Solve 1/3*1/2-3/4+frac{7/8}{7}

$$\frac { 1 } { 3 } \cdot \frac { \frac { 1 } { 2 } - \frac { 3 } { 4 } + \frac { 7 } { 8 } } { 7 }$$

Evaluate

$$\frac{5}{168}\approx 0.029761905$$

Solution Steps

Least common multiple of 2 and 4 is 4. Convert \frac{1}{2} and \frac{3}{4} to fractions with denominator 4.

$$\frac{1}{3}\times \frac{\frac{2}{4}-\frac{3}{4}+\frac{7}{8}}{7}$$

Since \frac{2}{4} and \frac{3}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{3}\times \frac{\frac{2-3}{4}+\frac{7}{8}}{7}$$

Subtract 3 from 2 to get -1.

$$\frac{1}{3}\times \frac{-\frac{1}{4}+\frac{7}{8}}{7}$$

Least common multiple of 4 and 8 is 8. Convert -\frac{1}{4} and \frac{7}{8} to fractions with denominator 8.

$$\frac{1}{3}\times \frac{-\frac{2}{8}+\frac{7}{8}}{7}$$

Since -\frac{2}{8} and \frac{7}{8} have the same denominator, add them by adding their numerators.

$$\frac{1}{3}\times \frac{\frac{-2+7}{8}}{7}$$

Add -2 and 7 to get 5.

$$\frac{1}{3}\times \frac{\frac{5}{8}}{7}$$

Express \frac{\frac{5}{8}}{7} as a single fraction.

$$\frac{1}{3}\times \frac{5}{8\times 7}$$

Multiply 8 and 7 to get 56.

$$\frac{1}{3}\times \frac{5}{56}$$

Multiply \frac{1}{3} times \frac{5}{56} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 5}{3\times 56}$$

Do the multiplications in the fraction \frac{1\times 5}{3\times 56}.

$$\frac{5}{168}$$

Factor

$$\frac{5}{2 ^ {3} \cdot 3 \cdot 7} = 0.02976190476190476$$