Algebraic Expression Calculator
Evaluate algebraic expressions with variables and see step-by-step substitution
Understanding Algebraic Expressions
An algebraic expression is a mathematical phrase that can contain numbers, variables, and operation symbols. Variables represent unknown values that can change, while constants are fixed numbers.
Components of Algebraic Expressions
- Variables: Letters (like x, y, z) that represent unknown values
- Coefficients: Numbers that multiply variables (in 3x, the coefficient is 3)
- Constants: Fixed numbers that don't change
- Operators: Symbols (+, -, ×, ÷) that show operations
How to Evaluate Expressions
- Write down the original expression
- Identify the given values for each variable
- Substitute the values in place of variables
- Follow the order of operations (PEMDAS)
- Simplify to get the final result
Example
Evaluate 3x + 2y - 5 when x = 4 and y = 3:
- = 3(4) + 2(3) - 5
- = 12 + 6 - 5
- = 13
Frequently Asked Questions
What is an algebraic expression?
An algebraic expression is a mathematical phrase containing variables, numbers, and operations. Unlike equations, expressions don't have an equal sign and can't be "solved" - they can only be evaluated or simplified.
What's the difference between an expression and an equation?
An expression is a mathematical phrase (like 3x + 2), while an equation sets two expressions equal to each other (like 3x + 2 = 11). Expressions are evaluated; equations are solved.
How do I substitute values into an expression?
Replace each variable with its given value, making sure to use parentheses around the substituted values. Then follow the order of operations to calculate the result.
What is the order of operations?
PEMDAS: Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right). Always follow this order when evaluating expressions.
Can an expression have more than two variables?
Yes! Expressions can have any number of variables. For example, 2a + 3b - 4c + d is a valid expression with four variables.
What happens if I don't have values for all variables?
Without values for all variables, you can't get a numeric result. However, you can still simplify the expression by combining like terms or applying algebraic properties.
Why use parentheses when substituting?
Parentheses ensure correct calculation, especially with negative numbers or when a coefficient precedes the variable. For example, 3x when x = -2 becomes 3(-2) = -6, not 3-2 = 1.
Can I use decimals and fractions as variable values?
Absolutely! Variables can take any real number value, including decimals, fractions, negative numbers, and even irrational numbers like π.
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