# How do you simplify 3 1/2 + 4 2/3?

Jul 29, 2016

Turn the mixed numbers into improper fractions, find a common denominator, and add.

#### Explanation:

What you have in your equation are called mixed numbers (A whole number + a fraction). We want to turn these mixed numbers into improper fractions (fractions where the numerator is bigger than the denominator), So, let's take the whole number and multiply it by the denominator, then add the numerator:

$3 \cdot 2 + 1 = 7$

$4 \cdot 3 + 2 = 14$

$\frac{7}{2} + \frac{14}{3}$

We can't add the fractions just yet, though. To do this, we need a common denominator. Let's use 6 as our denominator, since $2 \cdot 3 = 6$, and $3 \cdot 2 = 6$:

$\frac{21}{6} + \frac{28}{6}$

Next, we just add the fractions together:

$21 + 28 = 49$

$\frac{21}{6} + \frac{28}{6} = \frac{49}{6}$