Question

perform the operation below. express your answer as a mixed number in simplest form.
4\frac{1}{2} - 1\frac{4}{5}
answer attempt 1 out of 2

Explanation:

Step1: Convert mixed numbers to improper fractions

First, convert \(4\frac{1}{2}\) 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 \(4\frac{1}{2}\), we have \(a = 4\), \(b = 1\), \(c = 2\). Then \(\frac{4\times2 + 1}{2}=\frac{8 + 1}{2}=\frac{9}{2}\).

Next, convert \(1\frac{4}{5}\) to an improper fraction. Here, \(a = 1\), \(b = 4\), \(c = 5\). So \(\frac{1\times5+4}{5}=\frac{5 + 4}{5}=\frac{9}{5}\).

Step2: Find a common denominator and subtract

The denominators are 2 and 5. The least common denominator (LCD) of 2 and 5 is \(2\times5 = 10\).

Rewrite \(\frac{9}{2}\) with denominator 10: \(\frac{9\times5}{2\times5}=\frac{45}{10}\).

Rewrite \(\frac{9}{5}\) with denominator 10: \(\frac{9\times2}{5\times2}=\frac{18}{10}\).

Now subtract the two fractions: \(\frac{45}{10}-\frac{18}{10}=\frac{45 - 18}{10}=\frac{27}{10}\).

Step3: Convert the improper fraction back to a mixed number

To convert \(\frac{27}{10}\) to a mixed number, divide 27 by 10. 10 goes into 27 two times (since \(10\times2 = 20\)) with a remainder of \(27-20 = 7\). So \(\frac{27}{10}=2\frac{7}{10}\).

Answer:

\(2\frac{7}{10}\)