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
\[12x^{2}-4x+5\]
\[a^{2}+b^{2}\]
Advanced
\[\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}\]
How to Use Expressions
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” (\(\mapsto\)).
