Questions: What is Descartes's fraction? My fraction is equivalent to 8/6 and has a numerator that is 4 more than its denominator.

Solution Steps

The fraction is equivalent to \( \frac{8}{6} \), and its numerator is 4 more than its denominator.

Simplify \( \frac{8}{6} \) to its lowest terms: \[ \frac{8}{6} = \frac{4}{3} \]

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: \[ \frac{x + 4}{x} = \frac{4}{3} \]

Cross-multiply to solve for \( x \): \[ 3(x + 4) = 4x \] \[ 3x + 12 = 4x \] \[ 12 = 4x - 3x \] \[ x = 12 \]

The numerator is \( x + 4 \): \[ x + 4 = 12 + 4 = 16 \]

The fraction is: \[ \frac{16}{12} \]

Final Answer