Solve -1/2+5/3-125/4/27

$$- \frac{ 1 }{ 2 } + \frac{ 5 }{ 3 } - \frac{ \frac{ 125 }{ 4 } }{ 27 }$$

Evaluate

$$\frac{1}{108}\approx 0.009259259$$

Solution Steps

Least common multiple of 2 and 3 is 6. Convert -\frac{1}{2} and \frac{5}{3} to fractions with denominator 6.

$$-\frac{3}{6}+\frac{10}{6}-\frac{\frac{125}{4}}{27}$$

Since -\frac{3}{6} and \frac{10}{6} have the same denominator, add them by adding their numerators.

$$\frac{-3+10}{6}-\frac{\frac{125}{4}}{27}$$

Add -3 and 10 to get 7.

$$\frac{7}{6}-\frac{\frac{125}{4}}{27}$$

Express \frac{\frac{125}{4}}{27} as a single fraction.

$$\frac{7}{6}-\frac{125}{4\times 27}$$

Multiply 4 and 27 to get 108.

$$\frac{7}{6}-\frac{125}{108}$$

Least common multiple of 6 and 108 is 108. Convert \frac{7}{6} and \frac{125}{108} to fractions with denominator 108.

$$\frac{126}{108}-\frac{125}{108}$$

Since \frac{126}{108} and \frac{125}{108} have the same denominator, subtract them by subtracting their numerators.

$$\frac{126-125}{108}$$

Subtract 125 from 126 to get 1.

$$\frac{1}{108}$$

Factor

$$\frac{1}{2 ^ {2} \cdot 3 ^ {3}} = 0.009259259259259259$$