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

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.
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Solution

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

Step 6: Write the Final Fraction

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

Final Answer

\(\boxed{\frac{16}{12}}\)

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