Solve -(-87/6)-(-7sqrt{4})+(-64/7)+1-53/14

$$- ( - 8 \frac { 7 } { 6 } ) - ( - 7 \sqrt { 4 } ) + ( - 6 \frac { 4 } { 7 } ) + 1 - 5 \frac { 3 } { 14 }$$

Evaluate

$$\frac{260}{21}\approx 12.380952381$$

Solution Steps

Multiply 8 and 6 to get 48.

$$-\left(-\frac{48+7}{6}\right)-\left(-7\sqrt{4}\right)-\frac{6\times 7+4}{7}+1-\frac{5\times 14+3}{14}$$

Add 48 and 7 to get 55.

$$-\left(-\frac{55}{6}\right)-\left(-7\sqrt{4}\right)-\frac{6\times 7+4}{7}+1-\frac{5\times 14+3}{14}$$

The opposite of -\frac{55}{6} is \frac{55}{6}.

$$\frac{55}{6}-\left(-7\sqrt{4}\right)-\frac{6\times 7+4}{7}+1-\frac{5\times 14+3}{14}$$

Calculate the square root of 4 and get 2.

$$\frac{55}{6}-\left(-7\times 2\right)-\frac{6\times 7+4}{7}+1-\frac{5\times 14+3}{14}$$

Multiply -7 and 2 to get -14.

$$\frac{55}{6}-\left(-14\right)-\frac{6\times 7+4}{7}+1-\frac{5\times 14+3}{14}$$

The opposite of -14 is 14.

$$\frac{55}{6}+14-\frac{6\times 7+4}{7}+1-\frac{5\times 14+3}{14}$$

Convert 14 to fraction \frac{84}{6}.

$$\frac{55}{6}+\frac{84}{6}-\frac{6\times 7+4}{7}+1-\frac{5\times 14+3}{14}$$

Since \frac{55}{6} and \frac{84}{6} have the same denominator, add them by adding their numerators.

$$\frac{55+84}{6}-\frac{6\times 7+4}{7}+1-\frac{5\times 14+3}{14}$$

Add 55 and 84 to get 139.

$$\frac{139}{6}-\frac{6\times 7+4}{7}+1-\frac{5\times 14+3}{14}$$

Multiply 6 and 7 to get 42.

$$\frac{139}{6}-\frac{42+4}{7}+1-\frac{5\times 14+3}{14}$$

Add 42 and 4 to get 46.

$$\frac{139}{6}-\frac{46}{7}+1-\frac{5\times 14+3}{14}$$

Least common multiple of 6 and 7 is 42. Convert \frac{139}{6} and \frac{46}{7} to fractions with denominator 42.

$$\frac{973}{42}-\frac{276}{42}+1-\frac{5\times 14+3}{14}$$

Since \frac{973}{42} and \frac{276}{42} have the same denominator, subtract them by subtracting their numerators.

$$\frac{973-276}{42}+1-\frac{5\times 14+3}{14}$$

Subtract 276 from 973 to get 697.

$$\frac{697}{42}+1-\frac{5\times 14+3}{14}$$

Convert 1 to fraction \frac{42}{42}.

$$\frac{697}{42}+\frac{42}{42}-\frac{5\times 14+3}{14}$$

Since \frac{697}{42} and \frac{42}{42} have the same denominator, add them by adding their numerators.

$$\frac{697+42}{42}-\frac{5\times 14+3}{14}$$

Add 697 and 42 to get 739.

$$\frac{739}{42}-\frac{5\times 14+3}{14}$$

Multiply 5 and 14 to get 70.

$$\frac{739}{42}-\frac{70+3}{14}$$

Add 70 and 3 to get 73.

$$\frac{739}{42}-\frac{73}{14}$$

Least common multiple of 42 and 14 is 42. Convert \frac{739}{42} and \frac{73}{14} to fractions with denominator 42.

$$\frac{739}{42}-\frac{219}{42}$$

Since \frac{739}{42} and \frac{219}{42} have the same denominator, subtract them by subtracting their numerators.

$$\frac{739-219}{42}$$

Subtract 219 from 739 to get 520.

$$\frac{520}{42}$$

Reduce the fraction \frac{520}{42} to lowest terms by extracting and canceling out 2.

$$\frac{260}{21}$$

Factor

$$\frac{2 ^ {2} \cdot 5 \cdot 13}{3 \cdot 7} = 12\frac{8}{21} = 12.380952380952381$$