Question

1. $6\frac{8}{9} \div 1\frac{1}{3} =$
2. $3\frac{3}{4} \div 2\frac{2}{3} =$
3. $7\frac{7}{8} \div \frac{1}{4} =$

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 \(1\) by \(3\) and add \(1\): \(1\times3 + 1 = 4\), 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 have a common factor of \(3\): \(\frac{62}{\cancel{9}^3}\times\frac{\cancel{3}^1}{4}=\frac{62\times1}{3\times4}=\frac{62}{12}\).

Step4: Simplify the result

Simplify \(\frac{62}{12}\) by dividing numerator and denominator by \(2\): \(\frac{62\div2}{12\div2}=\frac{31}{6}\), which is \(5\frac{1}{6}\) as a mixed number.

Answer:

\(5\frac{1}{6}\) (or \(\frac{31}{6}\))