Solve 12/5div3/5-3/7*1/6-frac{50}{7}+frac{3}{14}

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

Evaluate

$$-3$$

Solution Steps

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

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

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

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

Cancel out 5 in both numerator and denominator.

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

Divide 12 by 3 to get 4.

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

Multiply \frac{3}{7} times \frac{1}{6} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{3\times 1}{7\times 6}.

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

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

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

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

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

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

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

Subtract 1 from 56 to get 55.

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

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

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

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

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

Subtract 100 from 55 to get -45.

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

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

$$-3$$