate the sequence in which mathematical operations are performed.

It is essential to follow the order of operations to ensure that mathematical expressions are evaluated correctly. The order of operations ensures that the same expression is always evaluated in the same way, regardless of who is evaluating it.

The following are the steps for solving a mathematical expression using the order of operations:

1. Start by evaluating expressions within parentheses or brackets, starting from the innermost set and working outward.
2. Next, evaluate any exponents or radicals.
3. Perform any multiplication or division, working from left to right.
4. Finally, perform any addition or subtraction, working from left to right.

Using PEMDAS, let's evaluate the following expression: 3 + 4 x 5 - 2 ^ 2

1. There are no parentheses or brackets, so we move to the next step.
2. There is one exponent, 2 ^ 2 = 4, so we evaluate that expression.
3. Next, we perform multiplication and division, starting from left to right. The expression 4 x 5 = 20, so we replace that expression with 20.
4. Finally, we perform addition and subtraction, again working from left to right. The expression 3 + 20 - 4 = 19, so our final answer is 19.

By following PEMDAS, we were able to evaluate the expression correctly.