Question

find $3\frac{1}{3} + 1\frac{1}{2}$. first, build a model to show $3\frac{1}{3}$.

Explanation:

Step1: Convert to improper fractions

$3\frac{1}{3} = \frac{3\times3 + 1}{3} = \frac{10}{3}$
$1\frac{1}{2} = \frac{1\times2 + 1}{2} = \frac{3}{2}$

Step2: Find common denominator

The least common denominator of 3 and 2 is 6.
$\frac{10}{3} = \frac{10\times2}{3\times2} = \frac{20}{6}$
$\frac{3}{2} = \frac{3\times3}{2\times3} = \frac{9}{6}$

Step3: Add the fractions

$\frac{20}{6} + \frac{9}{6} = \frac{20+9}{6} = \frac{29}{6}$

Step4: Convert to mixed number

$\frac{29}{6} = 4\frac{5}{6}$

Answer:

$4\frac{5}{6}$ (or $\frac{29}{6}$)

To build the model for $3\frac{1}{3}$:

1. Show 3 fully shaded whole squares.
2. Show 1 square divided into 3 equal parts, with 1 part shaded.