Basic Math Examples

$(\frac{2}{15} + \frac{3}{2}) (\frac{1}{2} - \frac{1}{8}) - \frac{1}{80}$

Step 1

Simplify each term.

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Step 1.1

To write $\frac{2}{15}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$(\frac{2}{15} \cdot \frac{2}{2} + \frac{3}{2}) (\frac{1}{2} - \frac{1}{8}) - \frac{1}{80}$

Step 1.2

To write $\frac{3}{2}$ as a fraction with a common denominator, multiply by $\frac{15}{15}$ .

$(\frac{2}{15} \cdot \frac{2}{2} + \frac{3}{2} \cdot \frac{15}{15}) (\frac{1}{2} - \frac{1}{8}) - \frac{1}{80}$

Step 1.3

Write each expression with a common denominator of $30$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.3.1

Multiply $\frac{2}{15}$ by $\frac{2}{2}$ .

$(\frac{2 \cdot 2}{15 \cdot 2} + \frac{3}{2} \cdot \frac{15}{15}) (\frac{1}{2} - \frac{1}{8}) - \frac{1}{80}$

Step 1.3.2

Multiply $15$ by $2$ .

$(\frac{2 \cdot 2}{30} + \frac{3}{2} \cdot \frac{15}{15}) (\frac{1}{2} - \frac{1}{8}) - \frac{1}{80}$

Step 1.3.3

Multiply $\frac{3}{2}$ by $\frac{15}{15}$ .

$(\frac{2 \cdot 2}{30} + \frac{3 \cdot 15}{2 \cdot 15}) (\frac{1}{2} - \frac{1}{8}) - \frac{1}{80}$

Step 1.3.4

Multiply $2$ by $15$ .

$(\frac{2 \cdot 2}{30} + \frac{3 \cdot 15}{30}) (\frac{1}{2} - \frac{1}{8}) - \frac{1}{80}$

Step 1.4

Combine the numerators over the common denominator.

$\frac{2 \cdot 2 + 3 \cdot 15}{30} (\frac{1}{2} - \frac{1}{8}) - \frac{1}{80}$

Step 1.5

Simplify the numerator.

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Step 1.5.1

Multiply $2$ by $2$ .

$\frac{4 + 3 \cdot 15}{30} (\frac{1}{2} - \frac{1}{8}) - \frac{1}{80}$

Step 1.5.2

Multiply $3$ by $15$ .

$\frac{4 + 45}{30} (\frac{1}{2} - \frac{1}{8}) - \frac{1}{80}$

Step 1.5.3

Add $4$ and $45$ .

$\frac{49}{30} (\frac{1}{2} - \frac{1}{8}) - \frac{1}{80}$

Step 1.6

To write $\frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{49}{30} (\frac{1}{2} \cdot \frac{4}{4} - \frac{1}{8}) - \frac{1}{80}$

Step 1.7

Write each expression with a common denominator of $8$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.7.1

Multiply $\frac{1}{2}$ by $\frac{4}{4}$ .

$\frac{49}{30} (\frac{4}{2 \cdot 4} - \frac{1}{8}) - \frac{1}{80}$

Step 1.7.2

Multiply $2$ by $4$ .

$\frac{49}{30} (\frac{4}{8} - \frac{1}{8}) - \frac{1}{80}$

Step 1.8

Combine the numerators over the common denominator.

$\frac{49}{30} \cdot \frac{4 - 1}{8} - \frac{1}{80}$

Step 1.9

Subtract $1$ from $4$ .

$\frac{49}{30} \cdot \frac{3}{8} - \frac{1}{80}$

Step 1.10

Cancel the common factor of $3$ .

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Step 1.10.1

Factor $3$ out of $30$ .

$\frac{49}{3 (10)} \cdot \frac{3}{8} - \frac{1}{80}$

Step 1.10.2

Cancel the common factor.

$\frac{49}{3 \cdot 10} \cdot \frac{3}{8} - \frac{1}{80}$

Step 1.10.3

Rewrite the expression.

$\frac{49}{10} \cdot \frac{1}{8} - \frac{1}{80}$

Step 1.11

Multiply $\frac{49}{10}$ by $\frac{1}{8}$ .

$\frac{49}{10 \cdot 8} - \frac{1}{80}$

Step 1.12

Multiply $10$ by $8$ .

$\frac{49}{80} - \frac{1}{80}$

Step 2

Simplify terms.

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Step 2.1

Combine the numerators over the common denominator.

$\frac{49 - 1}{80}$

Step 2.2

Subtract $1$ from $49$ .

$\frac{48}{80}$

Step 2.3

Cancel the common factor of $48$ and $80$ .

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Step 2.3.1

Factor $16$ out of $48$ .

$\frac{16 (3)}{80}$

Step 2.3.2

Cancel the common factors.

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Step 2.3.2.1

Factor $16$ out of $80$ .

$\frac{16 \cdot 3}{16 \cdot 5}$

Step 2.3.2.2

Cancel the common factor.

$\frac{16 \cdot 3}{16 \cdot 5}$

Step 2.3.2.3

Rewrite the expression.

$\frac{3}{5}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{3}{5}$

Decimal Form:

$0.6$