Question

divide: \\(\frac{\frac{5}{6}}{\frac{4}{7}}\\) provide an answer as a simplified proper fraction or mixed number.

Explanation:

Step1: Recall fraction division rule

To divide a fraction by another fraction, we multiply the first fraction by the reciprocal of the second fraction. So, \(\frac{\frac{5}{6}}{\frac{4}{7}}=\frac{5}{6}\times\frac{7}{4}\).

Step2: Multiply the numerators and denominators

Multiply the numerators: \(5\times7 = 35\). Multiply the denominators: \(6\times4=24\). So we get \(\frac{35}{24}\).

Step3: Convert to mixed number (optional, but check)

Since \(35\div24 = 1\) with a remainder of \(11\), \(\frac{35}{24}=1\frac{11}{24}\). But wait, wait, no - wait, the original problem is \(\frac{\frac{5}{6}}{\frac{4}{7}}\)? Wait, no, looking at the image, the division is \(\frac{5}{6}\) divided by \(\frac{4}{7}\)? Wait, the way it's written is a fraction of fractions: \(\frac{\frac{5}{6}}{\frac{4}{7}}\). So following the rule, invert the denominator fraction and multiply: \(\frac{5}{6}\times\frac{7}{4}=\frac{35}{24}=1\frac{11}{24}\)? Wait, no, wait, let's re - check. Wait, the problem is \(\frac{\frac{5}{6}}{\frac{4}{7}}\). So the formula for dividing two fractions \(\frac{a}{b}\div\frac{c}{d}=\frac{a}{b}\times\frac{d}{c}\). So here, \(a = 5\), \(b = 6\), \(c = 4\), \(d = 7\). So \(\frac{5}{6}\times\frac{7}{4}=\frac{35}{24}\). Now, \(\frac{35}{24}\) is an improper fraction. Converting to a mixed number: \(35\div24 = 1\) with a remainder of \(11\), so \(1\frac{11}{24}\). Wait, but let's check the calculation again. \(5\times7 = 35\), \(6\times4 = 24\). Yes, that's correct. So \(\frac{35}{24}\) simplifies to \(1\frac{11}{24}\) as a mixed number or remains \(\frac{35}{24}\) as an improper fraction. But the problem says "simplified proper fraction or mixed number". Since \(\frac{35}{24}\) is improper, we convert to mixed number: \(1\frac{11}{24}\). Wait, no, wait, maybe I misread the problem. Wait, the image shows \(\frac{\frac{5}{6}}{\frac{4}{7}}\)? Wait, no, looking at the image again, the division is \(\frac{5}{6}\) divided by \(\frac{4}{7}\)? Wait, the way it's typeset is a fraction where the numerator is \(\frac{5}{6}\) and the denominator is \(\frac{4}{7}\). So the calculation is correct.

Answer:

\(1\frac{11}{24}\)