Solve 2-4*2-3/6-8{5-14/frac{16{frac{20/48}}}}

$$2- \frac{ 4 \times 2-3 }{ \frac{ 6-8 }{ 5- \frac{ 14 }{ \frac{ 16 }{ \frac{ 20 }{ 48 } } } } }$$

Evaluate

$$\frac{2609}{192}\approx 13.588541667$$

Solution Steps

Multiply 4 and 2 to get 8.

$$2-\frac{8-3}{\frac{6-8}{5-\frac{14}{\frac{16}{\frac{20}{48}}}}}$$

Subtract 3 from 8 to get 5.

$$2-\frac{5}{\frac{6-8}{5-\frac{14}{\frac{16}{\frac{20}{48}}}}}$$

Subtract 8 from 6 to get -2.

$$2-\frac{5}{\frac{-2}{5-\frac{14}{\frac{16}{\frac{20}{48}}}}}$$

Divide 14 by \frac{16}{\frac{20}{48}} by multiplying 14 by the reciprocal of \frac{16}{\frac{20}{48}}.

$$2-\frac{5}{\frac{-2}{5-\frac{14\times \frac{20}{48}}{16}}}$$

Reduce the fraction \frac{20}{48} to lowest terms by extracting and canceling out 4.

$$2-\frac{5}{\frac{-2}{5-\frac{14\times \frac{5}{12}}{16}}}$$

Express 14\times \frac{5}{12} as a single fraction.

$$2-\frac{5}{\frac{-2}{5-\frac{\frac{14\times 5}{12}}{16}}}$$

Multiply 14 and 5 to get 70.

$$2-\frac{5}{\frac{-2}{5-\frac{\frac{70}{12}}{16}}}$$

Reduce the fraction \frac{70}{12} to lowest terms by extracting and canceling out 2.

$$2-\frac{5}{\frac{-2}{5-\frac{\frac{35}{6}}{16}}}$$

Express \frac{\frac{35}{6}}{16} as a single fraction.

$$2-\frac{5}{\frac{-2}{5-\frac{35}{6\times 16}}}$$

Multiply 6 and 16 to get 96.

$$2-\frac{5}{\frac{-2}{5-\frac{35}{96}}}$$

Convert 5 to fraction \frac{480}{96}.

$$2-\frac{5}{\frac{-2}{\frac{480}{96}-\frac{35}{96}}}$$

Since \frac{480}{96} and \frac{35}{96} have the same denominator, subtract them by subtracting their numerators.

$$2-\frac{5}{\frac{-2}{\frac{480-35}{96}}}$$

Subtract 35 from 480 to get 445.

$$2-\frac{5}{\frac{-2}{\frac{445}{96}}}$$

Divide -2 by \frac{445}{96} by multiplying -2 by the reciprocal of \frac{445}{96}.

$$2-\frac{5}{-2\times \frac{96}{445}}$$

Express -2\times \frac{96}{445} as a single fraction.

$$2-\frac{5}{\frac{-2\times 96}{445}}$$

Multiply -2 and 96 to get -192.

$$2-\frac{5}{\frac{-192}{445}}$$

Fraction \frac{-192}{445} can be rewritten as -\frac{192}{445} by extracting the negative sign.

$$2-\frac{5}{-\frac{192}{445}}$$

Divide 5 by -\frac{192}{445} by multiplying 5 by the reciprocal of -\frac{192}{445}.

$$2-5\left(-\frac{445}{192}\right)$$

Express 5\left(-\frac{445}{192}\right) as a single fraction.

$$2-\frac{5\left(-445\right)}{192}$$

Multiply 5 and -445 to get -2225.

$$2-\frac{-2225}{192}$$

Fraction \frac{-2225}{192} can be rewritten as -\frac{2225}{192} by extracting the negative sign.

$$2-\left(-\frac{2225}{192}\right)$$

The opposite of -\frac{2225}{192} is \frac{2225}{192}.

$$2+\frac{2225}{192}$$

Convert 2 to fraction \frac{384}{192}.

$$\frac{384}{192}+\frac{2225}{192}$$

Since \frac{384}{192} and \frac{2225}{192} have the same denominator, add them by adding their numerators.

$$\frac{384+2225}{192}$$

Add 384 and 2225 to get 2609.

$$\frac{2609}{192}$$

Factor

$$\frac{2609}{2 ^ {6} \cdot 3} = 13\frac{113}{192} = 13.588541666666666$$