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

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

Verify

Solution Steps

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

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

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

$$\frac{12}{5}=\frac{3}{5}-\frac{3}{42}-\frac{50}{7}+\frac{3}{14}$$

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

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

Least common multiple of 5 and 14 is 70. Convert \frac{3}{5} and \frac{1}{14} to fractions with denominator 70.

$$\frac{12}{5}=\frac{42}{70}-\frac{5}{70}-\frac{50}{7}+\frac{3}{14}$$

Since \frac{42}{70} and \frac{5}{70} have the same denominator, subtract them by subtracting their numerators.

$$\frac{12}{5}=\frac{42-5}{70}-\frac{50}{7}+\frac{3}{14}$$

Subtract 5 from 42 to get 37.

$$\frac{12}{5}=\frac{37}{70}-\frac{50}{7}+\frac{3}{14}$$

Least common multiple of 70 and 7 is 70. Convert \frac{37}{70} and \frac{50}{7} to fractions with denominator 70.

$$\frac{12}{5}=\frac{37}{70}-\frac{500}{70}+\frac{3}{14}$$

Since \frac{37}{70} and \frac{500}{70} have the same denominator, subtract them by subtracting their numerators.

$$\frac{12}{5}=\frac{37-500}{70}+\frac{3}{14}$$

Subtract 500 from 37 to get -463.

$$\frac{12}{5}=-\frac{463}{70}+\frac{3}{14}$$

Least common multiple of 70 and 14 is 70. Convert -\frac{463}{70} and \frac{3}{14} to fractions with denominator 70.

$$\frac{12}{5}=-\frac{463}{70}+\frac{15}{70}$$

Since -\frac{463}{70} and \frac{15}{70} have the same denominator, add them by adding their numerators.

$$\frac{12}{5}=\frac{-463+15}{70}$$

Add -463 and 15 to get -448.

$$\frac{12}{5}=\frac{-448}{70}$$

Reduce the fraction \frac{-448}{70} to lowest terms by extracting and canceling out 14.

$$\frac{12}{5}=-\frac{32}{5}$$

Compare \frac{12}{5} and -\frac{32}{5}.

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