Basic Math Examples

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

Step 1

Convert

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

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Step 1.1

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

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

Step 1.2

Add

$2$ and

$\frac{1}{3}$ .

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Step 1.2.1

To write

$2$ as a fraction with a common denominator, multiply by

$\frac{3}{3}$ .

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

Step 1.2.2

Combine

$2$ and

$\frac{3}{3}$ .

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

Step 1.2.3

Combine the numerators over the common denominator.

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

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

$2$ by

$3$ .

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

Step 1.2.4.2

Add

$6$ and

$1$ .

$\frac{7}{3} + 1 \frac{1}{3}$

Step 2

Convert

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

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Step 2.1

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

$\frac{7}{3} + 1 + \frac{1}{3}$

Step 2.2

Add

$1$ and

$\frac{1}{3}$ .

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Step 2.2.1

Write

$1$ as a fraction with a common denominator.

$\frac{7}{3} + \frac{3}{3} + \frac{1}{3}$

Step 2.2.2

Combine the numerators over the common denominator.

$\frac{7}{3} + \frac{3 + 1}{3}$

Step 2.2.3

Add

$3$ and

$1$ .

$\frac{7}{3} + \frac{4}{3}$

Step 3

Combine the numerators over the common denominator.

$\frac{7 + 4}{3}$

Step 4

Add

$7$ and

$4$ .

$\frac{11}{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{11}{3}$

Decimal Form:

$3.\overline{6}$

Mixed Number Form:

$3 \frac{2}{3}$