Question

1\frac{2}{8} \div \frac{3}{3} = \frac{5}{20} \div \frac{5}{5} =

Explanation:

Step1: Convert mixed number to improper fraction

First, convert \(1\frac{2}{8}\) to an improper fraction. \(1\frac{2}{8}=\frac{1\times8 + 2}{8}=\frac{10}{8}=\frac{5}{4}\) (simplified by dividing numerator and denominator by 2).

Step2: Divide by multiplying reciprocal

When dividing by a fraction, we multiply by its reciprocal. So, \(\frac{5}{4}\div\frac{3}{3}\) (wait, \(\frac{3}{3}=1\), maybe there is a typo? If it's \(\frac{3}{8}\) instead of \(\frac{3}{3}\), let's assume the correct denominator is 8 for a meaningful calculation. So \(\frac{5}{4}\div\frac{3}{8}=\frac{5}{4}\times\frac{8}{3}\)

Step3: Multiply the fractions

Multiply numerators and denominators: \(5\times8 = 40\), \(4\times3 = 12\), so \(\frac{40}{12}=\frac{10}{3}=3\frac{1}{3}\) (if we take the original as \(1\frac{2}{8}\div\frac{3}{8}\), then \(1\frac{2}{8}=\frac{10}{8}\), \(\frac{10}{8}\div\frac{3}{8}=\frac{10}{8}\times\frac{8}{3}=\frac{10}{3}\) same result).

For the second part: \(\frac{5}{20}\div\frac{5}{5}\), \(\frac{5}{5}=1\), so \(\frac{5}{20}\div1=\frac{5}{20}=\frac{1}{4}\). And \(\frac{5}{10}\times\frac{1}{2}=\frac{5\times1}{10\times2}=\frac{5}{20}=\frac{1}{4}\), which matches.

Assuming the first division is \(1\frac{2}{8}\div\frac{3}{8}\) (correcting the denominator for sense):

Step1: Convert mixed number

\(1\frac{2}{8}=\frac{10}{8}\)

Step2: Divide by fraction

\(\frac{10}{8}\div\frac{3}{8}=\frac{10}{8}\times\frac{8}{3}=\frac{10}{3}=3\frac{1}{3}\)

Answer:

For \(1\frac{2}{8}\div\frac{3}{8}\) (corrected), the answer is \(\frac{10}{3}\) or \(3\frac{1}{3}\); for \(\frac{5}{20}\div\frac{5}{5}\) and \(\frac{5}{10}\times\frac{1}{2}\), the answer is \(\frac{1}{4}\)