Question

5\frac{1}{3} \div 1\frac{1}{9} =

Explanation:

Step1: Convert mixed numbers to improper fractions

To convert \(5\frac{1}{3}\) to an improper fraction, we use the formula \(a\frac{b}{c}=\frac{a\times c + b}{c}\). So for \(5\frac{1}{3}\), we have \(a = 5\), \(b=1\), \(c = 3\). Then \(5\frac{1}{3}=\frac{5\times3 + 1}{3}=\frac{15 + 1}{3}=\frac{16}{3}\).

For \(1\frac{1}{9}\), using the same formula with \(a = 1\), \(b = 1\), \(c=9\), we get \(1\frac{1}{9}=\frac{1\times9+1}{9}=\frac{9 + 1}{9}=\frac{10}{9}\).

Step2: Divide the two improper fractions

Dividing fractions is done by multiplying the first fraction by the reciprocal of the second fraction. So \(\frac{16}{3}\div\frac{10}{9}=\frac{16}{3}\times\frac{9}{10}\).

Step3: Simplify the multiplication

First, we can simplify the fractions before multiplying. The 9 in the numerator and 3 in the denominator have a common factor of 3. So \(\frac{16}{\cancel{3}^1}\times\frac{\cancel{9}^3}{10}=\frac{16\times3}{1\times10}=\frac{48}{10}\).

Step4: Simplify the resulting fraction

We can simplify \(\frac{48}{10}\) by dividing both the numerator and the denominator by their greatest common divisor, which is 2. So \(\frac{48\div2}{10\div2}=\frac{24}{5}\). We can also write this as a mixed number: \(\frac{24}{5}=4\frac{4}{5}\) (since \(24\div5 = 4\) with a remainder of 4).

Answer:

\(\frac{24}{5}\) (or \(4\frac{4}{5}\))