Basic Math Examples

$2 \frac{1}{3} \div \frac{2}{5}$

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.

$(2 + \frac{1}{3}) \div \frac{2}{5}$

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

$\frac{3}{3}$ .

$(2 \cdot \frac{3}{3} + \frac{1}{3}) \div \frac{2}{5}$

Step 1.2.2

Combine

$2$ and

$\frac{3}{3}$ .

$(\frac{2 \cdot 3}{3} + \frac{1}{3}) \div \frac{2}{5}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{2 \cdot 3 + 1}{3} \div \frac{2}{5}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

$2$ by

$3$ .

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

Step 1.2.4.2

Add

$6$ and

$1$ .

$\frac{7}{3} \div \frac{2}{5}$

Step 2

To divide by a fraction, multiply by its reciprocal.

$\frac{7}{3} \cdot \frac{5}{2}$

Step 3

Multiply

$\frac{7}{3} \cdot \frac{5}{2}$ .

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Step 3.1

Multiply

$\frac{7}{3}$ by

$\frac{5}{2}$ .

$\frac{7 \cdot 5}{3 \cdot 2}$

Step 3.2

Multiply

$7$ by

$5$ .

$\frac{35}{3 \cdot 2}$

Step 3.3

Multiply

$3$ by

$2$ .

$\frac{35}{6}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{35}{6}$

Decimal Form:

$5.8\overline{3}$

Mixed Number Form:

$5 \frac{5}{6}$