The Lesson
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.
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Consider the expression below. One of the coefficients is a letter rather than a number:
a (a constant) is the coefficient of x2. 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.
x + x = 2x
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:
2x = 2 × x = x + x
If there was a coefficient of 3 in front of an x, we would have 3 x's:
3x = 3 × x = x + x + x
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.
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.

Positive, Negative and Fractional Coefficients
Coefficients can be positive, negative and fractional.