Question
(e) \( -\frac{9}{15}-\left(-\frac{26}{45}\right) \)
Ask by Johnson Hanson. in the United States
Jan 30,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\[
-\frac{1}{45}
\]
Solution
To evaluate the expression:
\[
-\frac{9}{15} - \left(-\frac{26}{45}\right)
\]
follow these steps:
1. **Simplify the Double Negative:**
\[
-\frac{9}{15} + \frac{26}{45}
\]
2. **Find a Common Denominator:**
The denominators are 15 and 45. The least common denominator (LCD) is 45.
3. **Convert Each Fraction:**
\[
-\frac{9}{15} = -\frac{9 \times 3}{15 \times 3} = -\frac{27}{45}
\]
\[
\frac{26}{45} \text{ remains the same}
\]
4. **Combine the Fractions:**
\[
-\frac{27}{45} + \frac{26}{45} = \frac{-27 + 26}{45} = \frac{-1}{45}
\]
**Final Answer:**
\[
-\frac{1}{45}
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Extra Insights
Let’s dive into a little math adventure! First, we can simplify the first fraction. \( -\frac{9}{15} \) can be reduced to \( -\frac{3}{5} \) since both the numerator and denominator are divisible by 3. Now, to make our life easier, we should convert \( -\frac{3}{5} \) into a fraction with a denominator of 45, so it would look like \( -\frac{27}{45} \). Next, we have \( -\left(-\frac{26}{45}\right) \), which simplifies to \( +\frac{26}{45} \). Now we can put it all together: \[ -\frac{27}{45} + \frac{26}{45} = \frac{-27 + 26}{45} = -\frac{1}{45}. \] So, the final answer is \( -\frac{1}{45} \). Math can sometimes feel like solving a puzzle, right? Just keep fitting the pieces together!
