Solve 1-6left(113.5+1/22.2right)/8^3-8

$$1- \frac{ 6 \left( 113.5+ \frac{ 1 }{ 2 } 2.2 \right) }{ { 8 }^{ 3 } -8 }$$

Evaluate

$$-\frac{51}{140}\approx -0.364285714$$

Solution Steps

Convert decimal number 2.2 to fraction \frac{22}{10}. Reduce the fraction \frac{22}{10} to lowest terms by extracting and canceling out 2.

$$1-\frac{6\left(113.5+\frac{1}{2}\times \frac{11}{5}\right)}{8^{3}-8}$$

Multiply \frac{1}{2} times \frac{11}{5} by multiplying numerator times numerator and denominator times denominator.

$$1-\frac{6\left(113.5+\frac{1\times 11}{2\times 5}\right)}{8^{3}-8}$$

Do the multiplications in the fraction \frac{1\times 11}{2\times 5}.

$$1-\frac{6\left(113.5+\frac{11}{10}\right)}{8^{3}-8}$$

Convert decimal number 113.5 to fraction \frac{1135}{10}. Reduce the fraction \frac{1135}{10} to lowest terms by extracting and canceling out 5.

$$1-\frac{6\left(\frac{227}{2}+\frac{11}{10}\right)}{8^{3}-8}$$

Least common multiple of 2 and 10 is 10. Convert \frac{227}{2} and \frac{11}{10} to fractions with denominator 10.

$$1-\frac{6\left(\frac{1135}{10}+\frac{11}{10}\right)}{8^{3}-8}$$

Since \frac{1135}{10} and \frac{11}{10} have the same denominator, add them by adding their numerators.

$$1-\frac{6\times \frac{1135+11}{10}}{8^{3}-8}$$

Add 1135 and 11 to get 1146.

$$1-\frac{6\times \frac{1146}{10}}{8^{3}-8}$$

Reduce the fraction \frac{1146}{10} to lowest terms by extracting and canceling out 2.

$$1-\frac{6\times \frac{573}{5}}{8^{3}-8}$$

Express 6\times \frac{573}{5} as a single fraction.

$$1-\frac{\frac{6\times 573}{5}}{8^{3}-8}$$

Multiply 6 and 573 to get 3438.

$$1-\frac{\frac{3438}{5}}{8^{3}-8}$$

Calculate 8 to the power of 3 and get 512.

$$1-\frac{\frac{3438}{5}}{512-8}$$

Subtract 8 from 512 to get 504.

$$1-\frac{\frac{3438}{5}}{504}$$

Express \frac{\frac{3438}{5}}{504} as a single fraction.

$$1-\frac{3438}{5\times 504}$$

Multiply 5 and 504 to get 2520.

$$1-\frac{3438}{2520}$$

Reduce the fraction \frac{3438}{2520} to lowest terms by extracting and canceling out 18.

$$1-\frac{191}{140}$$

Convert 1 to fraction \frac{140}{140}.

$$\frac{140}{140}-\frac{191}{140}$$

Since \frac{140}{140} and \frac{191}{140} have the same denominator, subtract them by subtracting their numerators.

$$\frac{140-191}{140}$$

Subtract 191 from 140 to get -51.

$$-\frac{51}{140}$$

Factor

$$-\frac{51}{140} = -0.36428571428571427$$