Solve 1/7-1/8+6/7=7/8-frac{7}{8}

$$\frac { 1 } { 7 } - \frac { 1 } { 8 } + \frac { 6 } { 7 } = \frac { 7 } { 8 } - \frac { 7 } { 8 }$$

Verify

Solution Steps

Least common multiple of 7 and 8 is 56. Convert \frac{1}{7} and \frac{1}{8} to fractions with denominator 56.

$$\frac{8}{56}-\frac{7}{56}+\frac{6}{7}=\frac{7}{8}-\frac{7}{8}$$

Since \frac{8}{56} and \frac{7}{56} have the same denominator, subtract them by subtracting their numerators.

$$\frac{8-7}{56}+\frac{6}{7}=\frac{7}{8}-\frac{7}{8}$$

Subtract 7 from 8 to get 1.

$$\frac{1}{56}+\frac{6}{7}=\frac{7}{8}-\frac{7}{8}$$

Least common multiple of 56 and 7 is 56. Convert \frac{1}{56} and \frac{6}{7} to fractions with denominator 56.

$$\frac{1}{56}+\frac{48}{56}=\frac{7}{8}-\frac{7}{8}$$

Since \frac{1}{56} and \frac{48}{56} have the same denominator, add them by adding their numerators.

$$\frac{1+48}{56}=\frac{7}{8}-\frac{7}{8}$$

Add 1 and 48 to get 49.

$$\frac{49}{56}=\frac{7}{8}-\frac{7}{8}$$

Reduce the fraction \frac{49}{56} to lowest terms by extracting and canceling out 7.

$$\frac{7}{8}=\frac{7}{8}-\frac{7}{8}$$

Subtract \frac{7}{8} from \frac{7}{8} to get 0.

$$\frac{7}{8}=0$$

Compare \frac{7}{8} and 0.

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