Question

12\frac{1}{7} - 5\frac{4}{5}

Explanation:

Step1: Convert mixed numbers to improper fractions

First, convert \(12\frac{1}{7}\) and \(5\frac{4}{5}\) to improper fractions. For \(12\frac{1}{7}\), we use the formula \(a\frac{b}{c}=\frac{a\times c + b}{c}\), so \(12\frac{1}{7}=\frac{12\times7 + 1}{7}=\frac{84 + 1}{7}=\frac{85}{7}\). For \(5\frac{4}{5}\), we have \(5\frac{4}{5}=\frac{5\times5 + 4}{5}=\frac{25 + 4}{5}=\frac{29}{5}\).

Step2: Find a common denominator

The denominators are 7 and 5, and their least common multiple is \(7\times5 = 35\). So we rewrite the fractions with the common denominator. \(\frac{85}{7}=\frac{85\times5}{7\times5}=\frac{425}{35}\) and \(\frac{29}{5}=\frac{29\times7}{5\times7}=\frac{203}{35}\).

Step3: Subtract the fractions

Now subtract the two fractions: \(\frac{425}{35}-\frac{203}{35}=\frac{425 - 203}{35}=\frac{222}{35}\).

Step4: Convert back to a mixed number (optional)

Convert \(\frac{222}{35}\) to a mixed number. Divide 222 by 35: \(35\times6 = 210\), and \(222-210 = 12\). So \(\frac{222}{35}=6\frac{12}{35}\).

Answer:

\(6\frac{12}{35}\) (or \(\frac{222}{35}\))