Question
Simplifying a ratio of multivar Simplify. \( \frac{32 a b c}{40 b c} \)
Ask by Carroll Barnett. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The simplified form of the ratio is \( \frac{4a}{5} \).
Solution
To simplify the ratio \(\frac{32 a b c}{40 b c}\), follow these steps:
1. **Factor the Coefficients:**
- Simplify the numerical part \(\frac{32}{40}\).
- Both 32 and 40 are divisible by 8:
\[
\frac{32 \div 8}{40 \div 8} = \frac{4}{5}
\]
2. **Cancel Common Variables:**
- The variables \(b\) and \(c\) appear in both the numerator and the denominator. They can be canceled out:
\[
\frac{a \cancel{b} \cancel{c}}{\cancel{b} \cancel{c}} = a
\]
3. **Combine the Simplified Parts:**
- Multiply the simplified numerical coefficient by the remaining variable:
\[
\frac{4}{5} \times a = \frac{4a}{5}
\]
**Final Simplified Form:**
\[
\frac{4a}{5}
\]
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Simplify this solution The Deep Dive
To simplify the ratio \( \frac{32 a b c}{40 b c} \), we can cancel the common terms in the numerator and the denominator. Here, both \( b \) and \( c \) are present in both parts of the ratio, so they can be eliminated. This gives us: \[ \frac{32 a}{40} \] Next, we simplify \( \frac{32}{40} \). Both 32 and 40 can be divided by their greatest common divisor, which is 8. So, we have: \[ \frac{32 \div 8}{40 \div 8} = \frac{4}{5} \] Thus, the simplified ratio is: \[ \frac{4a}{5} \]
