Problem 95 - Elementary Algebra

Question

Describe the order of operations.

Step-by-Step Solution

Answer

1. Parentheses 2. Exponents 3. Multiplication/Division 4. Addition/Subtraction

Step 1: Parentheses

First, perform all operations inside parentheses (or brackets). This includes solving any nested parentheses from the innermost to the outermost.

Step 2: Exponents

Next, evaluate all exponents (or powers and roots).

Step 3: Multiplication and Division

Then, perform all multiplication and division from left to right. These operations have the same level of priority and should be processed in the order they appear.

Step 4: Addition and Subtraction

Finally, perform all addition and subtraction from left to right. As with multiplication and division, these operations are done in the order they appear, from left to right.

Key Concepts

Parentheses

When solving a mathematical expression, the first step is always to deal with parentheses. Parentheses are used to group parts of an expression that should be evaluated first. This can include single numbers, terms, or even other expressions and operations. It's important to work from the innermost set of parentheses outwards.

Here's a quick guideline for handling parentheses:

• Start with the innermost parentheses.
• Solve all expressions within these parentheses.
• Move to the next outer pair of parentheses.
• Repeat until all parentheses are resolved.

Remember, resolving parentheses first clears up the expression and helps avoid mistakes in the later steps.

Exponents

Exponents are the next step in the order of operations. Exponents refer to numbers that are raised to a power, like in the expression 3^2 where 3 is the base and 2 is the exponent. Evaluating exponents means performing operations such as squaring (raising to the power of 2) or taking the square root.

Tips for dealing with exponents:

• Identify all the exponents in the expression.
• Solve each exponential expression sequentially.
• Handle any roots or fractional exponents as well.

By focusing on exponents next, you're simplifying the expression further and preparing for easier multiplication, division, addition, and subtraction.

Multiplication and Division

After parentheses and exponents, it’s time to tackle multiplication and division. These operations are performed from left to right, following the order they appear in the expression. Both operations have the same priority.

Strategies for multiplication and division:

• Read the expression from left to right.
• Perform multiplication or division as you encounter them.
• Continue until you reach the end of the expression.

An important thing to remember is that multiplication does not always come before division, and they should be handled in the sequence they appear in the problem.

Addition and Subtraction

The final step in the order of operations is addition and subtraction. As with multiplication and division, these operations are processed from left to right. They are also of equal priority, meaning you handle them in the order they are written.

How to manage addition and subtraction:

• Start at the leftmost part of the expression.
• Perform all additions and subtractions as they appear.
• Move through the expression until all are handled.

Completing addition and subtraction last ensures that all other simpler operations have been resolved, making this step straightforward and clear.