Solve 53/27+45/18:(-24/27)

$$5 \frac { 3 } { 27 } + 4 \frac { 5 } { 18 } : ( - 2 \frac { 4 } { 27 } )$$

Evaluate

$$\frac{3257}{1044}\approx 3.119731801$$

Solution Steps

Multiply 5 and 27 to get 135.

$$\frac{135+3}{27}+\frac{\frac{4\times 18+5}{18}}{-\frac{2\times 27+4}{27}}$$

Add 135 and 3 to get 138.

$$\frac{138}{27}+\frac{\frac{4\times 18+5}{18}}{-\frac{2\times 27+4}{27}}$$

Reduce the fraction \frac{138}{27} to lowest terms by extracting and canceling out 3.

$$\frac{46}{9}+\frac{\frac{4\times 18+5}{18}}{-\frac{2\times 27+4}{27}}$$

Multiply 4 and 18 to get 72.

$$\frac{46}{9}+\frac{\frac{72+5}{18}}{-\frac{2\times 27+4}{27}}$$

Add 72 and 5 to get 77.

$$\frac{46}{9}+\frac{\frac{77}{18}}{-\frac{2\times 27+4}{27}}$$

Multiply 2 and 27 to get 54.

$$\frac{46}{9}+\frac{\frac{77}{18}}{-\frac{54+4}{27}}$$

Add 54 and 4 to get 58.

$$\frac{46}{9}+\frac{\frac{77}{18}}{-\frac{58}{27}}$$

Divide \frac{77}{18} by -\frac{58}{27} by multiplying \frac{77}{18} by the reciprocal of -\frac{58}{27}.

$$\frac{46}{9}+\frac{77}{18}\left(-\frac{27}{58}\right)$$

Multiply \frac{77}{18} times -\frac{27}{58} by multiplying numerator times numerator and denominator times denominator.

$$\frac{46}{9}+\frac{77\left(-27\right)}{18\times 58}$$

Do the multiplications in the fraction \frac{77\left(-27\right)}{18\times 58}.

$$\frac{46}{9}+\frac{-2079}{1044}$$

Reduce the fraction \frac{-2079}{1044} to lowest terms by extracting and canceling out 9.

$$\frac{46}{9}-\frac{231}{116}$$

Least common multiple of 9 and 116 is 1044. Convert \frac{46}{9} and \frac{231}{116} to fractions with denominator 1044.

$$\frac{5336}{1044}-\frac{2079}{1044}$$

Since \frac{5336}{1044} and \frac{2079}{1044} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5336-2079}{1044}$$

Subtract 2079 from 5336 to get 3257.

$$\frac{3257}{1044}$$

Factor

$$\frac{3257}{2 ^ {2} \cdot 3 ^ {2} \cdot 29} = 3\frac{125}{1044} = 3.1197318007662833$$