Solve 20/6=5/3-4-21/6+7/8-4=-4-1

$$\frac{ 20 }{ 6 } = \frac{ 5 }{ 3 } -4- \frac{ 21 }{ 6 } + \frac{ 7 }{ 8 } -4 = -4-1$$

Verify

Solution Steps

Reduce the fraction \frac{20}{6} to lowest terms by extracting and canceling out 2.

$$\frac{10}{3}=\frac{5}{3}-4-\frac{21}{6}+\frac{7}{8}-4\text{ and }\frac{5}{3}-4-\frac{21}{6}+\frac{7}{8}-4=-4-1$$

Convert 4 to fraction \frac{12}{3}.

$$\frac{10}{3}=\frac{5}{3}-\frac{12}{3}-\frac{21}{6}+\frac{7}{8}-4\text{ and }\frac{5}{3}-4-\frac{21}{6}+\frac{7}{8}-4=-4-1$$

Since \frac{5}{3} and \frac{12}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{10}{3}=\frac{5-12}{3}-\frac{21}{6}+\frac{7}{8}-4\text{ and }\frac{5}{3}-4-\frac{21}{6}+\frac{7}{8}-4=-4-1$$

Subtract 12 from 5 to get -7.

$$\frac{10}{3}=-\frac{7}{3}-\frac{21}{6}+\frac{7}{8}-4\text{ and }\frac{5}{3}-4-\frac{21}{6}+\frac{7}{8}-4=-4-1$$

Reduce the fraction \frac{21}{6} to lowest terms by extracting and canceling out 3.

$$\frac{10}{3}=-\frac{7}{3}-\frac{7}{2}+\frac{7}{8}-4\text{ and }\frac{5}{3}-4-\frac{21}{6}+\frac{7}{8}-4=-4-1$$

Least common multiple of 3 and 2 is 6. Convert -\frac{7}{3} and \frac{7}{2} to fractions with denominator 6.

$$\frac{10}{3}=-\frac{14}{6}-\frac{21}{6}+\frac{7}{8}-4\text{ and }\frac{5}{3}-4-\frac{21}{6}+\frac{7}{8}-4=-4-1$$

Since -\frac{14}{6} and \frac{21}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{10}{3}=\frac{-14-21}{6}+\frac{7}{8}-4\text{ and }\frac{5}{3}-4-\frac{21}{6}+\frac{7}{8}-4=-4-1$$

Subtract 21 from -14 to get -35.

$$\frac{10}{3}=-\frac{35}{6}+\frac{7}{8}-4\text{ and }\frac{5}{3}-4-\frac{21}{6}+\frac{7}{8}-4=-4-1$$

Least common multiple of 6 and 8 is 24. Convert -\frac{35}{6} and \frac{7}{8} to fractions with denominator 24.

$$\frac{10}{3}=-\frac{140}{24}+\frac{21}{24}-4\text{ and }\frac{5}{3}-4-\frac{21}{6}+\frac{7}{8}-4=-4-1$$

Since -\frac{140}{24} and \frac{21}{24} have the same denominator, add them by adding their numerators.

$$\frac{10}{3}=\frac{-140+21}{24}-4\text{ and }\frac{5}{3}-4-\frac{21}{6}+\frac{7}{8}-4=-4-1$$

Add -140 and 21 to get -119.

$$\frac{10}{3}=-\frac{119}{24}-4\text{ and }\frac{5}{3}-4-\frac{21}{6}+\frac{7}{8}-4=-4-1$$

Convert 4 to fraction \frac{96}{24}.

$$\frac{10}{3}=-\frac{119}{24}-\frac{96}{24}\text{ and }\frac{5}{3}-4-\frac{21}{6}+\frac{7}{8}-4=-4-1$$

Since -\frac{119}{24} and \frac{96}{24} have the same denominator, subtract them by subtracting their numerators.

$$\frac{10}{3}=\frac{-119-96}{24}\text{ and }\frac{5}{3}-4-\frac{21}{6}+\frac{7}{8}-4=-4-1$$

Subtract 96 from -119 to get -215.

$$\frac{10}{3}=-\frac{215}{24}\text{ and }\frac{5}{3}-4-\frac{21}{6}+\frac{7}{8}-4=-4-1$$

Least common multiple of 3 and 24 is 24. Convert \frac{10}{3} and -\frac{215}{24} to fractions with denominator 24.

$$\frac{80}{24}=-\frac{215}{24}\text{ and }\frac{5}{3}-4-\frac{21}{6}+\frac{7}{8}-4=-4-1$$

Compare \frac{80}{24} and -\frac{215}{24}.

$$\text{false}\text{ and }\frac{5}{3}-4-\frac{21}{6}+\frac{7}{8}-4=-4-1$$

Convert 4 to fraction \frac{12}{3}.

$$\text{false}\text{ and }\frac{5}{3}-\frac{12}{3}-\frac{21}{6}+\frac{7}{8}-4=-4-1$$

Since \frac{5}{3} and \frac{12}{3} have the same denominator, subtract them by subtracting their numerators.

$$\text{false}\text{ and }\frac{5-12}{3}-\frac{21}{6}+\frac{7}{8}-4=-4-1$$

Subtract 12 from 5 to get -7.

$$\text{false}\text{ and }-\frac{7}{3}-\frac{21}{6}+\frac{7}{8}-4=-4-1$$

Reduce the fraction \frac{21}{6} to lowest terms by extracting and canceling out 3.

$$\text{false}\text{ and }-\frac{7}{3}-\frac{7}{2}+\frac{7}{8}-4=-4-1$$

Least common multiple of 3 and 2 is 6. Convert -\frac{7}{3} and \frac{7}{2} to fractions with denominator 6.

$$\text{false}\text{ and }-\frac{14}{6}-\frac{21}{6}+\frac{7}{8}-4=-4-1$$

Since -\frac{14}{6} and \frac{21}{6} have the same denominator, subtract them by subtracting their numerators.

$$\text{false}\text{ and }\frac{-14-21}{6}+\frac{7}{8}-4=-4-1$$

Subtract 21 from -14 to get -35.

$$\text{false}\text{ and }-\frac{35}{6}+\frac{7}{8}-4=-4-1$$

Least common multiple of 6 and 8 is 24. Convert -\frac{35}{6} and \frac{7}{8} to fractions with denominator 24.

$$\text{false}\text{ and }-\frac{140}{24}+\frac{21}{24}-4=-4-1$$

Since -\frac{140}{24} and \frac{21}{24} have the same denominator, add them by adding their numerators.

$$\text{false}\text{ and }\frac{-140+21}{24}-4=-4-1$$

Add -140 and 21 to get -119.

$$\text{false}\text{ and }-\frac{119}{24}-4=-4-1$$

Convert 4 to fraction \frac{96}{24}.

$$\text{false}\text{ and }-\frac{119}{24}-\frac{96}{24}=-4-1$$

Since -\frac{119}{24} and \frac{96}{24} have the same denominator, subtract them by subtracting their numerators.

$$\text{false}\text{ and }\frac{-119-96}{24}=-4-1$$

Subtract 96 from -119 to get -215.

$$\text{false}\text{ and }-\frac{215}{24}=-4-1$$

Subtract 1 from -4 to get -5.

$$\text{false}\text{ and }-\frac{215}{24}=-5$$

Convert -5 to fraction -\frac{120}{24}.

$$\text{false}\text{ and }-\frac{215}{24}=-\frac{120}{24}$$

Compare -\frac{215}{24} and -\frac{120}{24}.

$$\text{false}\text{ and }\text{false}$$

The conjunction of \text{false} and \text{false} is \text{false}.

$$\text{false}$$