Solve 1.125+12/3-25/6*-8/27

$$1.125+ 1 \frac { 2 } { 3 } - 2 \frac { 5 } { 6 } \times - \frac{ 8 }{ 27 }$$

Evaluate

$$\frac{2353}{648}\approx 3.63117284$$

Solution Steps

Multiply 1 and 3 to get 3.

$$1.125+\frac{3+2}{3}-\frac{2\times 6+5}{6}\left(-\frac{8}{27}\right)$$

Add 3 and 2 to get 5.

$$1.125+\frac{5}{3}-\frac{2\times 6+5}{6}\left(-\frac{8}{27}\right)$$

Convert decimal number 1.125 to fraction \frac{1125}{1000}. Reduce the fraction \frac{1125}{1000} to lowest terms by extracting and canceling out 125.

$$\frac{9}{8}+\frac{5}{3}-\frac{2\times 6+5}{6}\left(-\frac{8}{27}\right)$$

Least common multiple of 8 and 3 is 24. Convert \frac{9}{8} and \frac{5}{3} to fractions with denominator 24.

$$\frac{27}{24}+\frac{40}{24}-\frac{2\times 6+5}{6}\left(-\frac{8}{27}\right)$$

Since \frac{27}{24} and \frac{40}{24} have the same denominator, add them by adding their numerators.

$$\frac{27+40}{24}-\frac{2\times 6+5}{6}\left(-\frac{8}{27}\right)$$

Add 27 and 40 to get 67.

$$\frac{67}{24}-\frac{2\times 6+5}{6}\left(-\frac{8}{27}\right)$$

Multiply 2 and 6 to get 12.

$$\frac{67}{24}-\frac{12+5}{6}\left(-\frac{8}{27}\right)$$

Add 12 and 5 to get 17.

$$\frac{67}{24}-\frac{17}{6}\left(-\frac{8}{27}\right)$$

Multiply \frac{17}{6} times -\frac{8}{27} by multiplying numerator times numerator and denominator times denominator.

$$\frac{67}{24}-\frac{17\left(-8\right)}{6\times 27}$$

Do the multiplications in the fraction \frac{17\left(-8\right)}{6\times 27}.

$$\frac{67}{24}-\frac{-136}{162}$$

Reduce the fraction \frac{-136}{162} to lowest terms by extracting and canceling out 2.

$$\frac{67}{24}-\left(-\frac{68}{81}\right)$$

The opposite of -\frac{68}{81} is \frac{68}{81}.

$$\frac{67}{24}+\frac{68}{81}$$

Least common multiple of 24 and 81 is 648. Convert \frac{67}{24} and \frac{68}{81} to fractions with denominator 648.

$$\frac{1809}{648}+\frac{544}{648}$$

Since \frac{1809}{648} and \frac{544}{648} have the same denominator, add them by adding their numerators.

$$\frac{1809+544}{648}$$

Add 1809 and 544 to get 2353.

$$\frac{2353}{648}$$

Factor

$$\frac{13 \cdot 181}{2 ^ {3} \cdot 3 ^ {4}} = 3\frac{409}{648} = 3.631172839506173$$