Basic Math Examples

220 \div 85 \frac{1}{5}

$220 \div 85 \frac{1}{5}$

Step 1

Convert

85 \frac{1}{5}

$85 \frac{1}{5}$ to an improper fraction.

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Step 1.1

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

220 \div (85 + \frac{1}{5})

$220 \div (85 + \frac{1}{5})$

Step 1.2

Add

85

$85$ and

\frac{1}{5}

$\frac{1}{5}$ .

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Step 1.2.1

To write

85

$85$ as a fraction with a common denominator, multiply by

\frac{5}{5}

$\frac{5}{5}$ .

220 \div (85 \cdot \frac{5}{5} + \frac{1}{5})

$220 \div (85 \cdot \frac{5}{5} + \frac{1}{5})$

Step 1.2.2

Combine

85

$85$ and

\frac{5}{5}

$\frac{5}{5}$ .

220 \div (\frac{85 \cdot 5}{5} + \frac{1}{5})

$220 \div (\frac{85 \cdot 5}{5} + \frac{1}{5})$

Step 1.2.3

Combine the numerators over the common denominator.

220 \div \frac{85 \cdot 5 + 1}{5}

$220 \div \frac{85 \cdot 5 + 1}{5}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

85

$85$ by

5

$5$ .

220 \div \frac{425 + 1}{5}

$220 \div \frac{425 + 1}{5}$

Step 1.2.4.2

Add

425

$425$ and

1

$1$ .

220 \div \frac{426}{5}

$220 \div \frac{426}{5}$

220 \div \frac{426}{5}

$220 \div \frac{426}{5}$

220 \div \frac{426}{5}

$220 \div \frac{426}{5}$

220 \div \frac{426}{5}

$220 \div \frac{426}{5}$

Step 2

To divide by a fraction, multiply by its reciprocal.

220 (\frac{5}{426})

$220 (\frac{5}{426})$

Step 3

Cancel the common factor of

2

$2$ .

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Step 3.1

Factor

2

$2$ out of

220

$220$ .

2 (110) \frac{5}{426}

$2 (110) \frac{5}{426}$

Step 3.2

Factor

2

$2$ out of

426

$426$ .

2 \cdot 110 \frac{5}{2 \cdot 213}

$2 \cdot 110 \frac{5}{2 \cdot 213}$

Step 3.3

Cancel the common factor.

$2 \cdot 110 \frac{5}{2 \cdot 213}$

Step 3.4

Rewrite the expression.

$110 (\frac{5}{213})$

Step 4

Combine

$110$ and

$\frac{5}{213}$ .

$\frac{110 \cdot 5}{213}$

Step 5

Multiply

$110$ by

$5$ .

$\frac{550}{213}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{550}{213}$

Decimal Form:

$2.58215962 \dots$

Mixed Number Form:

$2 \frac{124}{213}$