Question
Real Tutor Solution
Tutor-Verified Answer
Answer
\[
\frac{-7}{12} + \frac{-4}{36} = \frac{-25}{36}
\]
Solution
To add the fractions \( \frac{-7}{12} \) and \( \frac{-4}{36} \), follow these steps:
### 1. Simplify the Fractions (if possible)
First, simplify \( \frac{-4}{36} \):
\[
\frac{-4}{36} = \frac{-1}{9} \quad \text{(divided numerator and denominator by 4)}
\]
Now, the problem becomes:
\[
\frac{-7}{12} + \frac{-1}{9}
\]
### 2. Find a Common Denominator
To add the fractions, they must have the same denominator. The denominators here are 12 and 9.
- **Prime factors:**
- 12: \( 2^2 \times 3 \)
- 9: \( 3^2 \)
- **Least Common Multiple (LCM):**
- LCM of 12 and 9 is \( 2^2 \times 3^2 = 36 \)
### 3. Convert Fractions to the Common Denominator
- **Convert \( \frac{-7}{12} \) to have a denominator of 36:**
\[
\frac{-7}{12} = \frac{-7 \times 3}{12 \times 3} = \frac{-21}{36}
\]
- **Convert \( \frac{-1}{9} \) to have a denominator of 36:**
\[
\frac{-1}{9} = \frac{-1 \times 4}{9 \times 4} = \frac{-4}{36}
\]
### 4. Add the Fractions
Now that both fractions have the same denominator:
\[
\frac{-21}{36} + \frac{-4}{36} = \frac{-25}{36}
\]
### Final Answer
\[
\frac{-7}{12} + \frac{-4}{36} = \frac{-25}{36}
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Bonus Knowledge
To solve \( \frac{-7}{12} + \frac{-4}{36} \), we first need a common denominator to combine the fractions. The least common multiple of 12 and 36 is 36. We can convert \( \frac{-7}{12} \) to have a denominator of 36 by multiplying both the numerator and the denominator by 3, resulting in \( \frac{-21}{36} \). Now we can add: \[ \frac{-21}{36} + \frac{-4}{36} = \frac{-25}{36}. \] So, \( \frac{-7}{12} + \frac{-4}{36} = \frac{-25}{36} \).
