Question

question
perform the operation below. express your answer as a mixed number in simplest form.
$4\frac{1}{8} - 2\frac{1}{2}$

Explanation:

Step1: Convert mixed numbers to improper fractions

First, convert \(4\frac{1}{8}\) and \(2\frac{1}{2}\) to improper fractions. For \(4\frac{1}{8}\), we use the formula \(a\frac{b}{c}=\frac{a\times c + b}{c}\), so \(4\frac{1}{8}=\frac{4\times8 + 1}{8}=\frac{33}{8}\). For \(2\frac{1}{2}\), we have \(2\frac{1}{2}=\frac{2\times2+ 1}{2}=\frac{5}{2}\).

Step2: Find a common denominator

The denominators are 8 and 2. The least common denominator of 8 and 2 is 8. So we convert \(\frac{5}{2}\) to a fraction with denominator 8. We multiply the numerator and denominator of \(\frac{5}{2}\) by 4: \(\frac{5\times4}{2\times4}=\frac{20}{8}\).

Step3: Subtract the fractions

Now we subtract the two fractions: \(\frac{33}{8}-\frac{20}{8}=\frac{33 - 20}{8}=\frac{13}{8}\).

Step4: Convert back to a mixed number

Convert \(\frac{13}{8}\) to a mixed number. We divide 13 by 8: \(13\div8 = 1\) with a remainder of 5. So \(\frac{13}{8}=1\frac{5}{8}\).

Answer:

\(1\frac{5}{8}\)