Question

evaluate and simplify.
$4\frac{1}{4} - 1\frac{1}{2} =$

Explanation:

Step1: Convert mixed numbers to improper fractions

First, convert \(4\frac{1}{4}\) 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 \(4\frac{1}{4}\), we have \(a = 4\), \(b = 1\), \(c = 4\). Then \(\frac{4\times4 + 1}{4}=\frac{16 + 1}{4}=\frac{17}{4}\).

Next, convert \(1\frac{1}{2}\) to an improper fraction. Here, \(a = 1\), \(b = 1\), \(c = 2\). So \(\frac{1\times2+1}{2}=\frac{2 + 1}{2}=\frac{3}{2}\).

Step2: Find a common denominator and subtract

The denominators are 4 and 2. The least common denominator is 4. So we rewrite \(\frac{3}{2}\) with a denominator of 4. Multiply the numerator and denominator of \(\frac{3}{2}\) by 2: \(\frac{3\times2}{2\times2}=\frac{6}{4}\).

Now subtract the two fractions: \(\frac{17}{4}-\frac{6}{4}=\frac{17 - 6}{4}=\frac{11}{4}\).

Step3: Convert back to a mixed number (optional, but common for such problems)

To convert \(\frac{11}{4}\) back to a mixed number, divide 11 by 4. 4 times 2 is 8, with a remainder of 3. So \(\frac{11}{4}=2\frac{3}{4}\).

Answer:

\(2\frac{3}{4}\) (or \(\frac{11}{4}\))