Solve 4+1/8-left(-10-6right)2/5+7--frac{1{4}-3}

$$\frac{ 4+ \frac{ 1 }{ 8 } - \left( -10-6 \right) 2 }{ 5+7-- \frac{ 1 }{ 4 } -3 }$$

Evaluate

$$\frac{289}{74}\approx 3.905405405$$

Solution Steps

Convert 4 to fraction \frac{32}{8}.

$$\frac{\frac{32}{8}+\frac{1}{8}-\left(-10-6\right)\times 2}{5+7-\left(-\frac{1}{4}\right)-3}$$

Since \frac{32}{8} and \frac{1}{8} have the same denominator, add them by adding their numerators.

$$\frac{\frac{32+1}{8}-\left(-10-6\right)\times 2}{5+7-\left(-\frac{1}{4}\right)-3}$$

Add 32 and 1 to get 33.

$$\frac{\frac{33}{8}-\left(-10-6\right)\times 2}{5+7-\left(-\frac{1}{4}\right)-3}$$

Subtract 6 from -10 to get -16.

$$\frac{\frac{33}{8}-\left(-16\times 2\right)}{5+7-\left(-\frac{1}{4}\right)-3}$$

Multiply -16 and 2 to get -32.

$$\frac{\frac{33}{8}-\left(-32\right)}{5+7-\left(-\frac{1}{4}\right)-3}$$

The opposite of -32 is 32.

$$\frac{\frac{33}{8}+32}{5+7-\left(-\frac{1}{4}\right)-3}$$

Convert 32 to fraction \frac{256}{8}.

$$\frac{\frac{33}{8}+\frac{256}{8}}{5+7-\left(-\frac{1}{4}\right)-3}$$

Since \frac{33}{8} and \frac{256}{8} have the same denominator, add them by adding their numerators.

$$\frac{\frac{33+256}{8}}{5+7-\left(-\frac{1}{4}\right)-3}$$

Add 33 and 256 to get 289.

$$\frac{\frac{289}{8}}{5+7-\left(-\frac{1}{4}\right)-3}$$

Add 5 and 7 to get 12.

$$\frac{\frac{289}{8}}{12-\left(-\frac{1}{4}\right)-3}$$

The opposite of -\frac{1}{4} is \frac{1}{4}.

$$\frac{\frac{289}{8}}{12+\frac{1}{4}-3}$$

Convert 12 to fraction \frac{48}{4}.

$$\frac{\frac{289}{8}}{\frac{48}{4}+\frac{1}{4}-3}$$

Since \frac{48}{4} and \frac{1}{4} have the same denominator, add them by adding their numerators.

$$\frac{\frac{289}{8}}{\frac{48+1}{4}-3}$$

Add 48 and 1 to get 49.

$$\frac{\frac{289}{8}}{\frac{49}{4}-3}$$

Convert 3 to fraction \frac{12}{4}.

$$\frac{\frac{289}{8}}{\frac{49}{4}-\frac{12}{4}}$$

Since \frac{49}{4} and \frac{12}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{289}{8}}{\frac{49-12}{4}}$$

Subtract 12 from 49 to get 37.

$$\frac{\frac{289}{8}}{\frac{37}{4}}$$

Divide \frac{289}{8} by \frac{37}{4} by multiplying \frac{289}{8} by the reciprocal of \frac{37}{4}.

$$\frac{289}{8}\times \frac{4}{37}$$

Multiply \frac{289}{8} times \frac{4}{37} by multiplying numerator times numerator and denominator times denominator.

$$\frac{289\times 4}{8\times 37}$$

Do the multiplications in the fraction \frac{289\times 4}{8\times 37}.

$$\frac{1156}{296}$$

Reduce the fraction \frac{1156}{296} to lowest terms by extracting and canceling out 4.

$$\frac{289}{74}$$

Factor

$$\frac{17 ^ {2}}{2 \cdot 37} = 3\frac{67}{74} = 3.9054054054054053$$