Question

1. $6\frac{1}{4} \div \frac{1}{8} = 50$
2. $6\frac{8}{9} \div 1\frac{1}{3} = $

$3\frac{3}{4} \div 2\frac{2}{3} = $

Explanation:

Step1: Convert mixed numbers to improper fractions

For \(6\frac{8}{9}\), multiply the whole number \(6\) by the denominator \(9\) and add the numerator \(8\): \(6\times9 + 8 = 54 + 8 = 62\), so \(6\frac{8}{9}=\frac{62}{9}\).
For \(1\frac{1}{3}\), multiply the whole number \(1\) by the denominator \(3\) and add the numerator \(1\): \(1\times3 + 1 = 4\), so \(1\frac{1}{3}=\frac{4}{3}\).

Step2: Divide the fractions (multiply by reciprocal)

Dividing by a fraction is the same as multiplying by its reciprocal. So \(\frac{62}{9}\div\frac{4}{3}=\frac{62}{9}\times\frac{3}{4}\).

Step3: Simplify and multiply

Simplify the fractions before multiplying. The \(3\) in the numerator and \(9\) in the denominator can be simplified: \(9\div3 = 3\), \(3\div3 = 1\). Now we have \(\frac{62}{3}\times\frac{1}{4}\). Multiply the numerators: \(62\times1 = 62\), multiply the denominators: \(3\times4 = 12\). So we get \(\frac{62}{12}\).

Step4: Simplify the result

Simplify \(\frac{62}{12}\) by dividing numerator and denominator by their greatest common divisor, which is \(2\). \(62\div2 = 31\), \(12\div2 = 6\). So \(\frac{31}{6}\) can be converted back to a mixed number: \(31\div6 = 5\) with a remainder of \(1\), so \(5\frac{1}{6}\).

Answer:

\(5\frac{1}{6}\)