Basic Math Examples

$5 \frac{1}{9} - 2 \frac{5}{9}$

Step 1

Convert

$5 \frac{1}{9}$ to an improper fraction.

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Step 1.1

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

$5 + \frac{1}{9} - 2 \frac{5}{9}$

Step 1.2

Add

$5$ and

$\frac{1}{9}$ .

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Step 1.2.1

To write

$5$ as a fraction with a common denominator, multiply by

$\frac{9}{9}$ .

$5 \cdot \frac{9}{9} + \frac{1}{9} - 2 \frac{5}{9}$

Step 1.2.2

Combine

$5$ and

$\frac{9}{9}$ .

$\frac{5 \cdot 9}{9} + \frac{1}{9} - 2 \frac{5}{9}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{5 \cdot 9 + 1}{9} - 2 \frac{5}{9}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

$5$ by

$9$ .

$\frac{45 + 1}{9} - 2 \frac{5}{9}$

Step 1.2.4.2

Add

$45$ and

$1$ .

$\frac{46}{9} - 2 \frac{5}{9}$

Step 2

Convert

$2 \frac{5}{9}$ to an improper fraction.

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Step 2.1

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

$\frac{46}{9} - (2 + \frac{5}{9})$

Step 2.2

Add

$2$ and

$\frac{5}{9}$ .

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Step 2.2.1

To write

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

$\frac{9}{9}$ .

$\frac{46}{9} - (2 \cdot \frac{9}{9} + \frac{5}{9})$

Step 2.2.2

Combine

$2$ and

$\frac{9}{9}$ .

$\frac{46}{9} - (\frac{2 \cdot 9}{9} + \frac{5}{9})$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{46}{9} - \frac{2 \cdot 9 + 5}{9}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply

$2$ by

$9$ .

$\frac{46}{9} - \frac{18 + 5}{9}$

Step 2.2.4.2

Add

$18$ and

$5$ .

$\frac{46}{9} - \frac{23}{9}$

Step 3

Combine the numerators over the common denominator.

$\frac{46 - 23}{9}$

Step 4

Subtract

$23$ from

$46$ .

$\frac{23}{9}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{23}{9}$

Decimal Form:

$2.\overline{5}$

Mixed Number Form:

$2 \frac{5}{9}$