Basic Math Examples

8 \div 3 \frac{1}{5}

$8 \div 3 \frac{1}{5}$

Step 1

Convert

3 \frac{1}{5}

$3 \frac{1}{5}$ to an improper fraction.

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Step 1.1

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

8 \div (3 + \frac{1}{5})

$8 \div (3 + \frac{1}{5})$

Step 1.2

Add

3

$3$ and

\frac{1}{5}

$\frac{1}{5}$ .

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Step 1.2.1

To write

3

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

\frac{5}{5}

$\frac{5}{5}$ .

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

$8 \div (3 \cdot \frac{5}{5} + \frac{1}{5})$

Step 1.2.2

Combine

3

$3$ and

\frac{5}{5}

$\frac{5}{5}$ .

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

$8 \div (\frac{3 \cdot 5}{5} + \frac{1}{5})$

Step 1.2.3

Combine the numerators over the common denominator.

8 \div \frac{3 \cdot 5 + 1}{5}

$8 \div \frac{3 \cdot 5 + 1}{5}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

3

$3$ by

5

$5$ .

8 \div \frac{15 + 1}{5}

$8 \div \frac{15 + 1}{5}$

Step 1.2.4.2

Add

15

$15$ and

1

$1$ .

8 \div \frac{16}{5}

$8 \div \frac{16}{5}$

8 \div \frac{16}{5}

$8 \div \frac{16}{5}$

8 \div \frac{16}{5}

$8 \div \frac{16}{5}$

8 \div \frac{16}{5}

$8 \div \frac{16}{5}$

Step 2

To divide by a fraction, multiply by its reciprocal.

8 (\frac{5}{16})

$8 (\frac{5}{16})$

Step 3

Cancel the common factor of

8

$8$ .

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Step 3.1

Factor

8

$8$ out of

16

$16$ .

8 \frac{5}{8 (2)}

$8 \frac{5}{8 (2)}$

Step 3.2

Cancel the common factor.

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

Step 3.3

Rewrite the expression.

$\frac{5}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{5}{2}$

Decimal Form:

$2.5$

Mixed Number Form:

$2 \frac{1}{2}$