Basic Math Examples

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

Step 1

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

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

Step 2

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

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

Step 3

Combine the numerators over the common denominator.

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

Step 4

Simplify the numerator.

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Step 4.1

Multiply $- 4$ by $5$ .

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

Step 4.2

Subtract $20$ from $3$ .

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

Step 5

Simplify each term.

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Step 5.1

To divide by a fraction, multiply by its reciprocal.

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

Step 5.2

Move the negative in front of the fraction.

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

Step 5.3

Simplify the denominator.

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Step 5.3.1

Multiply the numerator by the reciprocal of the denominator.

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

Step 5.3.2

Multiply $25 (- \frac{5}{17})$ .

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Step 5.3.2.1

Multiply $- 1$ by $25$ .

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

Step 5.3.2.2

Combine $- 25$ and $\frac{5}{17}$ .

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

Step 5.3.2.3

Multiply $- 25$ by $5$ .

$\frac{17}{\frac{- 125}{17}} \cdot 5 + \frac{1}{2}$

Step 5.3.3

Move the negative in front of the fraction.

$\frac{17}{- \frac{125}{17}} \cdot 5 + \frac{1}{2}$

Step 5.4

Multiply the numerator by the reciprocal of the denominator.

$17 (- \frac{17}{125}) \cdot 5 + \frac{1}{2}$

Step 5.5

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

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Step 5.5.1

Multiply $- 1$ by $17$ .

$- 17 (\frac{17}{125}) \cdot 5 + \frac{1}{2}$

Step 5.5.2

Combine $- 17$ and $\frac{17}{125}$ .

$\frac{- 17 \cdot 17}{125} \cdot 5 + \frac{1}{2}$

Step 5.5.3

Multiply $- 17$ by $17$ .

$\frac{- 289}{125} \cdot 5 + \frac{1}{2}$

Step 5.6

Cancel the common factor of $5$ .

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Step 5.6.1

Factor $5$ out of $125$ .

$\frac{- 289}{5 (25)} \cdot 5 + \frac{1}{2}$

Step 5.6.2

Cancel the common factor.

$\frac{- 289}{5 \cdot 25} \cdot 5 + \frac{1}{2}$

Step 5.6.3

Rewrite the expression.

$\frac{- 289}{25} + \frac{1}{2}$

Step 5.7

Move the negative in front of the fraction.

$- \frac{289}{25} + \frac{1}{2}$

Step 6

To write $- \frac{289}{25}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{289}{25} \cdot \frac{2}{2} + \frac{1}{2}$

Step 7

To write $\frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{25}{25}$ .

$- \frac{289}{25} \cdot \frac{2}{2} + \frac{1}{2} \cdot \frac{25}{25}$

Step 8

Write each expression with a common denominator of $50$ , by multiplying each by an appropriate factor of $1$ .

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Step 8.1

Multiply $\frac{289}{25}$ by $\frac{2}{2}$ .

$- \frac{289 \cdot 2}{25 \cdot 2} + \frac{1}{2} \cdot \frac{25}{25}$

Step 8.2

Multiply $25$ by $2$ .

$- \frac{289 \cdot 2}{50} + \frac{1}{2} \cdot \frac{25}{25}$

Step 8.3

Multiply $\frac{1}{2}$ by $\frac{25}{25}$ .

$- \frac{289 \cdot 2}{50} + \frac{25}{2 \cdot 25}$

Step 8.4

Multiply $2$ by $25$ .

$- \frac{289 \cdot 2}{50} + \frac{25}{50}$

Step 9

Combine the numerators over the common denominator.

$\frac{- 289 \cdot 2 + 25}{50}$

Step 10

Simplify the numerator.

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Step 10.1

Multiply $- 289$ by $2$ .

$\frac{- 578 + 25}{50}$

Step 10.2

Add $- 578$ and $25$ .

$\frac{- 553}{50}$

Step 11

Move the negative in front of the fraction.

$- \frac{553}{50}$

Step 12

The result can be shown in multiple forms.

Exact Form:

$- \frac{553}{50}$

Decimal Form:

$- 11.06$

Mixed Number Form:

$- 11 \frac{3}{50}$