Question

subtract. write your answer as a fraction or as a whole or mixed number.
18\frac{1}{11} - 10\frac{4}{5} = \square
submit

Explanation:

Step1: Convert mixed numbers to improper fractions

First, convert \(18\frac{1}{11}\) 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 \(18\frac{1}{11}\), we have \(a = 18\), \(b = 1\), \(c = 11\). Then \(\frac{18\times11 + 1}{11}=\frac{198 + 1}{11}=\frac{199}{11}\).

Next, convert \(10\frac{4}{5}\) to an improper fraction. Here, \(a = 10\), \(b = 4\), \(c = 5\). So \(\frac{10\times5 + 4}{5}=\frac{50 + 4}{5}=\frac{54}{5}\).

Step2: Find a common denominator

The denominators are 11 and 5. The least common denominator (LCD) of 11 and 5 is \(11\times5 = 55\).

Now, rewrite \(\frac{199}{11}\) with denominator 55: \(\frac{199\times5}{11\times5}=\frac{995}{55}\).

Rewrite \(\frac{54}{5}\) with denominator 55: \(\frac{54\times11}{5\times11}=\frac{594}{55}\).

Step3: Subtract the fractions

Now subtract the two fractions: \(\frac{995}{55}-\frac{594}{55}=\frac{995 - 594}{55}=\frac{401}{55}\).

Step4: Convert back to a mixed number

Now convert \(\frac{401}{55}\) back to a mixed number. Divide 401 by 55: \(55\times7 = 385\), \(401-385 = 16\). So \(\frac{401}{55}=7\frac{16}{55}\).

Answer:

\(7\frac{16}{55}\)