Question

(left(2\frac{5}{8} + 2\frac{1}{2}
ight))

Explanation:

Step1: Convert mixed numbers to improper fractions

First, convert \(2\frac{5}{8}\) to an improper fraction. The formula for converting a mixed number \(a\frac{b}{c}\) to an improper fraction is \(a\frac{b}{c}=\frac{a\times c + b}{c}\). So for \(2\frac{5}{8}\), we have \(a = 2\), \(b = 5\), \(c = 8\). Then \(\frac{2\times8 + 5}{8}=\frac{16 + 5}{8}=\frac{21}{8}\).

Next, convert \(2\frac{1}{2}\) to an improper fraction. Here \(a = 2\), \(b = 1\), \(c = 2\). So \(\frac{2\times2+1}{2}=\frac{4 + 1}{2}=\frac{5}{2}\).

Step2: Find a common denominator and add the fractions

The denominators are 8 and 2. The least common denominator (LCD) of 8 and 2 is 8. So we need to convert \(\frac{5}{2}\) to a fraction with denominator 8. To do this, we multiply the numerator and denominator by 4 (since \(8\div2 = 4\)). So \(\frac{5\times4}{2\times4}=\frac{20}{8}\).

Now we add the two fractions: \(\frac{21}{8}+\frac{20}{8}=\frac{21 + 20}{8}=\frac{41}{8}\).

Step3: Convert the improper fraction back to a mixed number (if needed)

To convert \(\frac{41}{8}\) to a mixed number, we divide 41 by 8. \(8\times5 = 40\), so the quotient is 5 and the remainder is \(41-40 = 1\). So \(\frac{41}{8}=5\frac{1}{8}\).

Answer:

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