Question

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

Explanation:

Step1: Convert mixed numbers to improper fractions

First, convert \(2\frac{1}{2}\) 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 \(2\frac{1}{2}\), we have \(a = 2\), \(b = 1\), \(c = 2\). Then \(\frac{2\times2 + 1}{2}=\frac{4 + 1}{2}=\frac{5}{2}\).

Next, convert \(1\frac{1}{4}\) to an improper fraction. Here, \(a = 1\), \(b = 1\), \(c = 4\). So \(\frac{1\times4+1}{4}=\frac{4 + 1}{4}=\frac{5}{4}\).

Step2: Find a common denominator and subtract

The denominators are 2 and 4. The least common denominator is 4. So we rewrite \(\frac{5}{2}\) with a denominator of 4. Multiply the numerator and denominator of \(\frac{5}{2}\) by 2: \(\frac{5\times2}{2\times2}=\frac{10}{4}\).

Now subtract the two fractions: \(\frac{10}{4}-\frac{5}{4}=\frac{10 - 5}{4}=\frac{5}{4}\).

Step3: Convert the improper fraction back to a mixed number

To convert \(\frac{5}{4}\) to a mixed number, divide the numerator by the denominator. \(5\div4 = 1\) with a remainder of \(1\). So the mixed number is \(1\frac{1}{4}\).

Answer:

\(1\frac{1}{4}\)