Question

a. $7\frac{3}{8} + 3\frac{1}{4} = $

Explanation:

Step1: Convert mixed numbers to improper fractions

First, convert \(7\frac{3}{8}\) 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 \(7\frac{3}{8}\), we have \(a = 7\), \(b = 3\), \(c = 8\). Then \(\frac{7\times8 + 3}{8}=\frac{56 + 3}{8}=\frac{59}{8}\).

Next, convert \(3\frac{1}{4}\) to an improper fraction. Using the same formula, \(a = 3\), \(b = 1\), \(c = 4\). So \(\frac{3\times4 + 1}{4}=\frac{12 + 1}{4}=\frac{13}{4}\).

Step2: Find a common denominator

The denominators are 8 and 4. The least common denominator of 8 and 4 is 8. So we need to convert \(\frac{13}{4}\) to a fraction with denominator 8. To do this, multiply the numerator and denominator by 2: \(\frac{13\times2}{4\times2}=\frac{26}{8}\).

Step3: Add the fractions

Now we add \(\frac{59}{8}\) and \(\frac{26}{8}\). When adding fractions with the same denominator, we add the numerators and keep the denominator the same. So \(\frac{59 + 26}{8}=\frac{85}{8}\).

Step4: Convert back to a mixed number (optional, but often preferred)

To convert \(\frac{85}{8}\) to a mixed number, divide 85 by 8. \(8\times10 = 80\), so the quotient is 10 and the remainder is \(85 - 80 = 5\). So \(\frac{85}{8}=10\frac{5}{8}\).

Answer:

\(10\frac{5}{8}\)