Solve 5-4-92/51-8/2=-6-92/51/4+frac{1}{3}

$$5 \frac{ -4 \frac{ -92 }{ 51 } -8 }{ 2 } = \frac{ -6 \frac{ -92 }{ 51 } }{ 4 } + \frac{ 1 }{ 3 }$$

Verify

Solution Steps

Multiply both sides of the equation by 12, the least common multiple of 2,4,3.

$$30\left(-4\times \frac{-92}{51}-8\right)=3\left(-6\right)\times \frac{-92}{51}+4$$

Fraction \frac{-92}{51} can be rewritten as -\frac{92}{51} by extracting the negative sign.

$$30\left(-4\left(-\frac{92}{51}\right)-8\right)=3\left(-6\right)\times \frac{-92}{51}+4$$

Express -4\left(-\frac{92}{51}\right) as a single fraction.

$$30\left(\frac{-4\left(-92\right)}{51}-8\right)=3\left(-6\right)\times \frac{-92}{51}+4$$

Multiply -4 and -92 to get 368.

$$30\left(\frac{368}{51}-8\right)=3\left(-6\right)\times \frac{-92}{51}+4$$

Convert 8 to fraction \frac{408}{51}.

$$30\left(\frac{368}{51}-\frac{408}{51}\right)=3\left(-6\right)\times \frac{-92}{51}+4$$

Since \frac{368}{51} and \frac{408}{51} have the same denominator, subtract them by subtracting their numerators.

$$30\times \frac{368-408}{51}=3\left(-6\right)\times \frac{-92}{51}+4$$

Subtract 408 from 368 to get -40.

$$30\left(-\frac{40}{51}\right)=3\left(-6\right)\times \frac{-92}{51}+4$$

Express 30\left(-\frac{40}{51}\right) as a single fraction.

$$\frac{30\left(-40\right)}{51}=3\left(-6\right)\times \frac{-92}{51}+4$$

Multiply 30 and -40 to get -1200.

$$\frac{-1200}{51}=3\left(-6\right)\times \frac{-92}{51}+4$$

Reduce the fraction \frac{-1200}{51} to lowest terms by extracting and canceling out 3.

$$-\frac{400}{17}=3\left(-6\right)\times \frac{-92}{51}+4$$

Multiply 3 and -6 to get -18.

$$-\frac{400}{17}=-18\times \frac{-92}{51}+4$$

Fraction \frac{-92}{51} can be rewritten as -\frac{92}{51} by extracting the negative sign.

$$-\frac{400}{17}=-18\left(-\frac{92}{51}\right)+4$$

Express -18\left(-\frac{92}{51}\right) as a single fraction.

$$-\frac{400}{17}=\frac{-18\left(-92\right)}{51}+4$$

Multiply -18 and -92 to get 1656.

$$-\frac{400}{17}=\frac{1656}{51}+4$$

Reduce the fraction \frac{1656}{51} to lowest terms by extracting and canceling out 3.

$$-\frac{400}{17}=\frac{552}{17}+4$$

Convert 4 to fraction \frac{68}{17}.

$$-\frac{400}{17}=\frac{552}{17}+\frac{68}{17}$$

Since \frac{552}{17} and \frac{68}{17} have the same denominator, add them by adding their numerators.

$$-\frac{400}{17}=\frac{552+68}{17}$$

Add 552 and 68 to get 620.

$$-\frac{400}{17}=\frac{620}{17}$$

Compare -\frac{400}{17} and \frac{620}{17}.

$$\text{false}$$