Question

Identify the terms, their coefficients for the following expression: $\dfrac{x}{2} + \dfrac{y}{2} - xy$.
A) Coefficient of $x$ in the term $\dfrac{x}{2}$ is $1$.
Coefficient of $y$ in the term $\dfrac{y}{2}$ is $1$.
Coefficient of $xy$ in the term $ - xy$ is $1$.

B) Coefficient of $x$ in the term $\dfrac{x}{2}$ is $1$.
Coefficient of $y$ in the term $\dfrac{y}{2}$ is $\dfrac{1}{2}$.
Coefficient of $xy$ in the term $ - xy$ is $1$.

C) Coefficient of $x$ in the term $\dfrac{x}{2}$ is $1$.
Coefficient of $y$ in the term $\dfrac{y}{2}$ is $1$.
Coefficient of $xy$ in the term $ - xy$ is $ - 1$.

D) Coefficient of $x$ in the term $\dfrac{x}{2}$ is $\dfrac{1}{2}$.
Coefficient of $y$ in the term $\dfrac{y}{2}$ is $\dfrac{1}{2}$.
Coefficient of $xy$ in the term $ - xy$ is $ - 1$.

Answer 1

Hint: A coefficient is a number or constant that is multiplied to a variable that is present in an equation. Leaving all the variables in an operand, all constants left are the coefficients of a number. For example: The coefficient of ${x^2}$ in $2{x^2}$ is $2$.

Complete step by step solution:
We are given with an equation $\dfrac{x}{2} + \dfrac{y}{2} - xy$. Separating the variables and constants from each operand, we can write the equation as:
$\dfrac{x}{2} + \dfrac{y}{2} - xy$
$ \Rightarrow \dfrac{1}{2}x + \dfrac{1}{2}y - xy$ ……(1)
And, for the last operand we know that $ - x$ can be written as $\left( { - 1} \right)x$.
So, we can write the last operand $ - xy$ as $ + \left( { - xy} \right) = + \left( { - 1} \right)xy$.
Substituting this value in the equation 1, we get:
$ \Rightarrow \dfrac{1}{2}x + \dfrac{1}{2}y + \left( { - xy} \right)$
$ \Rightarrow \dfrac{1}{2}x + \dfrac{1}{2}y + \left( { - 1} \right)xy$

As, we know that coefficients are the values that are with the variable, leaving the variable part all the remaining values are coefficients.For, example in the given equation above for the operand $ - xy$ as expressed $ + \left( { - xy} \right) = + \left( { - 1} \right)xy$, leaving the variables $xy$ we have the coefficient $\left( { - 1} \right)$.

Similarly, for other operands we have, the coefficients as: for $x$ in $\dfrac{1}{2}x$, the coefficient is $\dfrac{1}{2}$. And the coefficient of $y$ in $\dfrac{1}{2}y$, the coefficient is $\dfrac{1}{2}$.
Therefore, we can write:
Coefficient of $x$ in the term $\dfrac{x}{2}$ is $\dfrac{1}{2}$
Coefficient of $y$ in the term $\dfrac{y}{2}$ is $\dfrac{1}{2}$
Coefficient of $xy$ in the term $ - xy$ is $ - 1$.
Hence, option D is correct.

Note: Constants are the terms whose values are never changed. For example, 2, 4, 6, … are constants. Variables are the values that are changed for every constant value. It can be expressed by any alphabet like x, y, z, a, b, w, etc.