Question

what is the sum in simplest form?

$4\frac{1}{2} + 1\frac{3}{5} = \square$

options: $6\frac{1}{5}$, $5\frac{4}{7}$, $6\frac{1}{10}$, $5\frac{1}{10}$

Explanation:

Step1: Add the whole numbers

$4 + 1 = 5$

Step2: Add the fractions

Find a common denominator for $\frac{1}{2}$ and $\frac{3}{5}$. The common denominator is $10$.
$\frac{1}{2}=\frac{1\times5}{2\times5}=\frac{5}{10}$
$\frac{3}{5}=\frac{3\times2}{5\times2}=\frac{6}{10}$
Now add the fractions: $\frac{5}{10}+\frac{6}{10}=\frac{11}{10}$

Step3: Combine the whole number and the fraction

$\frac{11}{10}=1\frac{1}{10}$, so add this to the whole number from Step1: $5 + 1\frac{1}{10}=6\frac{1}{10}$

Answer:

$6\frac{1}{10}$ (corresponding to the option "6$\frac{1}{10}$")