Basic Math Examples

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

Step 1

Simplify the denominator.

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Step 1.1

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

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

Step 1.2

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

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

Step 1.3

Combine the numerators over the common denominator.

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

Step 1.4

Simplify the numerator.

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Step 1.4.1

Multiply $2$ by $2$ .

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

Step 1.4.2

Add $1$ and $4$ .

$(2 - \frac{3}{4} \div \frac{5}{2}) \div (\frac{3}{2} - \frac{1}{2}) \cdot (3 - \frac{1}{2})$

Step 2

Simplify the numerator.

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Step 2.1

To divide by a fraction, multiply by its reciprocal.

$(2 - (\frac{3}{4} \cdot \frac{2}{5})) \div (\frac{3}{2} - \frac{1}{2}) \cdot (3 - \frac{1}{2})$

Step 2.2

Cancel the common factor of $2$ .

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Step 2.2.1

Factor $2$ out of $4$ .

$(2 - (\frac{3}{2 (2)} \cdot \frac{2}{5})) \div (\frac{3}{2} - \frac{1}{2}) \cdot (3 - \frac{1}{2})$

Step 2.2.2

Cancel the common factor.

$(2 - (\frac{3}{2 \cdot 2} \cdot \frac{2}{5})) \div (\frac{3}{2} - \frac{1}{2}) \cdot (3 - \frac{1}{2})$

Step 2.2.3

Rewrite the expression.

$(2 - (\frac{3}{2} \cdot \frac{1}{5})) \div (\frac{3}{2} - \frac{1}{2}) \cdot (3 - \frac{1}{2})$

Step 2.3

Multiply $\frac{3}{2}$ by $\frac{1}{5}$ .

$(2 - \frac{3}{2 \cdot 5}) \div (\frac{3}{2} - \frac{1}{2}) \cdot (3 - \frac{1}{2})$

Step 2.4

Multiply $2$ by $5$ .

$(2 - \frac{3}{10}) \div (\frac{3}{2} - \frac{1}{2}) \cdot (3 - \frac{1}{2})$

Step 2.5

To write $2$ as a fraction with a common denominator, multiply by $\frac{10}{10}$ .

$(2 \cdot \frac{10}{10} - \frac{3}{10}) \div (\frac{3}{2} - \frac{1}{2}) \cdot (3 - \frac{1}{2})$

Step 2.6

Combine $2$ and $\frac{10}{10}$ .

$(\frac{2 \cdot 10}{10} - \frac{3}{10}) \div (\frac{3}{2} - \frac{1}{2}) \cdot (3 - \frac{1}{2})$

Step 2.7

Combine the numerators over the common denominator.

$\frac{2 \cdot 10 - 3}{10} \div (\frac{3}{2} - \frac{1}{2}) \cdot (3 - \frac{1}{2})$

Step 2.8

Simplify the numerator.

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Step 2.8.1

Multiply $2$ by $10$ .

$\frac{20 - 3}{10} \div (\frac{3}{2} - \frac{1}{2}) \cdot (3 - \frac{1}{2})$

Step 2.8.2

Subtract $3$ from $20$ .

$\frac{17}{10} \div (\frac{3}{2} - \frac{1}{2}) \cdot (3 - \frac{1}{2})$

Step 3

Simplify the denominator.

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Step 3.1

Combine the numerators over the common denominator.

$\frac{17}{10} \div \frac{3 - 1}{2} \cdot (3 - \frac{1}{2})$

Step 3.2

Subtract $1$ from $3$ .

$\frac{17}{10} \div \frac{2}{2} \cdot (3 - \frac{1}{2})$

Step 3.3

Divide $2$ by $2$ .

$\frac{17}{10} \div 1 \cdot (3 - \frac{1}{2})$

Step 4

Rewrite the division as a fraction.

$\frac{\frac{17}{10}}{1} \cdot (3 - \frac{1}{2})$

Step 5

Divide $\frac{17}{10}$ by $1$ .

$\frac{17}{10} \cdot (3 - \frac{1}{2})$

Step 6

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

$\frac{17}{10} \cdot (3 \cdot \frac{2}{2} - \frac{1}{2})$

Step 7

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

$\frac{17}{10} \cdot (\frac{3 \cdot 2}{2} - \frac{1}{2})$

Step 8

Combine the numerators over the common denominator.

$\frac{17}{10} \cdot \frac{3 \cdot 2 - 1}{2}$

Step 9

Simplify the numerator.

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Step 9.1

Multiply $3$ by $2$ .

$\frac{17}{10} \cdot \frac{6 - 1}{2}$

Step 9.2

Subtract $1$ from $6$ .

$\frac{17}{10} \cdot \frac{5}{2}$

Step 10

Cancel the common factor of $5$ .

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Step 10.1

Factor $5$ out of $10$ .

$\frac{17}{5 (2)} \cdot \frac{5}{2}$

Step 10.2

Cancel the common factor.

$\frac{17}{5 \cdot 2} \cdot \frac{5}{2}$

Step 10.3

Rewrite the expression.

$\frac{17}{2} \cdot \frac{1}{2}$

Step 11

Multiply $\frac{17}{2}$ by $\frac{1}{2}$ .

$\frac{17}{2 \cdot 2}$

Step 12

Multiply $2$ by $2$ .

$\frac{17}{4}$

Step 13

The result can be shown in multiple forms.

Exact Form:

$\frac{17}{4}$

Decimal Form:

$4.25$

Mixed Number Form:

$4 \frac{1}{4}$