Question

find the sum. write your answer as a mixed number. \\( 4\frac{5}{8} + \frac{7}{8} = \\) \\( \frac{?}{?} \\) \\( \boxed{} \\)

Explanation:

Step1: Add the fractions

Since the denominators are the same (8), we add the numerators: $\frac{5}{8} + \frac{7}{8} = \frac{5 + 7}{8} = \frac{12}{8}$

Step2: Simplify the fraction and add the whole number

Simplify $\frac{12}{8}$ to $\frac{3}{2}$ (or as a mixed number, $\frac{12}{8}=1\frac{4}{8}=1\frac{1}{2}$). Then add the whole number 4: $4 + 1\frac{1}{2} = 5\frac{1}{2}$ (Wait, actually, let's do it correctly. Wait, the mixed number is $4\frac{5}{8}$, so adding $\frac{7}{8}$: first, add the fractional parts: $\frac{5}{8} + \frac{7}{8} = \frac{12}{8} = 1\frac{4}{8} = 1\frac{1}{2}$. Then add the whole number part: $4 + 1\frac{1}{2} = 5\frac{1}{2}$? Wait, no, wait. Wait, $4\frac{5}{8} + \frac{7}{8}$: the whole number is 4, and the fractions are $\frac{5}{8} + \frac{7}{8} = \frac{12}{8} = 1\frac{4}{8} = 1\frac{1}{2}$. Then 4 + 1\frac{1}{2} = 5\frac{1}{2}$. Wait, but let's check again. $\frac{5}{8} + \frac{7}{8} = \frac{12}{8} = \frac{3}{2} = 1\frac{1}{2}$. Then 4 + 1\frac{1}{2} = 5\frac{1}{2}$. Alternatively, convert the mixed number to improper fraction: $4\frac{5}{8} = \frac{4*8 + 5}{8} = \frac{37}{8}$. Then add $\frac{7}{8}$: $\frac{37}{8} + \frac{7}{8} = \frac{44}{8} = \frac{11}{2} = 5\frac{1}{2}$. Yes, that's correct.

Answer:

$5\frac{1}{2}$