Solve 3/4-5/6+7/8:9/2=

$$\frac { 3 } { 4 } - \frac { 5 } { 6 } + \frac { 7 } { 8 } : \frac { 9 } { 2 } =$$

Evaluate

$$\frac{1}{9}\approx 0.111111111$$

Solution Steps

Least common multiple of 4 and 6 is 12. Convert \frac{3}{4} and \frac{5}{6} to fractions with denominator 12.

$$\frac{9}{12}-\frac{10}{12}+\frac{\frac{7}{8}}{\frac{9}{2}}$$

Since \frac{9}{12} and \frac{10}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{9-10}{12}+\frac{\frac{7}{8}}{\frac{9}{2}}$$

Subtract 10 from 9 to get -1.

$$-\frac{1}{12}+\frac{\frac{7}{8}}{\frac{9}{2}}$$

Divide \frac{7}{8} by \frac{9}{2} by multiplying \frac{7}{8} by the reciprocal of \frac{9}{2}.

$$-\frac{1}{12}+\frac{7}{8}\times \frac{2}{9}$$

Multiply \frac{7}{8} times \frac{2}{9} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{1}{12}+\frac{7\times 2}{8\times 9}$$

Do the multiplications in the fraction \frac{7\times 2}{8\times 9}.

$$-\frac{1}{12}+\frac{14}{72}$$

Reduce the fraction \frac{14}{72} to lowest terms by extracting and canceling out 2.

$$-\frac{1}{12}+\frac{7}{36}$$

Least common multiple of 12 and 36 is 36. Convert -\frac{1}{12} and \frac{7}{36} to fractions with denominator 36.

$$-\frac{3}{36}+\frac{7}{36}$$

Since -\frac{3}{36} and \frac{7}{36} have the same denominator, add them by adding their numerators.

$$\frac{-3+7}{36}$$

Add -3 and 7 to get 4.

$$\frac{4}{36}$$

Reduce the fraction \frac{4}{36} to lowest terms by extracting and canceling out 4.

$$\frac{1}{9}$$

Factor

$$\frac{1}{3 ^ {2}} = 0.1111111111111111$$