Question

what is the sum in simplest form?
$4\frac{1}{2} + 1\frac{3}{5} = \square$
options: $6\frac{1}{5}$, $5\frac{1}{10}$, $5\frac{4}{7}$, $6\frac{1}{10}$

Explanation:

Step1: Separate whole and fractional parts

Whole parts: \(4 + 1 = 5\)
Fractional parts: \(\frac{1}{2} + \frac{3}{5}\)

Step2: Find common denominator for fractions

LCM of 2 and 5 is 10.
\(\frac{1}{2} = \frac{1\times5}{2\times5} = \frac{5}{10}\)
\(\frac{3}{5} = \frac{3\times2}{5\times2} = \frac{6}{10}\)

Step3: Add fractional parts

\(\frac{5}{10} + \frac{6}{10} = \frac{11}{10} = 1\frac{1}{10}\)

Step4: Add whole and fractional results

\(5 + 1\frac{1}{10} = 6\frac{1}{10}\)

Answer:

D. \(6\frac{1}{10}\)