Lesson 59: Adding Mixed Numbers

New Concept

We rename the fraction parts of the mixed numbers so that the fractions have common denominators. Then we add.

What’s next

This is just the foundation. Next, you'll work through examples showing how to simplify sums, even when they create an improper fraction.

Property

To add mixed numbers, first find common denominators for the fractions. Then, add the whole numbers and the fractions separately. Finally, simplify the resulting fraction if needed.

Examples

$2\frac{1}{2} + 1\frac{1}{6} \rightarrow 2\frac{3}{6} + 1\frac{1}{6} = 3\frac{4}{6} = 3\frac{2}{3}$
$5\frac{1}{3} + 2\frac{1}{6} \rightarrow 5\frac{2}{6} + 2\frac{1}{6} = 7\frac{3}{6} = 7\frac{1}{2}$
$1\frac{1}{4} + 3\frac{5}{8} \rightarrow 1\frac{2}{8} + 3\frac{5}{8} = 4\frac{7}{8}$

Explanation

Think of it like combining pizza orders! You can't add half a pizza to a sixth of a pizza until you cut them into equal-sized pieces. Once you have common denominators, you just add up the whole pizzas and then the slices. It’s all about making sure you’re adding apples to apples, not apples to oranges!

Property

When adding mixed numbers results in an improper fraction, convert the improper fraction to a mixed number. Then, add this new whole number to the original sum of whole numbers.

Examples

$1\frac{1}{2} + 2\frac{2}{3} \rightarrow 1\frac{3}{6} + 2\frac{4}{6} = 3\frac{7}{6} \rightarrow 3 + 1\frac{1}{6} = 4\frac{1}{6}$
$3\frac{3}{4} + 1\frac{1}{3} \rightarrow 3\frac{9}{12} + 1\frac{4}{12} = 4\frac{13}{12} \rightarrow 4 + 1\frac{1}{12} = 5\frac{1}{12}$
$7\frac{1}{2} + 4\frac{5}{8} \rightarrow 7\frac{4}{8} + 4\frac{5}{8} = 11\frac{9}{8} \rightarrow 11 + 1\frac{1}{8} = 12\frac{1}{8}$

Explanation

Sometimes when you add up the fraction parts, you get more than a whole! It's like having 7 slices of a pizza cut into 6 pieces. You have one whole pizza and one slice left over. You just take that extra whole unit and give it to the whole number pile, making your final answer bigger and tidier.