Solve 12/5div3/5-3/7div6-1/frac{7{50}}+frac{sqrt{3divfrac{1}{3}}}{14}

$$\frac { 12 } { 5 } \div \frac { 3 } { 5 } - \frac { 3 } { 7 } \div 6 - \frac { 1 } { \frac { 7 } { 50 } } + \frac { \sqrt { 3 \div \frac { 1 } { 3 } } } { 14 }$$

Evaluate

$$-3$$

Solution Steps

Divide \frac{12}{5} by \frac{3}{5} by multiplying \frac{12}{5} by the reciprocal of \frac{3}{5}.

$$\frac{12}{5}\times \frac{5}{3}-\frac{\frac{3}{7}}{6}-\frac{1}{\frac{7}{50}}+\frac{\sqrt{\frac{3}{\frac{1}{3}}}}{14}$$

Multiply \frac{12}{5} times \frac{5}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{12\times 5}{5\times 3}-\frac{\frac{3}{7}}{6}-\frac{1}{\frac{7}{50}}+\frac{\sqrt{\frac{3}{\frac{1}{3}}}}{14}$$

Cancel out 5 in both numerator and denominator.

$$\frac{12}{3}-\frac{\frac{3}{7}}{6}-\frac{1}{\frac{7}{50}}+\frac{\sqrt{\frac{3}{\frac{1}{3}}}}{14}$$

Divide 12 by 3 to get 4.

$$4-\frac{\frac{3}{7}}{6}-\frac{1}{\frac{7}{50}}+\frac{\sqrt{\frac{3}{\frac{1}{3}}}}{14}$$

Express \frac{\frac{3}{7}}{6} as a single fraction.

$$4-\frac{3}{7\times 6}-\frac{1}{\frac{7}{50}}+\frac{\sqrt{\frac{3}{\frac{1}{3}}}}{14}$$

Multiply 7 and 6 to get 42.

$$4-\frac{3}{42}-\frac{1}{\frac{7}{50}}+\frac{\sqrt{\frac{3}{\frac{1}{3}}}}{14}$$

Reduce the fraction \frac{3}{42} to lowest terms by extracting and canceling out 3.

$$4-\frac{1}{14}-\frac{1}{\frac{7}{50}}+\frac{\sqrt{\frac{3}{\frac{1}{3}}}}{14}$$

Convert 4 to fraction \frac{56}{14}.

$$\frac{56}{14}-\frac{1}{14}-\frac{1}{\frac{7}{50}}+\frac{\sqrt{\frac{3}{\frac{1}{3}}}}{14}$$

Since \frac{56}{14} and \frac{1}{14} have the same denominator, subtract them by subtracting their numerators.

$$\frac{56-1}{14}-\frac{1}{\frac{7}{50}}+\frac{\sqrt{\frac{3}{\frac{1}{3}}}}{14}$$

Subtract 1 from 56 to get 55.

$$\frac{55}{14}-\frac{1}{\frac{7}{50}}+\frac{\sqrt{\frac{3}{\frac{1}{3}}}}{14}$$

Divide 1 by \frac{7}{50} by multiplying 1 by the reciprocal of \frac{7}{50}.

$$\frac{55}{14}-1\times \frac{50}{7}+\frac{\sqrt{\frac{3}{\frac{1}{3}}}}{14}$$

Multiply 1 and \frac{50}{7} to get \frac{50}{7}.

$$\frac{55}{14}-\frac{50}{7}+\frac{\sqrt{\frac{3}{\frac{1}{3}}}}{14}$$

Least common multiple of 14 and 7 is 14. Convert \frac{55}{14} and \frac{50}{7} to fractions with denominator 14.

$$\frac{55}{14}-\frac{100}{14}+\frac{\sqrt{\frac{3}{\frac{1}{3}}}}{14}$$

Since \frac{55}{14} and \frac{100}{14} have the same denominator, subtract them by subtracting their numerators.

$$\frac{55-100}{14}+\frac{\sqrt{\frac{3}{\frac{1}{3}}}}{14}$$

Subtract 100 from 55 to get -45.

$$-\frac{45}{14}+\frac{\sqrt{\frac{3}{\frac{1}{3}}}}{14}$$

Divide 3 by \frac{1}{3} by multiplying 3 by the reciprocal of \frac{1}{3}.

$$-\frac{45}{14}+\frac{\sqrt{3\times 3}}{14}$$

Multiply 3 and 3 to get 9.

$$-\frac{45}{14}+\frac{\sqrt{9}}{14}$$

Calculate the square root of 9 and get 3.

$$-\frac{45}{14}+\frac{3}{14}$$

Since -\frac{45}{14} and \frac{3}{14} have the same denominator, add them by adding their numerators.

$$\frac{-45+3}{14}$$

Add -45 and 3 to get -42.

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

Divide -42 by 14 to get -3.

$$-3$$

Factor

$$-3$$