Basic Math Examples

$2 \frac{1}{3} + \frac{5}{9} + \frac{5}{6}$

Step 1

Convert $2 \frac{1}{3}$ to an improper fraction.

Tap for more steps...

Step 1.1

A mixed number is an addition of its whole and fractional parts.

$2 + \frac{1}{3} + \frac{5}{9} + \frac{5}{6}$

Step 1.2

Add $2$ and $\frac{1}{3}$ .

Tap for more steps...

Step 1.2.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$2 \cdot \frac{3}{3} + \frac{1}{3} + \frac{5}{9} + \frac{5}{6}$

Step 1.2.2

Combine $2$ and $\frac{3}{3}$ .

$\frac{2 \cdot 3}{3} + \frac{1}{3} + \frac{5}{9} + \frac{5}{6}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{2 \cdot 3 + 1}{3} + \frac{5}{9} + \frac{5}{6}$

Step 1.2.4

Simplify the numerator.

Tap for more steps...

Step 1.2.4.1

Multiply $2$ by $3$ .

$\frac{6 + 1}{3} + \frac{5}{9} + \frac{5}{6}$

Step 1.2.4.2

Add $6$ and $1$ .

$\frac{7}{3} + \frac{5}{9} + \frac{5}{6}$

Step 2

Find the common denominator.

Tap for more steps...

Step 2.1

Multiply $\frac{7}{3}$ by $\frac{6}{6}$ .

$\frac{7}{3} \cdot \frac{6}{6} + \frac{5}{9} + \frac{5}{6}$

Step 2.2

Multiply $\frac{7}{3}$ by $\frac{6}{6}$ .

$\frac{7 \cdot 6}{3 \cdot 6} + \frac{5}{9} + \frac{5}{6}$

Step 2.3

Multiply $\frac{5}{9}$ by $\frac{2}{2}$ .

$\frac{7 \cdot 6}{3 \cdot 6} + \frac{5}{9} \cdot \frac{2}{2} + \frac{5}{6}$

Step 2.4

Multiply $\frac{5}{9}$ by $\frac{2}{2}$ .

$\frac{7 \cdot 6}{3 \cdot 6} + \frac{5 \cdot 2}{9 \cdot 2} + \frac{5}{6}$

Step 2.5

Multiply $\frac{5}{6}$ by $\frac{3}{3}$ .

$\frac{7 \cdot 6}{3 \cdot 6} + \frac{5 \cdot 2}{9 \cdot 2} + \frac{5}{6} \cdot \frac{3}{3}$

Step 2.6

Multiply $\frac{5}{6}$ by $\frac{3}{3}$ .

$\frac{7 \cdot 6}{3 \cdot 6} + \frac{5 \cdot 2}{9 \cdot 2} + \frac{5 \cdot 3}{6 \cdot 3}$

Step 2.7

Multiply $3$ by $6$ .

$\frac{7 \cdot 6}{18} + \frac{5 \cdot 2}{9 \cdot 2} + \frac{5 \cdot 3}{6 \cdot 3}$

Step 2.8

Reorder the factors of $9 \cdot 2$ .

$\frac{7 \cdot 6}{18} + \frac{5 \cdot 2}{2 \cdot 9} + \frac{5 \cdot 3}{6 \cdot 3}$

Step 2.9

Multiply $2$ by $9$ .

$\frac{7 \cdot 6}{18} + \frac{5 \cdot 2}{18} + \frac{5 \cdot 3}{6 \cdot 3}$

Step 2.10

Reorder the factors of $6 \cdot 3$ .

$\frac{7 \cdot 6}{18} + \frac{5 \cdot 2}{18} + \frac{5 \cdot 3}{3 \cdot 6}$

Step 2.11

Multiply $3$ by $6$ .

$\frac{7 \cdot 6}{18} + \frac{5 \cdot 2}{18} + \frac{5 \cdot 3}{18}$

Step 3

Combine the numerators over the common denominator.

$\frac{7 \cdot 6 + 5 \cdot 2 + 5 \cdot 3}{18}$

Step 4

Simplify each term.

Tap for more steps...

Step 4.1

Multiply $7$ by $6$ .

$\frac{42 + 5 \cdot 2 + 5 \cdot 3}{18}$

Step 4.2

Multiply $5$ by $2$ .

$\frac{42 + 10 + 5 \cdot 3}{18}$

Step 4.3

Multiply $5$ by $3$ .

$\frac{42 + 10 + 15}{18}$

Step 5

Simplify by adding numbers.

Tap for more steps...

Step 5.1

Add $42$ and $10$ .

$\frac{52 + 15}{18}$

Step 5.2

Add $52$ and $15$ .

$\frac{67}{18}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{67}{18}$

Decimal Form:

$3.7\overline{2}$

Mixed Number Form:

$3 \frac{13}{18}$