Question

One-fifth of the product of $p$ and $q$ added to the difference of $m$ and $n$. Form an algebraic expression for the given statement.

• A. $\frac{1}{5}pq$
  
• B. $m-n$
• C. $\frac{1}{5}pq+(m+n)$
  
• D. $\frac{1}{5}pq+(m-n)$
  

Answer 1

The correct option is D $\frac{1}{5}pq+(m-n)$


$\underset{–}{Step1:}$
First, we would evaluate the product of $p$ and $q$. this can be shown as:
$p\times q=pq$
Now, we would multiply the product of $p$ and $1$ by the fraction $\frac{1}{5}$ in order to get the one-fifth of the product of $p$ and $q$. This can be shown as:
$\frac{1}{5}\times \left(pq\right)=\frac{1}{5}pq$

$\underset{–}{Step2:}$
We would subtract $n$ from $m$ in order to get the difference of $m$ and $n$. This can be shown as:
$m-n$


$\underset{–}{Step3:}$
We would now add one-fifth of the product of $p$ and $q$ to the difference of $m$ and $n$. This can be shown as:
$\frac{1}{5}pq+(m-n)$

Therefore, option (d.) is the correct answer.