Basic Math Examples

3 \frac{3}{8} \div 2 \frac{1}{4}

$3 \frac{3}{8} \div 2 \frac{1}{4}$

Step 1

Convert

3 \frac{3}{8}

$3 \frac{3}{8}$ to an improper fraction.

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Step 1.1

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

(3 + \frac{3}{8}) \div 2 \frac{1}{4}

$(3 + \frac{3}{8}) \div 2 \frac{1}{4}$

Step 1.2

Add

3

$3$ and

\frac{3}{8}

$\frac{3}{8}$ .

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Step 1.2.1

To write

3

$3$ as a fraction with a common denominator, multiply by

\frac{8}{8}

$\frac{8}{8}$ .

(3 \cdot \frac{8}{8} + \frac{3}{8}) \div 2 \frac{1}{4}

$(3 \cdot \frac{8}{8} + \frac{3}{8}) \div 2 \frac{1}{4}$

Step 1.2.2

Combine

3

$3$ and

\frac{8}{8}

$\frac{8}{8}$ .

(\frac{3 \cdot 8}{8} + \frac{3}{8}) \div 2 \frac{1}{4}

$(\frac{3 \cdot 8}{8} + \frac{3}{8}) \div 2 \frac{1}{4}$

Step 1.2.3

Combine the numerators over the common denominator.

\frac{3 \cdot 8 + 3}{8} \div 2 \frac{1}{4}

$\frac{3 \cdot 8 + 3}{8} \div 2 \frac{1}{4}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

3

$3$ by

8

$8$ .

\frac{24 + 3}{8} \div 2 \frac{1}{4}

$\frac{24 + 3}{8} \div 2 \frac{1}{4}$

Step 1.2.4.2

Add

24

$24$ and

3

$3$ .

\frac{27}{8} \div 2 \frac{1}{4}

$\frac{27}{8} \div 2 \frac{1}{4}$

\frac{27}{8} \div 2 \frac{1}{4}

$\frac{27}{8} \div 2 \frac{1}{4}$

\frac{27}{8} \div 2 \frac{1}{4}

$\frac{27}{8} \div 2 \frac{1}{4}$

\frac{27}{8} \div 2 \frac{1}{4}

$\frac{27}{8} \div 2 \frac{1}{4}$

Step 2

Convert

2 \frac{1}{4}

$2 \frac{1}{4}$ to an improper fraction.

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Step 2.1

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

\frac{27}{8} \div (2 + \frac{1}{4})

$\frac{27}{8} \div (2 + \frac{1}{4})$

Step 2.2

Add

2

$2$ and

\frac{1}{4}

$\frac{1}{4}$ .

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Step 2.2.1

To write

2

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

\frac{4}{4}

$\frac{4}{4}$ .

\frac{27}{8} \div (2 \cdot \frac{4}{4} + \frac{1}{4})

$\frac{27}{8} \div (2 \cdot \frac{4}{4} + \frac{1}{4})$

Step 2.2.2

Combine

2

$2$ and

\frac{4}{4}

$\frac{4}{4}$ .

\frac{27}{8} \div (\frac{2 \cdot 4}{4} + \frac{1}{4})

$\frac{27}{8} \div (\frac{2 \cdot 4}{4} + \frac{1}{4})$

Step 2.2.3

Combine the numerators over the common denominator.

\frac{27}{8} \div \frac{2 \cdot 4 + 1}{4}

$\frac{27}{8} \div \frac{2 \cdot 4 + 1}{4}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply

2

$2$ by

4

$4$ .

\frac{27}{8} \div \frac{8 + 1}{4}

$\frac{27}{8} \div \frac{8 + 1}{4}$

Step 2.2.4.2

Add

8

$8$ and

1

$1$ .

\frac{27}{8} \div \frac{9}{4}

$\frac{27}{8} \div \frac{9}{4}$

\frac{27}{8} \div \frac{9}{4}

$\frac{27}{8} \div \frac{9}{4}$

\frac{27}{8} \div \frac{9}{4}

$\frac{27}{8} \div \frac{9}{4}$

\frac{27}{8} \div \frac{9}{4}

$\frac{27}{8} \div \frac{9}{4}$

Step 3

To divide by a fraction, multiply by its reciprocal.

\frac{27}{8} \cdot \frac{4}{9}

$\frac{27}{8} \cdot \frac{4}{9}$

Step 4

Cancel the common factor of

$9$ .

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Step 4.1

Factor

$9$ out of

$27$ .

$\frac{9 (3)}{8} \cdot \frac{4}{9}$

Step 4.2

Cancel the common factor.

$\frac{9 \cdot 3}{8} \cdot \frac{4}{9}$

Step 4.3

Rewrite the expression.

$\frac{3}{8} \cdot 4$

Step 5

Cancel the common factor of

$4$ .

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Step 5.1

Factor

$4$ out of

$8$ .

$\frac{3}{4 (2)} \cdot 4$

Step 5.2

Cancel the common factor.

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

Step 5.3

Rewrite the expression.

$\frac{3}{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{3}{2}$

Decimal Form:

$1.5$

Mixed Number Form:

$1 \frac{1}{2}$