Coefficients (Mathematics Glossary)
What Is a Coefficient?
A coefficient is a number that is placed in front of a variable.
The coefficient is multiplying the variable.
Dictionary Definition
The Oxford English Dictionary defines a coefficient as "a number or quantity placed (usually) before and multiplying another quantity known or unknown."
Real Examples of Coefficients
It is easier to understand coefficients with examples.

Consider the term below:
6 is the coefficient of x.

Consider the expression below. One of the coefficients is a letter rather than a number:
a (a constant) is the coefficient of x^{2}.
1 is the coefficient of x, even though no number or letter is written in front of it (see Note).
2 is the coefficient of y.
Understanding Coefficients
Think of a letter in algebra as an object. We can count the objects.
x is one x.
If we add one x to one x, we get two x's.
The coefficient of 2 is telling us we have 2 x's.
Another way of saying this is that the 2 is multiplying the x after it:
If there was a coefficient of 3 in front of an x, we would have 3 x's:
Letters As Coefficients
Letters can be used as coefficients.
For example, a standard linear equation is y = mx + c. The m is the coefficient of the x term.
The letter still represents a number. The m could be a 2 or a 3 for different linear equations.
More Real Examples of Coefficients
The slider below has some more real examples of coefficients.
Curriculum
Interactive Test
showHere's a second test on coefficients.
Here's a third test on coefficients.
Note
A Term Without a Number in Front of it Has a Coefficient of 1
Sometimes a term will not have a number in front of it.
Don't be fooled. It still has a coefficient. The coefficient is 1.
Positive, Negative and Fractional Coefficients
Coefficients can be positive, negative and fractional.