Basic Math Examples

$\frac{5}{36} \cdot 144 - \frac{3}{4} \div 12 \frac{1}{2}$

Step 1

Convert $12 \frac{1}{2}$ to an improper fraction.

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Step 1.1

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

$\frac{5}{36} \cdot 144 - \frac{3}{4} \div (12 + \frac{1}{2})$

Step 1.2

Add $12$ and $\frac{1}{2}$ .

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Step 1.2.1

To write $12$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{5}{36} \cdot 144 - \frac{3}{4} \div (12 \cdot \frac{2}{2} + \frac{1}{2})$

Step 1.2.2

Combine $12$ and $\frac{2}{2}$ .

$\frac{5}{36} \cdot 144 - \frac{3}{4} \div (\frac{12 \cdot 2}{2} + \frac{1}{2})$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{5}{36} \cdot 144 - \frac{3}{4} \div \frac{12 \cdot 2 + 1}{2}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $12$ by $2$ .

$\frac{5}{36} \cdot 144 - \frac{3}{4} \div \frac{24 + 1}{2}$

Step 1.2.4.2

Add $24$ and $1$ .

$\frac{5}{36} \cdot 144 - \frac{3}{4} \div \frac{25}{2}$

Step 2

Simplify each term.

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Step 2.1

Cancel the common factor of $36$ .

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Step 2.1.1

Factor $36$ out of $144$ .

$\frac{5}{36} \cdot (36 (4)) - \frac{3}{4} \div \frac{25}{2}$

Step 2.1.2

Cancel the common factor.

$\frac{5}{36} \cdot (36 \cdot 4) - \frac{3}{4} \div \frac{25}{2}$

Step 2.1.3

Rewrite the expression.

$5 \cdot 4 - \frac{3}{4} \div \frac{25}{2}$

Step 2.2

Multiply $5$ by $4$ .

$20 - \frac{3}{4} \div \frac{25}{2}$

Step 2.3

To divide by a fraction, multiply by its reciprocal.

$20 - (\frac{3}{4} \cdot \frac{2}{25})$

Step 2.4

Cancel the common factor of $2$ .

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Step 2.4.1

Factor $2$ out of $4$ .

$20 - (\frac{3}{2 (2)} \cdot \frac{2}{25})$

Step 2.4.2

Cancel the common factor.

$20 - (\frac{3}{2 \cdot 2} \cdot \frac{2}{25})$

Step 2.4.3

Rewrite the expression.

$20 - (\frac{3}{2} \cdot \frac{1}{25})$

Step 2.5

Multiply $\frac{3}{2}$ by $\frac{1}{25}$ .

$20 - \frac{3}{2 \cdot 25}$

Step 2.6

Multiply $2$ by $25$ .

$20 - \frac{3}{50}$

Step 3

To write $20$ as a fraction with a common denominator, multiply by $\frac{50}{50}$ .

$20 \cdot \frac{50}{50} - \frac{3}{50}$

Step 4

Combine $20$ and $\frac{50}{50}$ .

$\frac{20 \cdot 50}{50} - \frac{3}{50}$

Step 5

Combine the numerators over the common denominator.

$\frac{20 \cdot 50 - 3}{50}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $20$ by $50$ .

$\frac{1000 - 3}{50}$

Step 6.2

Subtract $3$ from $1000$ .

$\frac{997}{50}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{997}{50}$

Decimal Form:

$19.94$

Mixed Number Form:

$19 \frac{47}{50}$