Basic Math Examples

\frac{3}{4} \div 5 \frac{1}{2}

$\frac{3}{4} \div 5 \frac{1}{2}$

Step 1

Convert

5 \frac{1}{2}

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

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Step 1.1

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

\frac{3}{4} \div (5 + \frac{1}{2})

$\frac{3}{4} \div (5 + \frac{1}{2})$

Step 1.2

Add

5

$5$ and

\frac{1}{2}

$\frac{1}{2}$ .

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Step 1.2.1

To write

5

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

\frac{2}{2}

$\frac{2}{2}$ .

\frac{3}{4} \div (5 \cdot \frac{2}{2} + \frac{1}{2})

$\frac{3}{4} \div (5 \cdot \frac{2}{2} + \frac{1}{2})$

Step 1.2.2

Combine

5

$5$ and

\frac{2}{2}

$\frac{2}{2}$ .

\frac{3}{4} \div (\frac{5 \cdot 2}{2} + \frac{1}{2})

$\frac{3}{4} \div (\frac{5 \cdot 2}{2} + \frac{1}{2})$

Step 1.2.3

Combine the numerators over the common denominator.

\frac{3}{4} \div \frac{5 \cdot 2 + 1}{2}

$\frac{3}{4} \div \frac{5 \cdot 2 + 1}{2}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

5

$5$ by

2

$2$ .

\frac{3}{4} \div \frac{10 + 1}{2}

$\frac{3}{4} \div \frac{10 + 1}{2}$

Step 1.2.4.2

Add

10

$10$ and

1

$1$ .

\frac{3}{4} \div \frac{11}{2}

$\frac{3}{4} \div \frac{11}{2}$

\frac{3}{4} \div \frac{11}{2}

$\frac{3}{4} \div \frac{11}{2}$

\frac{3}{4} \div \frac{11}{2}

$\frac{3}{4} \div \frac{11}{2}$

\frac{3}{4} \div \frac{11}{2}

$\frac{3}{4} \div \frac{11}{2}$

Step 2

To divide by a fraction, multiply by its reciprocal.

\frac{3}{4} \cdot \frac{2}{11}

$\frac{3}{4} \cdot \frac{2}{11}$

Step 3

Cancel the common factor of

2

$2$ .

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Step 3.1

Factor

2

$2$ out of

4

$4$ .

\frac{3}{2 (2)} \cdot \frac{2}{11}

$\frac{3}{2 (2)} \cdot \frac{2}{11}$

Step 3.2

Cancel the common factor.

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

Step 3.3

Rewrite the expression.

$\frac{3}{2} \cdot \frac{1}{11}$

Step 4

Multiply

$\frac{3}{2}$ by

$\frac{1}{11}$ .

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

Step 5

Multiply

$2$ by

$11$ .

$\frac{3}{22}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{3}{22}$

Decimal Form:

$0.1\overline{36}$