Question
Real Tutor Solution
Tutor-Verified Answer
Answer
\(\frac{3b}{8}\)
Solution
To simplify the expression:
\[
\frac{15bcd}{40cd}
\]
**Step 1: Cancel Common Factors**
Both the numerator and the denominator have the factors \(c\) and \(d\). Assuming \(c \neq 0\) and \(d \neq 0\), we can cancel these out:
\[
\frac{15b \cancel{c} \cancel{d}}{40 \cancel{c} \cancel{d}} = \frac{15b}{40}
\]
**Step 2: Simplify the Numerical Coefficient**
Next, simplify the fraction \(\frac{15}{40}\):
- Both 15 and 40 are divisible by 5.
- Divide the numerator and the denominator by 5:
\[
\frac{15 \div 5}{40 \div 5} = \frac{3}{8}
\]
**Final Simplified Expression:**
\[
\frac{3b}{8}
\]
**Answer:** \(\dfrac{3\,b}{8}\)
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Bonus Knowledge
To simplify the expression \(\frac{15 b c d}{40 c d}\), we can first cancel out the common factors in the numerator and the denominator. The \(c\) and \(d\) terms in both the numerator and denominator cancel out, leaving us with: \[ \frac{15 b}{40} \] Next, we notice that both 15 and 40 can be simplified by their greatest common divisor, which is 5. Dividing both the numerator and denominator by 5, we get: \[ \frac{3 b}{8} \] So, the simplified expression is: \[ \frac{3 b}{8} \]
