Operations with Real Numbers and Expressions Calculator
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Reviewed by Calculator Editorial Team
This calculator helps you perform basic arithmetic operations and work with mathematical expressions involving real numbers. Whether you're solving equations, simplifying expressions, or performing calculations, this tool provides accurate results and clear explanations.
Basic Operations with Real Numbers
Real numbers include all rational and irrational numbers, both positive and negative, as well as zero. Basic operations with real numbers include addition, subtraction, multiplication, and division.
Basic Operations Formulas
- Addition: a + b = sum
- Subtraction: a - b = difference
- Multiplication: a × b = product
- Division: a ÷ b = quotient (b ≠ 0)
When performing operations with real numbers, it's important to follow the order of operations (PEMDAS/BODMAS): Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
Working with Expressions
Mathematical expressions are combinations of numbers, variables, and operators that can be evaluated to produce a result. Expressions can include constants, variables, and functions.
Expression Evaluation
To evaluate an expression, substitute the values of the variables and perform the operations according to the order of operations.
When working with expressions, you may need to simplify them by combining like terms, factoring, or expanding. This calculator can help you evaluate expressions and perform these simplifications.
Worked Examples
Example 1: Basic Arithmetic
Calculate (5 + 3) × (10 - 4) ÷ 2.
- First, perform the operations inside the parentheses: 5 + 3 = 8 and 10 - 4 = 6.
- Next, multiply the results: 8 × 6 = 48.
- Finally, divide by 2: 48 ÷ 2 = 24.
The final result is 24.
Example 2: Expression Evaluation
Evaluate the expression 3x² + 2x - 5 when x = 2.
- Substitute x = 2 into the expression: 3(2)² + 2(2) - 5.
- Calculate the square: 3 × 4 = 12.
- Multiply the remaining terms: 2 × 2 = 4.
- Combine the results: 12 + 4 - 5 = 11.
The evaluated result is 11.
Frequently Asked Questions
What is the difference between real numbers and integers?
Real numbers include all rational and irrational numbers, while integers are a subset of real numbers that include all whole numbers and their negatives, including zero.
How do I simplify a mathematical expression?
To simplify an expression, combine like terms, factor common terms, or expand using the distributive property. This calculator can help you evaluate and simplify expressions.
What is the order of operations in mathematics?
The order of operations is PEMDAS/BODMAS: Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).