Basic Math Examples

$\frac{1}{2} - \frac{1}{3} \cdot \frac{1}{4} + \frac{1}{5} \div \frac{1}{6}$

Step 1

Simplify each term.

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Step 1.1

Multiply $- \frac{1}{3} \cdot \frac{1}{4}$ .

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Step 1.1.1

Multiply $\frac{1}{4}$ by $\frac{1}{3}$ .

$\frac{1}{2} - \frac{1}{4 \cdot 3} + \frac{1}{5} \div \frac{1}{6}$

Step 1.1.2

Multiply $4$ by $3$ .

$\frac{1}{2} - \frac{1}{12} + \frac{1}{5} \div \frac{1}{6}$

Step 1.2

To divide by a fraction, multiply by its reciprocal.

$\frac{1}{2} - \frac{1}{12} + \frac{1}{5} \cdot 6$

Step 1.3

Combine $\frac{1}{5}$ and $6$ .

$\frac{1}{2} - \frac{1}{12} + \frac{6}{5}$

Step 2

Find the common denominator.

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Step 2.1

Multiply $\frac{1}{2}$ by $\frac{30}{30}$ .

$\frac{1}{2} \cdot \frac{30}{30} - \frac{1}{12} + \frac{6}{5}$

Step 2.2

Multiply $\frac{1}{2}$ by $\frac{30}{30}$ .

$\frac{30}{2 \cdot 30} - \frac{1}{12} + \frac{6}{5}$

Step 2.3

Multiply $\frac{1}{12}$ by $\frac{5}{5}$ .

$\frac{30}{2 \cdot 30} - (\frac{1}{12} \cdot \frac{5}{5}) + \frac{6}{5}$

Step 2.4

Multiply $\frac{1}{12}$ by $\frac{5}{5}$ .

$\frac{30}{2 \cdot 30} - \frac{5}{12 \cdot 5} + \frac{6}{5}$

Step 2.5

Multiply $\frac{6}{5}$ by $\frac{12}{12}$ .

$\frac{30}{2 \cdot 30} - \frac{5}{12 \cdot 5} + \frac{6}{5} \cdot \frac{12}{12}$

Step 2.6

Multiply $\frac{6}{5}$ by $\frac{12}{12}$ .

$\frac{30}{2 \cdot 30} - \frac{5}{12 \cdot 5} + \frac{6 \cdot 12}{5 \cdot 12}$

Step 2.7

Multiply $2$ by $30$ .

$\frac{30}{60} - \frac{5}{12 \cdot 5} + \frac{6 \cdot 12}{5 \cdot 12}$

Step 2.8

Reorder the factors of $12 \cdot 5$ .

$\frac{30}{60} - \frac{5}{5 \cdot 12} + \frac{6 \cdot 12}{5 \cdot 12}$

Step 2.9

Multiply $5$ by $12$ .

$\frac{30}{60} - \frac{5}{60} + \frac{6 \cdot 12}{5 \cdot 12}$

Step 2.10

Multiply $5$ by $12$ .

$\frac{30}{60} - \frac{5}{60} + \frac{6 \cdot 12}{60}$

Step 3

Combine the numerators over the common denominator.

$\frac{30 - 5 + 6 \cdot 12}{60}$

Step 4

Simplify the expression.

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Step 4.1

Multiply $6$ by $12$ .

$\frac{30 - 5 + 72}{60}$

Step 4.2

Subtract $5$ from $30$ .

$\frac{25 + 72}{60}$

Step 4.3

Add $25$ and $72$ .

$\frac{97}{60}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{97}{60}$

Decimal Form:

$1.61\overline{6}$

Mixed Number Form:

$1 \frac{37}{60}$