Before we can evaluate a sum or difference involving mixed numbers, the mixed numbers must first be rewritten as fractions.

$a \frac{b}{c}$	$\frac{a \cdot c + b}{c}$	Simplify
$5 \frac{1}{2}$	$\frac{5 \cdot 2 + 1}{2}$	$\frac{1 1}{2}$
$4 \frac{1}{3}$	$\frac{4 \cdot 3 + 1}{3}$	$\frac{1 3}{3}$

When adding or subtracting fractions, they should have the same denominator. In this case, we have two fractions with different denominators.

5 \frac{1}{2} + 4 \frac{1}{3} \Leftrightarrow \frac{1 1}{2} + \frac{1 3}{3}

Since

6

is a multiple of both

2

and

3,

we can first multiply both the numerator and denominator of

\frac{1 1}{2}

3

to create a common denominator.

\frac{1 1}{2} + \frac{1 3}{3}

$\frac{a}{b} = \frac{a \cdot 3}{b \cdot 3}$

\frac{1 1 \cdot 3}{2 \cdot 3} + \frac{1 3}{3}

\frac{3 3}{6} + \frac{1 3}{3}

Next, we can multiply both the numerator and denominator of

\frac{1 3}{3}

2

to create a common denominator.

\frac{3 3}{6} + \frac{1 3}{3}

$\frac{a}{b} = \frac{a \cdot 2}{b \cdot 2}$

\frac{3 3}{6} + \frac{1 3 \cdot 2}{3 \cdot 2}

\frac{3 3}{6} + \frac{2 6}{6}

Now that we have a common denominator, we can proceed to simplifying the expression.

\frac{3 3}{6} + \frac{2 6}{6}

Add fractions

\frac{3 3 + 2 6}{6}

Add terms

\frac{5 9}{6}

The quotient is

\frac{5 9}{6} .

We can also write this fraction as a mixed number.

\frac{5 9}{6}

Write as a sum

\frac{5 4 + 5}{6}

Write as a sum of fractions

\frac{5 4}{6} + \frac{5}{6}

Calculate quotient

9 + \frac{5}{6}

Add terms

9 \frac{5}{6}

The simplified expression is equal to

9 \frac{5}{6} .

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