Basic Math Examples

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

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

Step 1

Convert

5 \frac{3}{4}

$5 \frac{3}{4}$ to an improper fraction.

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Step 1.1

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

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

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

Step 1.2

Add

5

$5$ and

\frac{3}{4}

$\frac{3}{4}$ .

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Step 1.2.1

To write

5

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

\frac{4}{4}

$\frac{4}{4}$ .

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

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

Step 1.2.2

Combine

5

$5$ and

\frac{4}{4}

$\frac{4}{4}$ .

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

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

Step 1.2.3

Combine the numerators over the common denominator.

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

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

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

5

$5$ by

4

$4$ .

\frac{20 + 3}{4} \div 2 \frac{1}{4}

$\frac{20 + 3}{4} \div 2 \frac{1}{4}$

Step 1.2.4.2

Add

20

$20$ and

3

$3$ .

\frac{23}{4} \div 2 \frac{1}{4}

$\frac{23}{4} \div 2 \frac{1}{4}$

\frac{23}{4} \div 2 \frac{1}{4}

$\frac{23}{4} \div 2 \frac{1}{4}$

\frac{23}{4} \div 2 \frac{1}{4}

$\frac{23}{4} \div 2 \frac{1}{4}$

\frac{23}{4} \div 2 \frac{1}{4}

$\frac{23}{4} \div 2 \frac{1}{4}$

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{23}{4} \div (2 + \frac{1}{4})

$\frac{23}{4} \div (2 + \frac{1}{4})$

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{23}{4} \div (2 \cdot \frac{4}{4} + \frac{1}{4})

$\frac{23}{4} \div (2 \cdot \frac{4}{4} + \frac{1}{4})$

Step 2.2.2

Combine

2

$2$ and

\frac{4}{4}

$\frac{4}{4}$ .

\frac{23}{4} \div (\frac{2 \cdot 4}{4} + \frac{1}{4})

$\frac{23}{4} \div (\frac{2 \cdot 4}{4} + \frac{1}{4})$

Step 2.2.3

Combine the numerators over the common denominator.

\frac{23}{4} \div \frac{2 \cdot 4 + 1}{4}

$\frac{23}{4} \div \frac{2 \cdot 4 + 1}{4}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply

2

$2$ by

4

$4$ .

\frac{23}{4} \div \frac{8 + 1}{4}

$\frac{23}{4} \div \frac{8 + 1}{4}$

Step 2.2.4.2

Add

8

$8$ and

1

$1$ .

\frac{23}{4} \div \frac{9}{4}

$\frac{23}{4} \div \frac{9}{4}$

\frac{23}{4} \div \frac{9}{4}

$\frac{23}{4} \div \frac{9}{4}$

\frac{23}{4} \div \frac{9}{4}

$\frac{23}{4} \div \frac{9}{4}$

\frac{23}{4} \div \frac{9}{4}

$\frac{23}{4} \div \frac{9}{4}$

Step 3

To divide by a fraction, multiply by its reciprocal.

\frac{23}{4} \cdot \frac{4}{9}

$\frac{23}{4} \cdot \frac{4}{9}$

Step 4

Cancel the common factor of

4

$4$ .

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Step 4.1

Cancel the common factor.

$\frac{23}{4} \cdot \frac{4}{9}$

Step 4.2

Rewrite the expression.

$23 (\frac{1}{9})$

Step 5

Combine

$23$ and

$\frac{1}{9}$ .

$\frac{23}{9}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{23}{9}$

Decimal Form:

$2.\overline{5}$

Mixed Number Form:

$2 \frac{5}{9}$