Question
3. Evaluate \( \frac{m}{n t}+(-t)-\frac{n}{t} \) if \( \mathrm{m}=20, \mathrm{n}=4 \) and \( \mathrm{t}=-1 \)
Ask by Tucker Henry. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The final result of the expression is 0.
Solution
To evaluate the expression:
\[
\frac{m}{n t} + (-t) - \frac{n}{t}
\]
given \( m = 20 \), \( n = 4 \), and \( t = -1 \), follow these steps:
1. **Substitute the values:**
\[
\frac{20}{4 \times (-1)} + (-(-1)) - \frac{4}{-1}
\]
2. **Calculate each term individually:**
- **First term:**
\[
\frac{20}{4 \times (-1)} = \frac{20}{-4} = -5
\]
- **Second term:**
\[
-(-1) = 1
\]
- **Third term:**
\[
-\frac{4}{-1} = 4
\]
3. **Combine the results:**
\[
-5 + 1 + 4 = 0
\]
**Final Answer:**
\[
0
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Mind Expander
Let's plug in the values \( m = 20 \), \( n = 4 \), and \( t = -1 \) into the expression \( \frac{m}{n t} + (-t) - \frac{n}{t} \). First, calculate \( n t \): \[ n t = 4 \times (-1) = -4 \] Now, calculate \( \frac{m}{n t} \): \[ \frac{m}{n t} = \frac{20}{-4} = -5 \] Next, calculate \( -t \): \[ -t = -(-1) = 1 \] Now, calculate \( \frac{n}{t} \): \[ \frac{n}{t} = \frac{4}{-1} = -4 \] Now combine all the parts: \[ \frac{m}{n t} + (-t) - \frac{n}{t} = -5 + 1 - (-4) \] Simplifying, we have: \[ -5 + 1 + 4 = 0 \] Therefore, the final evaluation is: \[ \boxed{0} \]
