Basic Math Examples

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

Step 1

Convert

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

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Step 1.1

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

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

Step 1.2

Add

$7$ and

$\frac{1}{2}$ .

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Step 1.2.1

To write

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

$\frac{2}{2}$ .

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

Step 1.2.2

Combine

$7$ and

$\frac{2}{2}$ .

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

Step 1.2.3

Combine the numerators over the common denominator.

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

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

$7$ by

$2$ .

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

Step 1.2.4.2

Add

$14$ and

$1$ .

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

Step 2

Convert

$3 \frac{1}{2}$ to an improper fraction.

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Step 2.1

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

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

Step 2.2

Add

$3$ and

$\frac{1}{2}$ .

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Step 2.2.1

To write

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

$\frac{2}{2}$ .

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

Step 2.2.2

Combine

$3$ and

$\frac{2}{2}$ .

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

Step 2.2.3

Combine the numerators over the common denominator.

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

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply

$3$ by

$2$ .

$\frac{15}{2} \div \frac{6 + 1}{2}$

Step 2.2.4.2

Add

$6$ and

$1$ .

$\frac{15}{2} \div \frac{7}{2}$

Step 3

To divide by a fraction, multiply by its reciprocal.

$\frac{15}{2} \cdot \frac{2}{7}$

Step 4

Cancel the common factor of

$2$ .

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Step 4.1

Cancel the common factor.

$\frac{15}{2} \cdot \frac{2}{7}$

Step 4.2

Rewrite the expression.

$15 (\frac{1}{7})$

Step 5

Combine

$15$ and

$\frac{1}{7}$ .

$\frac{15}{7}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{15}{7}$

Decimal Form:

$2.\overline{142857}$

Mixed Number Form:

$2 \frac{1}{7}$