Which phrase represents the expression 7x + 2 ?

two plus a number multiplied by seven

two less than a number multiplied multiplied by seven

Expressions in Math - Definition, Types, Examples

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Updated: Jan 21, 2025

Lesson

Mathematics uses symbols, numbers, and operations to convey meaning. These combinations are called expressions.

Expressions allow us to represent quantities, relationships, and even real-world situations. They can be simple or complex, but they always serve the purpose of conveying mathematical information in a concise and powerful way.

Expression Definition in Math

An expression in mathematics is a combination of numbers, symbols, and operations that represents a value or a relationship. However, expressions do not include an equals sign.

Key components of an expression in Math:

Numbers: These can be whole numbers, decimals, fractions, or even irrational numbers like pi.
Symbols: These include variables (like x, y, or z), which represent unknown quantities, and mathematical symbols like parentheses, brackets, and braces.
Operations: These are actions performed on the numbers and variables, such as addition (+), subtraction (-), multiplication (* or •), division (/ or ÷), exponents (like x²), and roots (like √x).

Examples:

5 + 3
2x - 7
3(y + 4)
√(a² + b²)
4πr²

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Expressions and equations quiz

Types of Expressions in Math

Expression Type	Definition	Examples
Numerical Expression	Contains only numbers and mathematical operations. No variables are present.	5 + 3, 12 ÷ 4
Fractional Expression	Contains fractions along with numbers and operations. May or may not include variables.	1/2 + 3/4, (x + 2) / 5
Algebraic Expression	Contains variables, numbers, and operations. Represents a value or relationship that can change depending on the value of the variable(s).	2x - 7, a² + 2ab + b²

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Expressions, Equations, Functions, & Relations

Expression vs Equation

While both equations and expressions involve mathematical symbols and operations, expressions and equations have distinct roles. Here's a comparison:

Feature	Expression	Equation
Definition	A combination of numbers, symbols, and operations that represents a value or relationship.	A statement that two expressions are equal.
Equals Sign	Does not include an equals sign (=).	Includes an equals sign (=).
Purpose	Represents a value or a relationship.	Shows the equality between two expressions.
Solution	Cannot be solved, but can be evaluated or simplified.	Can be solved to find the value(s) of the variable(s) that make the statement true.
Analogy	A phrase in a sentence.	A complete sentence.
Example	2x + 5, 3y - 8, a² + b²	2x + 5 = 11, 3y - 8 = 7, a² + b² = 25

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Algebraic Expressions

Simplifying Expression in Math

Simplifying an expression means writing it in its most compact and understandable form.

Here's how to simplify expressions:

Remove parentheses: Use the distributive property to multiply terms outside parentheses by terms inside.

Example: 3(x + 2) becomes 3x + 6

Combine like terms: Add or subtract terms that have the same variables raised to the same powers.

Example: 5x + 2x - 3y becomes 7x - 3y

Apply order of operations (PEMDAS/BODMAS):

Parentheses / Brackets

Exponents / Orders

Multiplication and Division (from left to right)

Addition and Subtraction (from left to right)

Examples:

Simplify: 2(x - 3) + 4x - 5
- Distribute: 2x - 6 + 4x - 5
- Combine like terms: 6x - 11
Simplify: 3a² + 2a - 5 + a² - 4a
- Combine like terms: 4a² - 2a - 5
Simplify: 5(2y - 1) - 3(y + 2)
- Distribute: 10y - 5 - 3y - 6