# Numerical coefficient

## Definition

A coefficient in number form that multiplies at least one literal to form an algebraic term is called a numerical coefficient.

Algebraic terms are formed by the product of one number and one or more literal numbers. The number in the term is a coefficient due to its multiplication with other literals. Hence, the multiplying number in any algebraic term is called a numerical coefficient of literal portion of the algebraic term.

### Examples

$(1) \,\,\,\,\,$ $8a$

The algebraic term $8a$ can be written as $8a = 8 \times a$.

$8$ is multiplying the literal $a$ and moreover it is a number. So, the numeral $8$ is called a numerical coefficient of $a$ in the algebraic term $8a$.

$(2) \,\,\,\,\,$ $-6xy$

The term can be written as $-6xy = -6 \times xy$.

The algebraic term $-6xy$ is actually formed by $-6$, $x$ and $y$. In this case, $-6$ is multiplying the literals $x$ and $y$ but it is a number. So, the number $-6$ is called the numerical coefficient of $xy$ in algebraic term $-6xy$.

$(3) \,\,\,\,\,$ $p^2q$

It seems there is no numerical coefficient for the term $p^2q$ but the algebraic term is written once. So, it can be written as $p^2q = 1 \times p^2q$.

Therefore, the number $1$ is a numerical coefficient of $p^2q$ in this example.

$(4) \,\,\,\,\,$ $-rs^2n^3$

The above same logic is also used to express the algebraic term as $-rs^2n^3 = -1 \times rs^2n^3$.

The number $-1$ is the literal coefficient of $rs^2n^3$ in this case.

$(5) \,\,\,\,\,$ $\dfrac{2mn^3}{3}$

It is a special case and two numbers involved in forming the algebraic term along with two literals. However, the number $2$ is multiplying the product of literals $mn^3$ but the number $3$ is dividing the same product. So, don’t think $2$ is only the numerical coefficient of $mn^3$ and $3$ is not.

The algebraic term $\dfrac{2mn^3}{3}$ can be written as $\dfrac{2mn^3}{3} = \dfrac{2}{3} \times mn^3$

Therefore, the ration number $\dfrac{2}{3}$ is called the numerical coefficient of $mn^3$ in this special case.

According to these understandable examples, there is only one number in every algebraic term possibly. So, identity the number in any algebraic term and call it as a numerical coefficient for the remaining multiplying literal coefficients.

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