Evaluating and simplifying expressions with order of operations
Practice algebra problems about the order of operations when evaluating and simplifying expressions.
When evaluating and simplifying algebraic expressions, there is often an order of operations used to perform the evaluation and simplification. In general the order is:
- Resolve the expression within the innermost parentheses of an expression
- Raise to the power or extract a root
- Perform multiplication and division (e.g. from left to right)
- Perform addition and subtraction (e.g. from left to right)
Example of using order of operations
Let's take the following example expression:
\[ 5 \cdot 2^{2} - \sqrt{25} \div 5 + 2^{2} \cdot 8 \div 4 - 2 \]
We'll start with raising all \( 2^{2} \) and evaluating it to 4, along with evaluating the principal square root of \( \sqrt{25} \) as 5:
\[ 5 \cdot 4 - 5 \div 5 + 4 \cdot 8 \div 4 - 2 \]
Now we'll perform all multiplication and division operations from left to right:
\[ 20 - 1 + 8 - 2 \]
Finally we'll perform all addition and subtraction operations from left to right:
\[ 25 \]
Therefore the expression is found to be 25.
Practice problem
Attempt finding the value of the following expression:
\[ \frac{3 \times 6 \div 9}{2} - 2 \sqrt{100} \div 5 + 4 \cdot 2^{3} - \frac{14 \cdot 2}{28} \]
