# What is an Expression?

## What is an expression?

An expression is a part of a math sentence. They are kind of like the math version of a subject or a predicate in an English sentence.

Usually, expressions have multiple numbers or variables that are connected by operations like addition, subtraction, multiplication, division, powers, or roots.

## Expression Examples

Expressions can be very simple, like a single number or a variable. Or they can be very complex, like the quadratic formula.

### Simple

$28y$

$x+7$

### Moderate

$12x^{2}-4x+5$

$a^{2}+b^{2}$

$\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$

## Expressions in Math Sentences

Expressions can be written on their own (like the examples above) or they can be written as part of a math sentence.

All math sentences have the same basic structure, no matter how complicated they are. In English, sentences have 2 basic parts (a subject and a predicate). In math, sentences have 3 basic parts (two expressions and a relationship).

Expression Relationship Expression

When the relationship connecting the two expressions is an equal sign, the math sentence is called an equation. When the relationship is a greater than or less than sign, the math sentence is called an inequality.

### Equations

${\red 2+3}={\yellow 5}$

${\red y}={\yellow mx+b}$

${\red (x-h)^2 + (y-k)^2}={\yellow r^2}$

### Inequalities

${\red 12}>{\yellow 9}$

${\red 7+6}<{\yellow 7\times 6}$

${\red y}\geq{\yellow 4x}$

You can also have other relationships like “is not equal to” ($$\neq$$), “is an element of” ($$\in$$), or “is perpendicular to” ($$\perp$$).

${\red 3-1}\neq{\yellow 17}$

${\red 4} \in {\yellow \mathbb{Z} }$

${\red \overline{AB}}\perp{\yellow \overrightarrow{AC}}$

## Types of Relationships

These are the most commonly used relationships in high school math. Once you start learning set theory, you may use other relationships like “is an element of” ($$\in$$), “is a subset of” ($$\subset$$), or “maps to” ($$\mapsto$$).