Question
Find the numerator of the equivalent fraction with denominator 75 . \( \frac{8}{15} \) Equivalent Fraction
Ask by Evans Huff. in the United States
Jan 10,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The numerator of the equivalent fraction with denominator 75 is 40.
Solution
To find an equivalent fraction to \( \frac{8}{15} \) with a denominator of 75, follow these steps:
1. **Understand Equivalent Fractions:**
Two fractions are equivalent if they represent the same value, meaning the numerator and denominator are scaled by the same factor.
2. **Set Up the Proportion:**
\[
\frac{8}{15} = \frac{x}{75}
\]
Here, \( x \) is the numerator we need to find.
3. **Find the Scaling Factor:**
Determine how much the denominator needs to be multiplied to reach 75 from 15.
\[
\text{Scaling Factor} = \frac{75}{15} = 5
\]
4. **Apply the Scaling Factor to the Numerator:**
Multiply the original numerator by the same scaling factor to maintain the equivalence.
\[
x = 8 \times 5 = 40
\]
5. **Write the Equivalent Fraction:**
\[
\frac{8}{15} = \frac{40}{75}
\]
**Answer:**
The numerator of the equivalent fraction with denominator 75 is **40**.
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution The Deep Dive
To find an equivalent fraction to \( \frac{8}{15} \) with a denominator of 75, you can cross-multiply and set up the equation: \( \frac{8}{15} = \frac{x}{75} \). By multiplying, you get \( 8 \times 75 = 15 \times x \), which simplifies to 600 = 15x. Dividing both sides by 15 gives you \( x = 40 \). So, the numerator of the equivalent fraction \( \frac{40}{75} \) is **40**! And voilà, you've got a fraction that means the same thing, just dressed differently! Isn't math just a nifty tool for finding connections between numbers?
