Basic Math Examples

$\frac{11}{\frac{10}{\frac{19}{20}}} - \frac{1}{\frac{20}{\frac{8}{5}}}$

Step 1

Simplify each term.

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Step 1.1

Multiply the numerator by the reciprocal of the denominator.

$11 \frac{\frac{19}{20}}{10} - \frac{1}{\frac{20}{\frac{8}{5}}}$

Step 1.2

Multiply the numerator by the reciprocal of the denominator.

$11 (\frac{19}{20} \cdot \frac{1}{10}) - \frac{1}{\frac{20}{\frac{8}{5}}}$

Step 1.3

Multiply $\frac{19}{20} \cdot \frac{1}{10}$ .

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Step 1.3.1

Multiply $\frac{19}{20}$ by $\frac{1}{10}$ .

$11 \frac{19}{20 \cdot 10} - \frac{1}{\frac{20}{\frac{8}{5}}}$

Step 1.3.2

Multiply $20$ by $10$ .

$11 (\frac{19}{200}) - \frac{1}{\frac{20}{\frac{8}{5}}}$

Step 1.4

Multiply $11 (\frac{19}{200})$ .

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Step 1.4.1

Combine $11$ and $\frac{19}{200}$ .

$\frac{11 \cdot 19}{200} - \frac{1}{\frac{20}{\frac{8}{5}}}$

Step 1.4.2

Multiply $11$ by $19$ .

$\frac{209}{200} - \frac{1}{\frac{20}{\frac{8}{5}}}$

Step 1.5

Multiply the numerator by the reciprocal of the denominator.

$\frac{209}{200} - (1 \frac{\frac{8}{5}}{20})$

Step 1.6

Multiply $\frac{\frac{8}{5}}{20}$ by $1$ .

$\frac{209}{200} - \frac{\frac{8}{5}}{20}$

Step 1.7

Multiply the numerator by the reciprocal of the denominator.

$\frac{209}{200} - (\frac{8}{5} \cdot \frac{1}{20})$

Step 1.8

Cancel the common factor of $4$ .

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Step 1.8.1

Factor $4$ out of $8$ .

$\frac{209}{200} - (\frac{4 (2)}{5} \cdot \frac{1}{20})$

Step 1.8.2

Factor $4$ out of $20$ .

$\frac{209}{200} - (\frac{4 \cdot 2}{5} \cdot \frac{1}{4 \cdot 5})$

Step 1.8.3

Cancel the common factor.

$\frac{209}{200} - (\frac{4 \cdot 2}{5} \cdot \frac{1}{4 \cdot 5})$

Step 1.8.4

Rewrite the expression.

$\frac{209}{200} - (\frac{2}{5} \cdot \frac{1}{5})$

Step 1.9

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

$\frac{209}{200} - \frac{2}{5 \cdot 5}$

Step 1.10

Multiply $5$ by $5$ .

$\frac{209}{200} - \frac{2}{25}$

Step 2

To write $- \frac{2}{25}$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$\frac{209}{200} - \frac{2}{25} \cdot \frac{8}{8}$

Step 3

Write each expression with a common denominator of $200$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{2}{25}$ by $\frac{8}{8}$ .

$\frac{209}{200} - \frac{2 \cdot 8}{25 \cdot 8}$

Step 3.2

Multiply $25$ by $8$ .

$\frac{209}{200} - \frac{2 \cdot 8}{200}$

Step 4

Combine the numerators over the common denominator.

$\frac{209 - 2 \cdot 8}{200}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $- 2$ by $8$ .

$\frac{209 - 16}{200}$

Step 5.2

Subtract $16$ from $209$ .

$\frac{193}{200}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{193}{200}$

Decimal Form:

$0.965$