Basic Math Examples

$\frac{\sqrt{16}}{- 5} - \frac{- 5}{16}$

Step 1

Simplify each term.

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Step 1.1

Simplify the numerator.

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Step 1.1.1

Rewrite $16$ as $4^{2}$ .

$\frac{\sqrt{4^{2}}}{- 5} - \frac{- 5}{16}$

Step 1.1.2

Pull terms out from under the radical, assuming positive real numbers.

$\frac{4}{- 5} - \frac{- 5}{16}$

Step 1.2

Move the negative in front of the fraction.

$- \frac{4}{5} - \frac{- 5}{16}$

Step 1.3

Move the negative in front of the fraction.

$- \frac{4}{5} - - \frac{5}{16}$

Step 1.4

Multiply $- - \frac{5}{16}$ .

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Step 1.4.1

Multiply $- 1$ by $- 1$ .

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

Step 1.4.2

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

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

Step 2

To write $- \frac{4}{5}$ as a fraction with a common denominator, multiply by $\frac{16}{16}$ .

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

Step 3

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

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

Step 4

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

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Step 4.1

Multiply $\frac{4}{5}$ by $\frac{16}{16}$ .

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

Step 4.2

Multiply $5$ by $16$ .

$- \frac{4 \cdot 16}{80} + \frac{5}{16} \cdot \frac{5}{5}$

Step 4.3

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

$- \frac{4 \cdot 16}{80} + \frac{5 \cdot 5}{16 \cdot 5}$

Step 4.4

Multiply $16$ by $5$ .

$- \frac{4 \cdot 16}{80} + \frac{5 \cdot 5}{80}$

Step 5

Combine the numerators over the common denominator.

$\frac{- 4 \cdot 16 + 5 \cdot 5}{80}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $- 4$ by $16$ .

$\frac{- 64 + 5 \cdot 5}{80}$

Step 6.2

Multiply $5$ by $5$ .

$\frac{- 64 + 25}{80}$

Step 6.3

Add $- 64$ and $25$ .

$\frac{- 39}{80}$

Step 7

Move the negative in front of the fraction.

$- \frac{39}{80}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$- \frac{39}{80}$

Decimal Form:

$- 0.4875$