Basic Math Examples

$\frac{17}{\frac{\frac{25}{\frac{3}{5} - 4}}{\frac{1}{5} + \frac{1}{2}}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$17 \frac{\frac{1}{5} + \frac{1}{2}}{\frac{25}{\frac{3}{5} - 4}}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$17 ((\frac{1}{5} + \frac{1}{2}) \frac{\frac{3}{5} - 4}{25})$

Step 3

Simplify the numerator.

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Step 3.1

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

$17 ((\frac{1}{5} + \frac{1}{2}) \frac{\frac{3}{5} - 4 \cdot \frac{5}{5}}{25})$

Step 3.2

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

$17 ((\frac{1}{5} + \frac{1}{2}) \frac{\frac{3}{5} + \frac{- 4 \cdot 5}{5}}{25})$

Step 3.3

Combine the numerators over the common denominator.

$17 ((\frac{1}{5} + \frac{1}{2}) \frac{\frac{3 - 4 \cdot 5}{5}}{25})$

Step 3.4

Simplify the numerator.

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Step 3.4.1

Multiply $- 4$ by $5$ .

$17 ((\frac{1}{5} + \frac{1}{2}) \frac{\frac{3 - 20}{5}}{25})$

Step 3.4.2

Subtract $20$ from $3$ .

$17 ((\frac{1}{5} + \frac{1}{2}) \frac{\frac{- 17}{5}}{25})$

Step 3.5

Move the negative in front of the fraction.

$17 ((\frac{1}{5} + \frac{1}{2}) \frac{- \frac{17}{5}}{25})$

Step 4

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

$17 ((\frac{1}{5} \cdot \frac{2}{2} + \frac{1}{2}) \frac{- \frac{17}{5}}{25})$

Step 5

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

$17 ((\frac{1}{5} \cdot \frac{2}{2} + \frac{1}{2} \cdot \frac{5}{5}) \frac{- \frac{17}{5}}{25})$

Step 6

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

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Step 6.1

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

$17 ((\frac{2}{5 \cdot 2} + \frac{1}{2} \cdot \frac{5}{5}) \frac{- \frac{17}{5}}{25})$

Step 6.2

Multiply $5$ by $2$ .

$17 ((\frac{2}{10} + \frac{1}{2} \cdot \frac{5}{5}) \frac{- \frac{17}{5}}{25})$

Step 6.3

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

$17 ((\frac{2}{10} + \frac{5}{2 \cdot 5}) \frac{- \frac{17}{5}}{25})$

Step 6.4

Multiply $2$ by $5$ .

$17 ((\frac{2}{10} + \frac{5}{10}) \frac{- \frac{17}{5}}{25})$

Step 7

Combine the numerators over the common denominator.

$17 (\frac{2 + 5}{10} \cdot \frac{- \frac{17}{5}}{25})$

Step 8

Add $2$ and $5$ .

$17 (\frac{7}{10} \cdot \frac{- \frac{17}{5}}{25})$

Step 9

Multiply the numerator by the reciprocal of the denominator.

$17 (\frac{7}{10} (- \frac{17}{5} \cdot \frac{1}{25}))$

Step 10

Multiply $- \frac{17}{5} \cdot \frac{1}{25}$ .

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Step 10.1

Multiply $\frac{1}{25}$ by $\frac{17}{5}$ .

$17 (\frac{7}{10} (- \frac{17}{25 \cdot 5}))$

Step 10.2

Multiply $25$ by $5$ .

$17 (\frac{7}{10} (- \frac{17}{125}))$

Step 11

Multiply $\frac{7}{10} (- \frac{17}{125})$ .

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Step 11.1

Multiply $\frac{7}{10}$ by $\frac{17}{125}$ .

$17 (- \frac{7 \cdot 17}{10 \cdot 125})$

Step 11.2

Multiply $7$ by $17$ .

$17 (- \frac{119}{10 \cdot 125})$

Step 11.3

Multiply $10$ by $125$ .

$17 (- \frac{119}{1250})$

Step 12

Multiply $17 (- \frac{119}{1250})$ .

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Step 12.1

Multiply $- 1$ by $17$ .

$- 17 (\frac{119}{1250})$

Step 12.2

Combine $- 17$ and $\frac{119}{1250}$ .

$\frac{- 17 \cdot 119}{1250}$

Step 12.3

Multiply $- 17$ by $119$ .

$\frac{- 2023}{1250}$

Step 13

Move the negative in front of the fraction.

$- \frac{2023}{1250}$

Step 14

The result can be shown in multiple forms.

Exact Form:

$- \frac{2023}{1250}$

Decimal Form:

$- 1.6184$

Mixed Number Form:

$- 1 \frac{773}{1250}$