Question
Real Tutor Solution
Tutor-Verified Answer
Answer
\[
\frac{3a}{7c}
\]
Solution
To simplify the expression:
\[
\frac{27 a b}{63 b c}
\]
**Step 1: Factor the Numbers**
- **27** can be factored into \( 3 \times 9 \) or \( 3^3 \).
- **63** can be factored into \( 7 \times 9 \) or \( 7 \times 3^2 \).
**Step 2: Simplify the Fraction**
\[
\frac{27 a b}{63 b c} = \frac{3^3 \cdot a \cdot b}{7 \cdot 3^2 \cdot b \cdot c}
\]
**Step 3: Cancel Common Factors**
- **\( b \)** appears in both the numerator and the denominator, so it cancels out.
- **\( 3^2 \)** in the denominator cancels with part of **\( 3^3 \)** in the numerator, leaving one **3** in the numerator.
\[
\frac{3 \cdot a}{7 \cdot c} = \frac{3a}{7c}
\]
**Final Simplified Form:**
\[
\frac{3a}{7c}
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Bonus Knowledge
To simplify the expression \( \frac{27 a b}{63 b c} \), we can start by canceling the common factors in the numerator and the denominator. Both the numerator and the denominator have a common factor of \( b \), so we can cancel it out. This gives us: \[ \frac{27 a}{63 c} \] Next, we can simplify the coefficients \( 27 \) and \( 63 \). The greatest common divisor (GCD) of \( 27 \) and \( 63 \) is \( 9 \). Dividing both the numerator and the denominator by \( 9 \): \[ \frac{27 a \div 9}{63 c \div 9} = \frac{3 a}{7 c} \] So, the simplified expression is: \[ \frac{3 a}{7 c} \]
