Solve 1/9+-1/8+-1/7+1/6

$$\frac { 1 } { 9 } + \frac { - 1 } { 8 } + \frac { - 1 } { 7 } + \frac { 1 } { 6 }$$

Evaluate

$$\frac{5}{504}\approx 0.009920635$$

Solution Steps

Fraction \frac{-1}{8} can be rewritten as -\frac{1}{8} by extracting the negative sign.

$$\frac{1}{9}-\frac{1}{8}+\frac{-1}{7}+\frac{1}{6}$$

Least common multiple of 9 and 8 is 72. Convert \frac{1}{9} and \frac{1}{8} to fractions with denominator 72.

$$\frac{8}{72}-\frac{9}{72}+\frac{-1}{7}+\frac{1}{6}$$

Since \frac{8}{72} and \frac{9}{72} have the same denominator, subtract them by subtracting their numerators.

$$\frac{8-9}{72}+\frac{-1}{7}+\frac{1}{6}$$

Subtract 9 from 8 to get -1.

$$-\frac{1}{72}+\frac{-1}{7}+\frac{1}{6}$$

Fraction \frac{-1}{7} can be rewritten as -\frac{1}{7} by extracting the negative sign.

$$-\frac{1}{72}-\frac{1}{7}+\frac{1}{6}$$

Least common multiple of 72 and 7 is 504. Convert -\frac{1}{72} and \frac{1}{7} to fractions with denominator 504.

$$-\frac{7}{504}-\frac{72}{504}+\frac{1}{6}$$

Since -\frac{7}{504} and \frac{72}{504} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-7-72}{504}+\frac{1}{6}$$

Subtract 72 from -7 to get -79.

$$-\frac{79}{504}+\frac{1}{6}$$

Least common multiple of 504 and 6 is 504. Convert -\frac{79}{504} and \frac{1}{6} to fractions with denominator 504.

$$-\frac{79}{504}+\frac{84}{504}$$

Since -\frac{79}{504} and \frac{84}{504} have the same denominator, add them by adding their numerators.

$$\frac{-79+84}{504}$$

Add -79 and 84 to get 5.

$$\frac{5}{504}$$

Factor

$$\frac{5}{2 ^ {3} \cdot 3 ^ {2} \cdot 7} = 0.00992063492063492$$