Basic Math Examples

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

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

Step 1

Convert

$2 \frac{1}{5}$ to an improper fraction.

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Step 1.1

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

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

Step 1.2

Add

$2$ and

$\frac{1}{5}$ .

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Step 1.2.1

To write

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

$\frac{5}{5}$ .

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

Step 1.2.2

Combine

$2$ and

$\frac{5}{5}$ .

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

Step 1.2.3

Combine the numerators over the common denominator.

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

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

$2$ by

$5$ .

$\frac{10 + 1}{5} \div 1 \frac{1}{2}$

Step 1.2.4.2

Add

$10$ and

$1$ .

$\frac{11}{5} \div 1 \frac{1}{2}$

Step 2

Convert

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

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Step 2.1

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

$\frac{11}{5} \div (1 + \frac{1}{2})$

Step 2.2

Add

$1$ and

$\frac{1}{2}$ .

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Step 2.2.1

Write

$1$ as a fraction with a common denominator.

$\frac{11}{5} \div (\frac{2}{2} + \frac{1}{2})$

Step 2.2.2

Combine the numerators over the common denominator.

$\frac{11}{5} \div \frac{2 + 1}{2}$

Step 2.2.3

Add

$2$ and

$1$ .

$\frac{11}{5} \div \frac{3}{2}$

Step 3

To divide by a fraction, multiply by its reciprocal.

$\frac{11}{5} \cdot \frac{2}{3}$

Step 4

Multiply

$\frac{11}{5} \cdot \frac{2}{3}$ .

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Step 4.1

Multiply

$\frac{11}{5}$ by

$\frac{2}{3}$ .

$\frac{11 \cdot 2}{5 \cdot 3}$

Step 4.2

Multiply

$11$ by

$2$ .

$\frac{22}{5 \cdot 3}$

Step 4.3

Multiply

$5$ by

$3$ .

$\frac{22}{15}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{22}{15}$

Decimal Form:

$1.4\overline{6}$

Mixed Number Form:

$1 \frac{7}{15}$