Basic Math Examples

$2 \frac{7}{9} \div 2 \frac{2}{3}$

Step 1

Convert

$2 \frac{7}{9}$ to an improper fraction.

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Step 1.1

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

$(2 + \frac{7}{9}) \div 2 \frac{2}{3}$

Step 1.2

Add

$2$ and

$\frac{7}{9}$ .

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Step 1.2.1

To write

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

$\frac{9}{9}$ .

$(2 \cdot \frac{9}{9} + \frac{7}{9}) \div 2 \frac{2}{3}$

Step 1.2.2

Combine

$2$ and

$\frac{9}{9}$ .

$(\frac{2 \cdot 9}{9} + \frac{7}{9}) \div 2 \frac{2}{3}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{2 \cdot 9 + 7}{9} \div 2 \frac{2}{3}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

$2$ by

$9$ .

$\frac{18 + 7}{9} \div 2 \frac{2}{3}$

Step 1.2.4.2

Add

$18$ and

$7$ .

$\frac{25}{9} \div 2 \frac{2}{3}$

Step 2

Convert

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

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Step 2.1

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

$\frac{25}{9} \div (2 + \frac{2}{3})$

Step 2.2

Add

$2$ and

$\frac{2}{3}$ .

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Step 2.2.1

To write

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

$\frac{3}{3}$ .

$\frac{25}{9} \div (2 \cdot \frac{3}{3} + \frac{2}{3})$

Step 2.2.2

Combine

$2$ and

$\frac{3}{3}$ .

$\frac{25}{9} \div (\frac{2 \cdot 3}{3} + \frac{2}{3})$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{25}{9} \div \frac{2 \cdot 3 + 2}{3}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply

$2$ by

$3$ .

$\frac{25}{9} \div \frac{6 + 2}{3}$

Step 2.2.4.2

Add

$6$ and

$2$ .

$\frac{25}{9} \div \frac{8}{3}$

Step 3

To divide by a fraction, multiply by its reciprocal.

$\frac{25}{9} \cdot \frac{3}{8}$

Step 4

Cancel the common factor of

$3$ .

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Step 4.1

Factor

$3$ out of

$9$ .

$\frac{25}{3 (3)} \cdot \frac{3}{8}$

Step 4.2

Cancel the common factor.

$\frac{25}{3 \cdot 3} \cdot \frac{3}{8}$

Step 4.3

Rewrite the expression.

$\frac{25}{3} \cdot \frac{1}{8}$

Step 5

Multiply

$\frac{25}{3}$ by

$\frac{1}{8}$ .

$\frac{25}{3 \cdot 8}$

Step 6

Multiply

$3$ by

$8$ .

$\frac{25}{24}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{25}{24}$

Decimal Form:

$1.041\overline{6}$

Mixed Number Form:

$1 \frac{1}{24}$