A coefficient is a known factor of a variable, written as a multiplier. In basic algebra, it is the number portion of a term. For example, 5 is the coefficient of x in the term 5x. Any number can be a coefficient, including whole numbers, fractions and decimals. For example, 2y, 3/4a and 7.382q are all terms with a valid coefficient. Sometimes a constant (a number with no variable) is also considered the coefficient of a variable to the power of 0.
Although its placement has no bearing on the product, the coefficient traditionally precedes the variable. For example, if p equals 2, 8p and p8 both equal 16; however, 8p is the proper way to write the term. Treat the coefficient and the variable as one unit by placing no space or multiplication symbol between them.
When adding or subtracting like terms (terms with identical variables), add or subtract the coefficients and leave the variable as it is. For example, 4y + 7y = 11y. If the ending coefficient equals 1, as in 3j - 2j = 1j, leave off the coefficient. Conversely, remember that if a variable appears alone, it really has a coefficient of 1. For example, d + 4d is the same as 1d + 4d. When multiplying or dividing terms, multiply or divide the coefficients and aggregate the terms. For example, 10s * 5w = 50sw.
Mathematicians often express algebraic equations using formulas, such as x = -b/a. In these kinds of formulas, the coefficients are represented by letters, but the reader is meant to understand that these letters are not variables. When you use a formula like this, substitute the values of the coefficients belonging to each term into the equation before you begin to solve it. For example, if the equation is 5x + 7, write the formula as x = -7/5.