Question

How do you evaluate $\dfrac{m}{q} + n{p^2}$ for $m = 24,n = 6,p = 9$ and $q = 8$?

Answer 1

Hint: To find the value of an expression, we substitute the values of the variables in the expression and then simplify. Here, values of all the variables are given, plug in the given numbers for the variables. Then, use PEMDAS to evaluate it further.

Complete step-by-step solution:
To find the value of an expression, we substitute the values of the variables in the expression and then simplify.
Here, the given algebraic expression is $\dfrac{m}{q} + n{p^2}$.
Given values of variables: $m = 24,n = 6,p = 9$ and $q = 8$
Now, plug in the given numbers for the variables.
$\dfrac{{24}}{8} + 6 \cdot {9^2}$
Now, use PEMDAS to evaluate.
Since, parenthesis have a high precedence and should be worked from the innermost to the outermost.
Here, there is no parenthesis, so I will move to the next step.
Next, we would work on any expressions that are raised to a power exponent.
Here, ${9^2} = 81$ can be written as
$\dfrac{{24}}{8} + 6 \cdot 81$
Next, if we have multiplication and division those should be evaluated from the leftmost moving to the right.
So, it can be written as
$3 + 486$
Lastly, if we have any addition and subtraction those should be evaluated from the leftmost moving to the right.
So, it can be written as
$489$
Therefore, $\dfrac{m}{q} + n{p^2} = 489$ for $m = 24,n = 6,p = 9$ and $q = 8$.

Note: PEMDAS is the order of operations.
The list below is from highest precedence to lowest precedence.
P→ Parenthesis
E→ Exponents
MD→ Multiplication & Division from Left to Right
AS→ Addition & Subtraction from Left to Right
Parenthesis have a high precedence and should be worked from the innermost to the outermost.
Next you would work on any expressions that are raised to a power exponent.
Next if you have multiplication and division those should be evaluated from the leftmost moving to the right.
Lastly, if you have any addition and subtraction those should be evaluated from the leftmost moving to the right.
This is an agreed upon method resolving or evaluating expressions and equations. Without this agreement people working on mathematics would come to different conclusions based on the operations they chose to evaluate at random.
If you ever come to the point where you want some part of an expression or equation to be evaluated at a higher precedence than you just have to enclose it in parenthesis.