Solve (7/8-5/6)+(8/9-7/9)=

$$( \frac { 7 } { 8 } - \frac { 5 } { 6 } ) + ( \frac { 8 } { 9 } - \frac { 7 } { 9 } ) =$$

Evaluate

$$\frac{11}{72}\approx 0.152777778$$

Solution Steps

Least common multiple of 8 and 6 is 24. Convert \frac{7}{8} and \frac{5}{6} to fractions with denominator 24.

$$\frac{21}{24}-\frac{20}{24}+\frac{8}{9}-\frac{7}{9}$$

Since \frac{21}{24} and \frac{20}{24} have the same denominator, subtract them by subtracting their numerators.

$$\frac{21-20}{24}+\frac{8}{9}-\frac{7}{9}$$

Subtract 20 from 21 to get 1.

$$\frac{1}{24}+\frac{8}{9}-\frac{7}{9}$$

Least common multiple of 24 and 9 is 72. Convert \frac{1}{24} and \frac{8}{9} to fractions with denominator 72.

$$\frac{3}{72}+\frac{64}{72}-\frac{7}{9}$$

Since \frac{3}{72} and \frac{64}{72} have the same denominator, add them by adding their numerators.

$$\frac{3+64}{72}-\frac{7}{9}$$

Add 3 and 64 to get 67.

$$\frac{67}{72}-\frac{7}{9}$$

Least common multiple of 72 and 9 is 72. Convert \frac{67}{72} and \frac{7}{9} to fractions with denominator 72.

$$\frac{67}{72}-\frac{56}{72}$$

Since \frac{67}{72} and \frac{56}{72} have the same denominator, subtract them by subtracting their numerators.

$$\frac{67-56}{72}$$

Subtract 56 from 67 to get 11.

$$\frac{11}{72}$$

Factor

$$\frac{11}{2 ^ {3} \cdot 3 ^ {2}} = 0.1527777777777778$$