Evaluate $\frac{c}{2}-3+\frac{6}{d}$ when $c=14$ and $d=3$.

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01-11-2026
Mathematics

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Evaluate $\frac{c}{2}-3+\frac{6}{d}$ when $c=14$ and $d=3$.

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GinnyAnswer GinnyAnswer · Answer 1 · 2026-11-01T21:37:37-05:00

Substitute $c = 14$ and $d = 3$ into the expression $\frac{c}{2} - 3 + \frac{6}{d}$.
Evaluate $\frac{14}{2} = 7$ and $\frac{6}{3} = 2$.
Simplify the resulting expression $7 - 3 + 2$.
The final result is $\boxed{6}$.

Explanation

Problem Analysis

We are given an expression $\frac{c}{2} - 3 + \frac{6}{d}$ and tasked with evaluating it for the specific values $c = 14$ and $d = 3$. To solve this, we will systematically substitute these values into the expression and perform the arithmetic operations according to the order of operations.

Substitution and Intermediate Calculations

First, we substitute $c = 14$ into the term $\frac{c}{2}$:
\[\frac{14}{2} = 7\]
Next, we substitute $d = 3$ into the term $\frac{6}{d}$:
\[\frac{6}{3} = 2\]

Final Evaluation

Now that we have the numerical values for the individual parts of the expression, we substitute them back into the original expression:
\[7 - 3 + 2\]
Performing the operations from left to right:
\[7 - 3 = 4\]
\[4 + 2 = 6\]
Thus, the value of the expression is 6.

Examples

This type of expression evaluation is fundamental in many fields, such as physics or economics, where formulas are used to calculate results based on specific input parameters. For example, if you are calculating the total cost of a project where $c$ represents the number of labor hours at a specific hourly rate and $d$ represents the number of material units purchased, substituting the actual values into your cost formula allows you to quickly determine your total budget needs. Understanding how to manage variables and perform arithmetic operations correctly ensures that your planning is accurate and efficient.