Algebra Examples

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

$7 \frac{1}{2} \div 3 \frac{1}{8}$

Step 1

Convert

7 \frac{1}{2}

$7 \frac{1}{2}$ to an improper fraction.

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Step 1.1

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

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

$(7 + \frac{1}{2}) \div 3 \frac{1}{8}$

Step 1.2

Add

7

$7$ and

\frac{1}{2}

$\frac{1}{2}$ .

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Step 1.2.1

To write

7

$7$ as a fraction with a common denominator, multiply by

\frac{2}{2}

$\frac{2}{2}$ .

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

$(7 \cdot \frac{2}{2} + \frac{1}{2}) \div 3 \frac{1}{8}$

Step 1.2.2

Combine

7

$7$ and

\frac{2}{2}

$\frac{2}{2}$ .

(\frac{7 \cdot 2}{2} + \frac{1}{2}) \div 3 \frac{1}{8}

$(\frac{7 \cdot 2}{2} + \frac{1}{2}) \div 3 \frac{1}{8}$

Step 1.2.3

Combine the numerators over the common denominator.

\frac{7 \cdot 2 + 1}{2} \div 3 \frac{1}{8}

$\frac{7 \cdot 2 + 1}{2} \div 3 \frac{1}{8}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

7

$7$ by

2

$2$ .

\frac{14 + 1}{2} \div 3 \frac{1}{8}

$\frac{14 + 1}{2} \div 3 \frac{1}{8}$

Step 1.2.4.2

Add

14

$14$ and

1

$1$ .

\frac{15}{2} \div 3 \frac{1}{8}

$\frac{15}{2} \div 3 \frac{1}{8}$

\frac{15}{2} \div 3 \frac{1}{8}

$\frac{15}{2} \div 3 \frac{1}{8}$

\frac{15}{2} \div 3 \frac{1}{8}

$\frac{15}{2} \div 3 \frac{1}{8}$

\frac{15}{2} \div 3 \frac{1}{8}

$\frac{15}{2} \div 3 \frac{1}{8}$

Step 2

Convert

3 \frac{1}{8}

$3 \frac{1}{8}$ to an improper fraction.

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Step 2.1

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

\frac{15}{2} \div (3 + \frac{1}{8})

$\frac{15}{2} \div (3 + \frac{1}{8})$

Step 2.2

Add

3

$3$ and

\frac{1}{8}

$\frac{1}{8}$ .

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Step 2.2.1

To write

3

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

\frac{8}{8}

$\frac{8}{8}$ .

\frac{15}{2} \div (3 \cdot \frac{8}{8} + \frac{1}{8})

$\frac{15}{2} \div (3 \cdot \frac{8}{8} + \frac{1}{8})$

Step 2.2.2

Combine

3

$3$ and

\frac{8}{8}

$\frac{8}{8}$ .

\frac{15}{2} \div (\frac{3 \cdot 8}{8} + \frac{1}{8})

$\frac{15}{2} \div (\frac{3 \cdot 8}{8} + \frac{1}{8})$

Step 2.2.3

Combine the numerators over the common denominator.

\frac{15}{2} \div \frac{3 \cdot 8 + 1}{8}

$\frac{15}{2} \div \frac{3 \cdot 8 + 1}{8}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply

3

$3$ by

8

$8$ .

\frac{15}{2} \div \frac{24 + 1}{8}

$\frac{15}{2} \div \frac{24 + 1}{8}$

Step 2.2.4.2

Add

24

$24$ and

1

$1$ .

\frac{15}{2} \div \frac{25}{8}

$\frac{15}{2} \div \frac{25}{8}$

\frac{15}{2} \div \frac{25}{8}

$\frac{15}{2} \div \frac{25}{8}$

\frac{15}{2} \div \frac{25}{8}

$\frac{15}{2} \div \frac{25}{8}$

\frac{15}{2} \div \frac{25}{8}

$\frac{15}{2} \div \frac{25}{8}$

Step 3

To divide by a fraction, multiply by its reciprocal.

\frac{15}{2} \cdot \frac{8}{25}

$\frac{15}{2} \cdot \frac{8}{25}$

Step 4

Cancel the common factor of

5

$5$ .

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Step 4.1

Factor

5

$5$ out of

15

$15$ .

\frac{5 (3)}{2} \cdot \frac{8}{25}

$\frac{5 (3)}{2} \cdot \frac{8}{25}$

Step 4.2

Factor

5

$5$ out of

25

$25$ .

\frac{5 \cdot 3}{2} \cdot \frac{8}{5 \cdot 5}

$\frac{5 \cdot 3}{2} \cdot \frac{8}{5 \cdot 5}$

Step 4.3

Cancel the common factor.

$\frac{5 \cdot 3}{2} \cdot \frac{8}{5 \cdot 5}$

Step 4.4

Rewrite the expression.

$\frac{3}{2} \cdot \frac{8}{5}$

Step 5

Cancel the common factor of

$2$ .

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Step 5.1

Factor

$2$ out of

$8$ .

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

Step 5.2

Cancel the common factor.

$\frac{3}{2} \cdot \frac{2 \cdot 4}{5}$

Step 5.3

Rewrite the expression.

$3 (\frac{4}{5})$

Step 6

Combine

$3$ and

$\frac{4}{5}$ .

$\frac{3 \cdot 4}{5}$

Step 7

Multiply

$3$ by

$4$ .

$\frac{12}{5}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{12}{5}$

Decimal Form:

$2.4$

Mixed Number Form:

$2 \frac{2}{5}$