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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 x

    6 is the coefficient of x.

  • Consider the expression below. One of the coefficients is a letter rather than a number:

    a x squared plus x plus 2 y.

    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.

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
Algebra Lessons
Interactive Test
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Here'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.

a variable without a coefficient.

Don't be fooled. It still has a coefficient. The coefficient is 1.

a variable without a coefficient written in front of it has a coefficient of 1.

Positive, Negative and Fractional Coefficients

Coefficients can be positive, negative and fractional.

a positive coefficient, a negative coefficient and a fractional coefficient