Question

Write down the numerical as well as literal coefficient of each of the following expressions
(i). $-2p^3{q}^2$
(ii). ${\displaystyle \frac{5}{9}}xy{z}^2$
(iii). ${\displaystyle \frac{3}{a^2}}$
(iv). ${\displaystyle \frac{2ab}{c}}$

Answer 1

Hint: In this question, we are given some expressions are asked to find the numerical and literal coefficients, therefore, we should first understand the meaning of numerical and literal coefficients and then use this definition to find the numerical and literal coefficients in each of the given expressions.

Complete step-by-step answer:

In the question, we are given some expressions and we have to find the numerical and literal coefficients. Therefore, we should first understand their definitions which are stated as follows
Numerical Coefficient- It is the part which consists of numbers in the expression, for example in 2x, 2 is the numerical coefficient……………………. (1.1)
Literal Coefficient- It is the part which consists of one or more symbols, for example in 2x, x is the literal coefficient……………………. (1.2)

(i). The given expression is $-2p^3{q}^2$. We find that the part consisting of numbers is $-2$ and the part consisting of symbols is $p^3{q}^2$. Therefore, using the definitions in (1.1) and (1.2), we obtain that in this case
Numerical Coefficient=-2
Literal Coefficient=$p^3{q}^2$
(ii). The given expression is ${\displaystyle \frac{5}{9}}xy{z}^2$. We find that the part consisting of numbers is ${\displaystyle \frac{5}{9}}$ and the part consisting of symbols is $xy{z}^2$. Therefore, using the definitions in (1.1) and (1.2), we obtain that in this case
Numerical Coefficient=${\displaystyle \frac{5}{9}}$
Literal Coefficient=$xy{z}^2$
(iii). The given expression is${\displaystyle \frac{3}{a^2}}$. We find that the part consisting of numbers is $3$ and the part consisting of symbols is ${\displaystyle \frac{1}{a^2}}$. Therefore, using the definitions in (1.1) and (1.2), we obtain that in this case
Numerical Coefficient=$3$
Literal Coefficient=${\displaystyle \frac{1}{a^2}}$
(iv). The given expression is${\displaystyle \frac{2ab}{c}}$. We find that the part consisting of numbers is $2$ and the part consisting of symbols is ${\displaystyle \frac{ab}{c}}$. Therefore, using the definitions in (1.1) and (1.2), we obtain that in this case
Numerical Coefficient=$2$
Literal Coefficient=${\displaystyle \frac{ab}{c}}$

Note: We should note that in the literal coefficients, it is not necessary that only one symbol is present. For example in (iv), the literal coefficient is ${\displaystyle \frac{ab}{c}}$ which consists of three symbols a, b and c. However, we should be careful not to include any symbol in numerical coefficient and not to include any number in the literal coefficient.