# Adding Mixed Numbers

Learn how to add Mixed Numbers in few simple steps.

## Step by step guide to Adding Mixed Numbers

Use the following steps for adding mixed numbers.

• Add whole numbers of the mixed numbers.
• Add the fractions of each mixed number.
• Find the Least Common Denominator (LCD) if necessary.
• Add whole numbers and fractions.
• Write your answer in lowest terms.

### Example 1:

Add mixed numbers. $$1 \ \frac{1}{2} \ + \ 2 \ \frac{2}{3}=$$

Solution:

Rewriting our equation with parts separated, $$1+\frac{1}{2}+2+\frac{2}{3}$$,

Solving the whole number parts $$1+2=3$$,

Solving the fraction parts $$\frac{1}{2}+\frac{2}{3}$$, and rewrite to solve with the equivalent fractions.
$$\frac{3}{6}+\frac{4}{6}=\frac{7}{6}=1 \ \frac{1}{6}$$, then Combining the whole and fraction parts $$3+1+\frac{1}{6}=4 \ \frac{1}{6}$$

### Example 2:

Add mixed numbers. $$2 \ \frac{1}{4} \ + \ 1 \ \frac{2}{5}=$$

Solution:

Rewriting our equation with parts separated, $$2+\frac{1}{4}+1+\frac{2}{5}$$,

Solving the whole number parts $$2+1=3$$,

Solving the fraction parts $$\frac{1}{4}+\frac{2}{5}$$, and rewrite to solve with the equivalent fractions.
$$\frac{5}{20}+\frac{8}{20}=\frac{13}{20}$$, then Combining the whole and fraction parts $$3+\frac{13}{20}=3 \ \frac{13}{20}$$

### Example 3:

Add mixed numbers. $$1 \ \frac{3}{4} \ + \ 2\ \frac{3}{8}=$$

Solution:

Rewriting our equation with parts separated, $$1+\frac{3}{4}+2+\frac{3}{8}$$,

Solving the whole number parts $$1+2=3$$, Solving the fraction parts $$\frac{3}{4}+\frac{3}{8}$$, and rewrite to solve with the equivalent fractions.
$$\frac{6}{8}+\frac{3}{8}=\frac{9}{8}=1 \ \frac{1}{8}$$ , then combining the whole and fraction parts $$3+1+\frac{1}{8}=4 \frac{1}{8}$$

### Example 4:

Add mixed numbers. $$1 \ \frac{2}{3} \ + \ 4\ \frac{1}{6}=$$

Solution:

Rewriting our equation with parts separated, $$1+\frac{2}{3}+4+\frac{1}{6 }$$,

Solving the whole number parts $$1+4=5$$, Solving the fraction parts $$\frac{2}{3}+\frac{1}{6 }$$, and rewrite to solve with the equivalent fractions.
$$\frac{2}{3}+\frac{1}{6}=\frac{5}{6 }$$, then combining the whole and fraction parts $$5+\frac{5}{6}=5 \ \frac{5}{6}$$

## Exercises

1. $$\color{blue}{4 \frac{1}{2} + 5 \frac{1}{2}}$$
2. $$\color{blue}{2 \frac{3}{8} + 3 \frac{1}{8}}$$
3. $$\color{blue}{6 \frac{1}{5} + 3 \frac{2}{5}}$$
4. $$\color{blue}{1 \frac{1}{3} + 2 \frac{2}{3}}$$
5. $$\color{blue}{5 \frac{1}{6} + 5 \frac{1}{2}}$$
6. $$\color{blue}{3 \frac{1}{3} + 1 \frac{1}{3}}$$

1. $$\color{blue}{10}$$
2. $$\color{blue}{5\frac{1}{2}}$$
3. $$\color{blue}{9\frac{3}{5}}$$
4. $$\color {blue}{4}$$
5. $$\color{blue}{10\frac{2}{3}}$$
6. $$\color{blue}{4\frac{2}{3}}$$

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