Basic Math Examples

$3 \frac{1}{2} \div 12 \frac{1}{4}$

Step 1

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

Tap for more steps...

Step 1.1

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

$(3 + \frac{1}{2}) \div 12 \frac{1}{4}$

Step 1.2

Add $3$ and $\frac{1}{2}$ .

Tap for more steps...

Step 1.2.1

To write $3$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$(3 \cdot \frac{2}{2} + \frac{1}{2}) \div 12 \frac{1}{4}$

Step 1.2.2

Combine $3$ and $\frac{2}{2}$ .

$(\frac{3 \cdot 2}{2} + \frac{1}{2}) \div 12 \frac{1}{4}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{3 \cdot 2 + 1}{2} \div 12 \frac{1}{4}$

Step 1.2.4

Simplify the numerator.

Tap for more steps...

Step 1.2.4.1

Multiply $3$ by $2$ .

$\frac{6 + 1}{2} \div 12 \frac{1}{4}$

Step 1.2.4.2

Add $6$ and $1$ .

$\frac{7}{2} \div 12 \frac{1}{4}$

Step 2

Convert $12 \frac{1}{4}$ to an improper fraction.

Tap for more steps...

Step 2.1

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

$\frac{7}{2} \div (12 + \frac{1}{4})$

Step 2.2

Add $12$ and $\frac{1}{4}$ .

Tap for more steps...

Step 2.2.1

To write $12$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{7}{2} \div (12 \cdot \frac{4}{4} + \frac{1}{4})$

Step 2.2.2

Combine $12$ and $\frac{4}{4}$ .

$\frac{7}{2} \div (\frac{12 \cdot 4}{4} + \frac{1}{4})$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{7}{2} \div \frac{12 \cdot 4 + 1}{4}$

Step 2.2.4

Simplify the numerator.

Tap for more steps...

Step 2.2.4.1

Multiply $12$ by $4$ .

$\frac{7}{2} \div \frac{48 + 1}{4}$

Step 2.2.4.2

Add $48$ and $1$ .

$\frac{7}{2} \div \frac{49}{4}$

Step 3

To divide by a fraction, multiply by its reciprocal.

$\frac{7}{2} \cdot \frac{4}{49}$

Step 4

Cancel the common factor of $7$ .

Tap for more steps...

Step 4.1

Factor $7$ out of $49$ .

$\frac{7}{2} \cdot \frac{4}{7 (7)}$

Step 4.2

Cancel the common factor.

$\frac{7}{2} \cdot \frac{4}{7 \cdot 7}$

Step 4.3

Rewrite the expression.

$\frac{1}{2} \cdot \frac{4}{7}$

Step 5

Cancel the common factor of $2$ .

Tap for more steps...

Step 5.1

Factor $2$ out of $4$ .

$\frac{1}{2} \cdot \frac{2 (2)}{7}$

Step 5.2

Cancel the common factor.

$\frac{1}{2} \cdot \frac{2 \cdot 2}{7}$

Step 5.3

Rewrite the expression.

$\frac{2}{7}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{2}{7}$

Decimal Form:

$0.\overline{285714}$