Mathematics is made up of symbols that can be combined to make statements about the world around us. Sometimes those symbols represent numbers and sometimes they are more abstract, representing spaces, symmetries or groups. Mathematical expressions are formed when these symbols are combined with mathematical operations such as addition, subtraction, or multiplication to name just a few.
Example 1: Arithmetic Operations

The most basic kind of mathematical expression are arithmetic operations. Arithmetic operations consist of any combination of numbers with a mathematical operation, such as multiplication, addition, subtraction or division. For example, 9 + 14/2  6*(5 + 3) is an arithmetic operation equal to 32.
Example 2: Functions

Another common type of mathematical expression are functions. Functions consist of numbers, variables and mathematical operations, and are often used in physics, biology and economics to design models that approximate observations about the world. For example, 2x + 7 = 13 is a function and the value of x in this case is 3.
Example 3: Summations

Another kind of expression commonly found in mathematics is a summation. Summations add together all the elements of a particular set and are represented by the Σ symbol, or sigma. For example, if A = {1, 2, 3, 4], Σ(A) = 1+2+3+4, which is equal to 10.
Other Expressions

Some mathematical expressions that have not been discussed here but are very common in mathematical work are derivatives, integrals and factorials. These are similar in structure to the three types of expressions described above and are often used in calculus and abstract math.
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