Basic Math Examples

$\frac{1}{4} \cdot \frac{1}{20} \div \frac{1}{5} + (\frac{1}{4} - \frac{1}{5})$

Step 1

Remove parentheses.

$\frac{1}{4} \cdot \frac{1}{20} \div \frac{1}{5} + \frac{1}{4} - \frac{1}{5}$

Step 2

Find the common denominator.

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Step 2.1

Multiply $\frac{1}{4} \cdot \frac{1}{20} \div \frac{1}{5}$ by $\frac{20}{20}$ .

$\frac{1}{4} \cdot \frac{1}{20} \div \frac{1}{5} \cdot \frac{20}{20} + \frac{1}{4} - \frac{1}{5}$

Step 2.2

Multiply $\frac{1}{4} \cdot \frac{1}{20} \div \frac{1}{5}$ by $\frac{20}{20}$ .

$\frac{\frac{1}{4} \cdot \frac{1}{20} \cdot 20}{\frac{1}{5} \cdot 20} + \frac{1}{4} - \frac{1}{5}$

Step 2.3

Multiply $\frac{1}{4}$ by $\frac{\frac{5}{5}}{\frac{5}{5}}$ .

$\frac{\frac{1}{4} \cdot \frac{1}{20} \cdot 20}{\frac{1}{5} \cdot 20} + \frac{1}{4} \cdot \frac{\frac{5}{5}}{\frac{5}{5}} - \frac{1}{5}$

Step 2.4

Multiply $\frac{1}{4}$ by $\frac{\frac{5}{5}}{\frac{5}{5}}$ .

$\frac{\frac{1}{4} \cdot \frac{1}{20} \cdot 20}{\frac{1}{5} \cdot 20} + \frac{\frac{5}{5}}{4 (\frac{5}{5})} - \frac{1}{5}$

Step 2.5

Multiply $\frac{1}{5}$ by $\frac{\frac{4}{5}}{\frac{4}{5}}$ .

$\frac{\frac{1}{4} \cdot \frac{1}{20} \cdot 20}{\frac{1}{5} \cdot 20} + \frac{\frac{5}{5}}{4 (\frac{5}{5})} - (\frac{1}{5} \cdot \frac{\frac{4}{5}}{\frac{4}{5}})$

Step 2.6

Multiply $\frac{1}{5}$ by $\frac{\frac{4}{5}}{\frac{4}{5}}$ .

$\frac{\frac{1}{4} \cdot \frac{1}{20} \cdot 20}{\frac{1}{5} \cdot 20} + \frac{\frac{5}{5}}{4 (\frac{5}{5})} - \frac{\frac{4}{5}}{5 (\frac{4}{5})}$

Step 2.7

Combine $4$ and $\frac{5}{5}$ .

$\frac{\frac{1}{4} \cdot \frac{1}{20} \cdot 20}{\frac{1}{5} \cdot 20} + \frac{\frac{5}{5}}{\frac{4 \cdot 5}{5}} - \frac{\frac{4}{5}}{5 (\frac{4}{5})}$

Step 2.8

Multiply $4$ by $5$ .

$\frac{\frac{1}{4} \cdot \frac{1}{20} \cdot 20}{\frac{1}{5} \cdot 20} + \frac{\frac{5}{5}}{\frac{20}{5}} - \frac{\frac{4}{5}}{5 (\frac{4}{5})}$

Step 2.9

Combine $5$ and $\frac{4}{5}$ .

$\frac{\frac{1}{4} \cdot \frac{1}{20} \cdot 20}{\frac{1}{5} \cdot 20} + \frac{\frac{5}{5}}{\frac{20}{5}} - \frac{\frac{4}{5}}{\frac{5 \cdot 4}{5}}$

Step 2.10

Multiply $5$ by $4$ .

$\frac{\frac{1}{4} \cdot \frac{1}{20} \cdot 20}{\frac{1}{5} \cdot 20} + \frac{\frac{5}{5}}{\frac{20}{5}} - \frac{\frac{4}{5}}{\frac{20}{5}}$

Step 3

Combine fractions.

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Step 3.1

Combine the numerators over the common denominator.

$\frac{\frac{1}{4} \cdot \frac{1}{20} \cdot 20}{20 (\frac{1}{5})} + \frac{\frac{5}{5} - \frac{4}{5}}{\frac{20}{5}}$

Step 3.2

Combine the numerators over the common denominator.

$\frac{\frac{1}{4} \cdot \frac{1}{20} \cdot 20}{20 (\frac{1}{5})} + \frac{\frac{5 - 4}{5}}{\frac{20}{5}}$

Step 3.3

Subtract $4$ from $5$ .

$\frac{\frac{1}{4} \cdot \frac{1}{20} \cdot 20}{20 (\frac{1}{5})} + \frac{\frac{1}{5}}{\frac{20}{5}}$

Step 4

Simplify each term.

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Step 4.1

Cancel the common factor of $20$ .

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Step 4.1.1

Cancel the common factor.

$\frac{\frac{1}{4} \cdot \frac{1}{20} \cdot 20}{20 (\frac{1}{5})} + \frac{\frac{1}{5}}{\frac{20}{5}}$

Step 4.1.2

Rewrite the expression.

$\frac{\frac{1}{4} \cdot \frac{1}{20}}{\frac{1}{5}} + \frac{\frac{1}{5}}{\frac{20}{5}}$

Step 4.2

Multiply the numerator by the reciprocal of the denominator.

$\frac{1}{4} \cdot \frac{1}{20} \cdot 5 + \frac{\frac{1}{5}}{\frac{20}{5}}$

Step 4.3

Multiply $\frac{1}{4} \cdot \frac{1}{20} \cdot 5$ .

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Step 4.3.1

Multiply $\frac{1}{4}$ by $\frac{1}{20}$ .

$\frac{1}{4 \cdot 20} \cdot 5 + \frac{\frac{1}{5}}{\frac{20}{5}}$

Step 4.3.2

Multiply $4$ by $20$ .

$\frac{1}{80} \cdot 5 + \frac{\frac{1}{5}}{\frac{20}{5}}$

Step 4.3.3

Combine $\frac{1}{80}$ and $5$ .

$\frac{5}{80} + \frac{\frac{1}{5}}{\frac{20}{5}}$

Step 4.4

Cancel the common factor of $5$ and $80$ .

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Step 4.4.1

Factor $5$ out of $5$ .

$\frac{5 (1)}{80} + \frac{\frac{1}{5}}{\frac{20}{5}}$

Step 4.4.2

Cancel the common factors.

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Step 4.4.2.1

Factor $5$ out of $80$ .

$\frac{5 \cdot 1}{5 \cdot 16} + \frac{\frac{1}{5}}{\frac{20}{5}}$

Step 4.4.2.2

Cancel the common factor.

$\frac{5 \cdot 1}{5 \cdot 16} + \frac{\frac{1}{5}}{\frac{20}{5}}$

Step 4.4.2.3

Rewrite the expression.

$\frac{1}{16} + \frac{\frac{1}{5}}{\frac{20}{5}}$

Step 4.5

Cancel the common factor of $20$ and $5$ .

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Step 4.5.1

Factor $5$ out of $20$ .

$\frac{1}{16} + \frac{\frac{1}{5}}{\frac{5 \cdot 4}{5}}$

Step 4.5.2

Cancel the common factors.

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Step 4.5.2.1

Factor $5$ out of $5$ .

$\frac{1}{16} + \frac{\frac{1}{5}}{\frac{5 \cdot 4}{5 (1)}}$

Step 4.5.2.2

Cancel the common factor.

$\frac{1}{16} + \frac{\frac{1}{5}}{\frac{5 \cdot 4}{5 \cdot 1}}$

Step 4.5.2.3

Rewrite the expression.

$\frac{1}{16} + \frac{\frac{1}{5}}{\frac{4}{1}}$

Step 4.5.2.4

Divide $4$ by $1$ .

$\frac{1}{16} + \frac{\frac{1}{5}}{4}$

Step 4.6

Multiply the numerator by the reciprocal of the denominator.

$\frac{1}{16} + \frac{1}{5} \cdot \frac{1}{4}$

Step 4.7

Multiply $\frac{1}{5} \cdot \frac{1}{4}$ .

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Step 4.7.1

Multiply $\frac{1}{5}$ by $\frac{1}{4}$ .

$\frac{1}{16} + \frac{1}{5 \cdot 4}$

Step 4.7.2

Multiply $5$ by $4$ .

$\frac{1}{16} + \frac{1}{20}$

Step 5

To write $\frac{1}{16}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{1}{16} \cdot \frac{5}{5} + \frac{1}{20}$

Step 6

To write $\frac{1}{20}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{1}{16} \cdot \frac{5}{5} + \frac{1}{20} \cdot \frac{4}{4}$

Step 7

Write each expression with a common denominator of $80$ , by multiplying each by an appropriate factor of $1$ .

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Step 7.1

Multiply $\frac{1}{16}$ by $\frac{5}{5}$ .

$\frac{5}{16 \cdot 5} + \frac{1}{20} \cdot \frac{4}{4}$

Step 7.2

Multiply $16$ by $5$ .

$\frac{5}{80} + \frac{1}{20} \cdot \frac{4}{4}$

Step 7.3

Multiply $\frac{1}{20}$ by $\frac{4}{4}$ .

$\frac{5}{80} + \frac{4}{20 \cdot 4}$

Step 7.4

Multiply $20$ by $4$ .

$\frac{5}{80} + \frac{4}{80}$

Step 8

Combine the numerators over the common denominator.

$\frac{5 + 4}{80}$

Step 9

Add $5$ and $4$ .

$\frac{9}{80}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$\frac{9}{80}$

Decimal Form:

$0.1125$