Question

1. $1\frac{1}{3} \div 9 = \frac{\quad}{\quad} \div \frac{\quad}{\quad} = \frac{\quad}{\quad} \times \frac{\quad}{\quad} = \frac{\quad}{\quad}$

Explanation:

Step1: Convert mixed number to improper fraction

First, convert \(1\frac{1}{3}\) to an improper fraction. \(1\frac{1}{3}=\frac{1\times3 + 1}{3}=\frac{4}{3}\). So the problem becomes \(\frac{4}{3}\div9\).

Step2: Recall division of fractions rule

Dividing by a number is the same as multiplying by its reciprocal. So \(\frac{4}{3}\div9=\frac{4}{3}\div\frac{9}{1}\).

Step3: Multiply by reciprocal

Using the rule \(\frac{a}{b}\div\frac{c}{d}=\frac{a}{b}\times\frac{d}{c}\), we have \(\frac{4}{3}\times\frac{1}{9}\).

Step4: Multiply numerators and denominators

Multiply the numerators: \(4\times1 = 4\). Multiply the denominators: \(3\times9 = 27\). So the result is \(\frac{4}{27}\).

Answer:

\(1\frac{1}{3}\div9=\frac{4}{3}\div\frac{9}{1}=\frac{4}{3}\times\frac{1}{9}=\frac{4}{27}\) (Filling the blanks: \(\frac{4}{3}\), \(\frac{9}{1}\), \(\frac{4}{3}\), \(\frac{1}{9}\), \(\frac{4}{27}\))