Question

7\frac{1}{3} = l \times 2\frac{1}{3}
7\frac{1}{3} \div 2\frac{1}{3} =

Explanation:

Step1: Convert mixed numbers to improper fractions

First, convert \(7\frac{1}{3}\) to an improper fraction. The formula for converting a mixed number \(a\frac{b}{c}\) to an improper fraction is \(\frac{a\times c + b}{c}\). So for \(7\frac{1}{3}\), we have \(a = 7\), \(b = 1\), \(c = 3\). Then \(\frac{7\times3+1}{3}=\frac{21 + 1}{3}=\frac{22}{3}\).

Next, convert \(2\frac{1}{4}\) to an improper fraction. Using the same formula, with \(a = 2\), \(b = 1\), \(c = 4\), we get \(\frac{2\times4+1}{4}=\frac{8 + 1}{4}=\frac{9}{4}\).

Step2: Perform the division of fractions

Dividing two fractions \(\frac{m}{n}\div\frac{p}{q}\) is equivalent to multiplying the first fraction by the reciprocal of the second fraction, i.e., \(\frac{m}{n}\times\frac{q}{p}\). So \(\frac{22}{3}\div\frac{9}{4}=\frac{22}{3}\times\frac{4}{9}\).

Step3: Multiply the numerators and denominators

Multiply the numerators: \(22\times4 = 88\). Multiply the denominators: \(3\times9 = 27\). So the result is \(\frac{88}{27}\). If we want to convert this back to a mixed number, we divide 88 by 27. \(27\times3 = 81\), so \(88-81 = 7\). Thus, \(\frac{88}{27}=3\frac{7}{27}\).

Answer:

If we consider the improper fraction, the answer is \(\frac{88}{27}\), and as a mixed number, it is \(3\frac{7}{27}\).