Question
\( \frac{\mathrm{a}}{8}=\frac{\square}{96} \) (Simplify your answer.) Enter the correct numerator to match the new denominator.
Ask by Ball Harmon. in the United States
Jan 30,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The numerator should be \(12a\).
Solution
To solve the equation:
\[
\frac{a}{8} = \frac{\square}{96}
\]
we need to find the numerator that makes both fractions equal when the denominator is changed from 8 to 96.
1. **Determine the scaling factor:**
\[
\text{Scaling factor} = \frac{96}{8} = 12
\]
2. **Apply the scaling factor to the numerator:**
\[
\text{New numerator} = a \times 12 = 12a
\]
So, the equation becomes:
\[
\frac{a}{8} = \frac{12a}{96}
\]
**Answer:** \(12a\)
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Simplify this solution Bonus Knowledge
To find the correct numerator to match the new denominator, we can use cross-multiplication. We have the equation \( \frac{\mathrm{a}}{8}=\frac{\square}{96} \). Cross-multiplying gives us: \[ \mathrm{a} \times 96 = \square \times 8 \] To find the new numerator (let's call it \( x \)), we can express \( x \) in terms of \( a \): \[ x = \frac{a \times 96}{8} \] Now, simplifying \( \frac{96}{8} = 12 \): \[ x = a \times 12 \] So, the correct numerator to match the new denominator is \( 12a \).
