# How To Evaluate Algebraic Expressions | Summary and Q&A

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August 29, 2022
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The Organic Chemistry Tutor
How To Evaluate Algebraic Expressions

## TL;DR

Learn how to substitute values and evaluate algebraic expressions using the order of operations.

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### Q: How do you evaluate an algebraic expression?

To evaluate an algebraic expression, substitute the given values for the variables and perform the calculations according to the order of operations. This involves replacing the variables with their corresponding values and then following the sequence of operations (parentheses, exponents, multiplication/division, and addition/subtraction) to obtain the final result.

### Q: Why is it important to follow the order of operations when evaluating expressions?

Following the order of operations ensures that calculations are done in a consistent and standardized manner. It prevents ambiguity and ensures that everyone arrives at the same correct result. By prioritizing certain operations over others, the order of operations safeguards the accuracy and reliability of mathematical expressions.

### Q: Why is it recommended to check your work when evaluating algebraic expressions?

Checking your work is important to verify the accuracy of your calculations and identify any potential errors. By plugging the expression into a calculator using the substituted values, you can compare the result obtained through manual evaluation with the calculator's result. If both match, it confirms the correctness of your evaluation.

### Q: How can parentheses and exponents affect the evaluation of an algebraic expression?

When parentheses are present in an expression, you first evaluate the operations inside the parentheses before moving on to other calculations. Exponents indicate repeated multiplication, so they take precedence before other operations. By correctly handling parentheses and exponents, you ensure the accurate evaluation of algebraic expressions.

### Q: What steps can be taken to simplify fractions in an algebraic expression?

To simplify fractions in an algebraic expression, you can reduce them to lowest terms if possible. You can also express them as mixed numbers or convert them into decimal values. These steps make the expression more concise and may be more practical for certain applications.

### Q: How can the height of a ball thrown into the air be determined using an algebraic expression?

The height of a ball thrown into the air can be determined using an algebraic expression that relates the height to time. By substituting the given value for time into the expression and performing the necessary calculations, the height of the ball at that specific time can be evaluated.

## Summary & Key Takeaways

• To evaluate an algebraic expression, substitute the given values for the variables and perform the calculations according to the order of operations.

• Check your work by plugging the expression into a calculator using the substituted values to ensure accuracy.

• Examples demonstrate the evaluation process, covering different scenarios and expressions.