Basic Math Examples

$\frac{1}{10} \div \frac{1}{5} \cdot \frac{1}{2} + \frac{1}{8} \cdot (\frac{4}{5} - \frac{1}{2}) + (\frac{1}{8} - \frac{1}{4})$

Step 1

Remove parentheses.

$\frac{1}{10} \div \frac{1}{5} \cdot \frac{1}{2} + \frac{1}{8} \cdot (\frac{4}{5} - \frac{1}{2}) + \frac{1}{8} - \frac{1}{4}$

Step 2

Simplify each term.

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Step 2.1

To divide by a fraction, multiply by its reciprocal.

$\frac{1}{10} \cdot 5 \cdot \frac{1}{2} + \frac{1}{8} \cdot (\frac{4}{5} - \frac{1}{2}) + \frac{1}{8} - \frac{1}{4}$

Step 2.2

Cancel the common factor of $5$ .

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Step 2.2.1

Factor $5$ out of $10$ .

$\frac{1}{5 (2)} \cdot 5 \cdot \frac{1}{2} + \frac{1}{8} \cdot (\frac{4}{5} - \frac{1}{2}) + \frac{1}{8} - \frac{1}{4}$

Step 2.2.2

Cancel the common factor.

$\frac{1}{5 \cdot 2} \cdot 5 \cdot \frac{1}{2} + \frac{1}{8} \cdot (\frac{4}{5} - \frac{1}{2}) + \frac{1}{8} - \frac{1}{4}$

Step 2.2.3

Rewrite the expression.

$\frac{1}{2} \cdot \frac{1}{2} + \frac{1}{8} \cdot (\frac{4}{5} - \frac{1}{2}) + \frac{1}{8} - \frac{1}{4}$

Step 2.3

Multiply $\frac{1}{2} \cdot \frac{1}{2}$ .

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Step 2.3.1

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

$\frac{1}{2 \cdot 2} + \frac{1}{8} \cdot (\frac{4}{5} - \frac{1}{2}) + \frac{1}{8} - \frac{1}{4}$

Step 2.3.2

Multiply $2$ by $2$ .

$\frac{1}{4} + \frac{1}{8} \cdot (\frac{4}{5} - \frac{1}{2}) + \frac{1}{8} - \frac{1}{4}$

Step 2.4

To write $\frac{4}{5}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{1}{4} + \frac{1}{8} \cdot (\frac{4}{5} \cdot \frac{2}{2} - \frac{1}{2}) + \frac{1}{8} - \frac{1}{4}$

Step 2.5

To write $- \frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{1}{4} + \frac{1}{8} \cdot (\frac{4}{5} \cdot \frac{2}{2} - \frac{1}{2} \cdot \frac{5}{5}) + \frac{1}{8} - \frac{1}{4}$

Step 2.6

Write each expression with a common denominator of $10$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.6.1

Multiply $\frac{4}{5}$ by $\frac{2}{2}$ .

$\frac{1}{4} + \frac{1}{8} \cdot (\frac{4 \cdot 2}{5 \cdot 2} - \frac{1}{2} \cdot \frac{5}{5}) + \frac{1}{8} - \frac{1}{4}$

Step 2.6.2

Multiply $5$ by $2$ .

$\frac{1}{4} + \frac{1}{8} \cdot (\frac{4 \cdot 2}{10} - \frac{1}{2} \cdot \frac{5}{5}) + \frac{1}{8} - \frac{1}{4}$

Step 2.6.3

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

$\frac{1}{4} + \frac{1}{8} \cdot (\frac{4 \cdot 2}{10} - \frac{5}{2 \cdot 5}) + \frac{1}{8} - \frac{1}{4}$

Step 2.6.4

Multiply $2$ by $5$ .

$\frac{1}{4} + \frac{1}{8} \cdot (\frac{4 \cdot 2}{10} - \frac{5}{10}) + \frac{1}{8} - \frac{1}{4}$

Step 2.7

Combine the numerators over the common denominator.

$\frac{1}{4} + \frac{1}{8} \cdot \frac{4 \cdot 2 - 5}{10} + \frac{1}{8} - \frac{1}{4}$

Step 2.8

Simplify the numerator.

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Step 2.8.1

Multiply $4$ by $2$ .

$\frac{1}{4} + \frac{1}{8} \cdot \frac{8 - 5}{10} + \frac{1}{8} - \frac{1}{4}$

Step 2.8.2

Subtract $5$ from $8$ .

$\frac{1}{4} + \frac{1}{8} \cdot \frac{3}{10} + \frac{1}{8} - \frac{1}{4}$

Step 2.9

Multiply $\frac{1}{8} \cdot \frac{3}{10}$ .

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Step 2.9.1

Multiply $\frac{1}{8}$ by $\frac{3}{10}$ .

$\frac{1}{4} + \frac{3}{8 \cdot 10} + \frac{1}{8} - \frac{1}{4}$

Step 2.9.2

Multiply $8$ by $10$ .

$\frac{1}{4} + \frac{3}{80} + \frac{1}{8} - \frac{1}{4}$

Step 3

Combine fractions.

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Step 3.1

Combine the numerators over the common denominator.

$\frac{1 - 1}{4} + \frac{3}{80} + \frac{1}{8}$

Step 3.2

Subtract $1$ from $1$ .

$\frac{0}{4} + \frac{3}{80} + \frac{1}{8}$

Step 4

Find the common denominator.

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Step 4.1

Multiply $\frac{0}{4}$ by $\frac{20}{20}$ .

$\frac{0}{4} \cdot \frac{20}{20} + \frac{3}{80} + \frac{1}{8}$

Step 4.2

Multiply $\frac{0}{4}$ by $\frac{20}{20}$ .

$\frac{0 \cdot 20}{4 \cdot 20} + \frac{3}{80} + \frac{1}{8}$

Step 4.3

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

$\frac{0 \cdot 20}{4 \cdot 20} + \frac{3}{80} + \frac{1}{8} \cdot \frac{10}{10}$

Step 4.4

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

$\frac{0 \cdot 20}{4 \cdot 20} + \frac{3}{80} + \frac{10}{8 \cdot 10}$

Step 4.5

Multiply $4$ by $20$ .

$\frac{0 \cdot 20}{80} + \frac{3}{80} + \frac{10}{8 \cdot 10}$

Step 4.6

Multiply $8$ by $10$ .

$\frac{0 \cdot 20}{80} + \frac{3}{80} + \frac{10}{80}$

Step 5

Combine the numerators over the common denominator.

$\frac{0 \cdot 20 + 3 + 10}{80}$

Step 6

Simplify the expression.

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Step 6.1

Multiply $0$ by $20$ .

$\frac{0 + 3 + 10}{80}$

Step 6.2

Add $0$ and $3$ .

$\frac{3 + 10}{80}$

Step 6.3

Add $3$ and $10$ .

$\frac{13}{80}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{13}{80}$

Decimal Form:

$0.1625$