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

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

Evaluate

$$\frac{635}{504}\approx 1.259920635$$

Solution Steps

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

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

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

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

Add 8 and 9 to get 17.

$$\frac{17}{72}+\frac{-1}{7}+\frac{7}{6}$$

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

$$\frac{17}{72}-\frac{1}{7}+\frac{7}{6}$$

Least common multiple of 72 and 7 is 504. Convert \frac{17}{72} and \frac{1}{7} to fractions with denominator 504.

$$\frac{119}{504}-\frac{72}{504}+\frac{7}{6}$$

Since \frac{119}{504} and \frac{72}{504} have the same denominator, subtract them by subtracting their numerators.

$$\frac{119-72}{504}+\frac{7}{6}$$

Subtract 72 from 119 to get 47.

$$\frac{47}{504}+\frac{7}{6}$$

Least common multiple of 504 and 6 is 504. Convert \frac{47}{504} and \frac{7}{6} to fractions with denominator 504.

$$\frac{47}{504}+\frac{588}{504}$$

Since \frac{47}{504} and \frac{588}{504} have the same denominator, add them by adding their numerators.

$$\frac{47+588}{504}$$

Add 47 and 588 to get 635.

$$\frac{635}{504}$$

Factor

$$\frac{5 \cdot 127}{2 ^ {3} \cdot 3 ^ {2} \cdot 7} = 1\frac{131}{504} = 1.2599206349206349$$