Questions: What is Descartes's fraction?
My fraction is equivalent to 8/6 and has a numerator that is 4 more than its denominator.
Transcript text: 13.
DIGDEEPER!
What is Descartes's
14. fraction?
My fraction is equivalent to $\frac{8}{6}$ and has a numerator that is 4 more than its denominator.
Solution
Solution Steps
Step 1: Understand the Given Information
The fraction is equivalent to \( \frac{8}{6} \), and its numerator is 4 more than its denominator.
Step 2: Simplify the Given Fraction
Simplify \( \frac{8}{6} \) to its lowest terms:
\[
\frac{8}{6} = \frac{4}{3}
\]
Step 3: Set Up the Equation
Let the denominator of the desired fraction be \( x \). Then, the numerator is \( x + 4 \). The fraction is:
\[
\frac{x + 4}{x}
\]
Since this fraction is equivalent to \( \frac{4}{3} \), we set up the equation:
\[
\frac{x + 4}{x} = \frac{4}{3}
\]
Step 4: Solve for \( x \)
Cross-multiply to solve for \( x \):
\[
3(x + 4) = 4x
\]
\[
3x + 12 = 4x
\]
\[
12 = 4x - 3x
\]
\[
x = 12
\]
Step 5: Find the Numerator
The numerator is \( x + 4 \):
\[
x + 4 = 12 + 4 = 16
\]