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 multiply the whole number \( 5 \) by the denominator \( 3 \) and add the numerator \( 1 \). So, \( 5\frac{1}{3}=\frac{5\times3 + 1}{3}=\frac{16}{3} \).

To convert \( 1\frac{1}{9} \) to an improper fraction, we multiply the whole number \( 1 \) by the denominator \( 9 \) and add the numerator \( 1 \). So, \( 1\frac{1}{9}=\frac{1\times9+1}{9}=\frac{10}{9} \).

Step2: Divide the fractions

Dividing by a fraction is the same as multiplying by its reciprocal. 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 \( 3 \). Dividing \( 9 \) by \( 3 \) gives \( 3 \), and dividing \( 3 \) by \( 3 \) gives \( 1 \). So now we have \( \frac{16}{1}\times\frac{3}{10} \).

Multiplying the numerators: \( 16\times3 = 48 \).

Multiplying the denominators: \( 1\times10 = 10 \).

So, \( \frac{48}{10} \) can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is \( 2 \). \( \frac{48\div2}{10\div2}=\frac{24}{5} \).

Converting \( \frac{24}{5} \) back to a mixed number (if needed), we get \( 4\frac{4}{5} \), but as an improper fraction, it's \( \frac{24}{5} \) or as a decimal, \( 4.8 \). However, in fraction form, the simplified improper fraction is \( \frac{24}{5} \) or the mixed number \( 4\frac{4}{5} \).

Answer:

\( \frac{24}{5} \) (or \( 4\frac{4}{5} \) or \( 4.8 \))