Solve 5/8*(4/3)^2-1/5*3-3/4+frac{3{2}*frac{4}{5}-1}

$$\frac { \frac { 5 } { 8 } \cdot ( \frac { 4 } { 3 } ) ^ { 2 } - \frac { 1 } { 5 } \cdot 3 - 3 } { 4 + \frac { 3 } { 2 } \cdot \frac { 4 } { 5 } - 1 }$$

Evaluate

$$-\frac{16}{27}\approx -0.592592593$$

Solution Steps

Calculate \frac{4}{3} to the power of 2 and get \frac{16}{9}.

$$\frac{\frac{5}{8}\times \frac{16}{9}-\frac{1}{5}\times 3-3}{4+\frac{3}{2}\times \frac{4}{5}-1}$$

Multiply \frac{5}{8} times \frac{16}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{5\times 16}{8\times 9}-\frac{1}{5}\times 3-3}{4+\frac{3}{2}\times \frac{4}{5}-1}$$

Do the multiplications in the fraction \frac{5\times 16}{8\times 9}.

$$\frac{\frac{80}{72}-\frac{1}{5}\times 3-3}{4+\frac{3}{2}\times \frac{4}{5}-1}$$

Reduce the fraction \frac{80}{72} to lowest terms by extracting and canceling out 8.

$$\frac{\frac{10}{9}-\frac{1}{5}\times 3-3}{4+\frac{3}{2}\times \frac{4}{5}-1}$$

Multiply \frac{1}{5} and 3 to get \frac{3}{5}.

$$\frac{\frac{10}{9}-\frac{3}{5}-3}{4+\frac{3}{2}\times \frac{4}{5}-1}$$

Least common multiple of 9 and 5 is 45. Convert \frac{10}{9} and \frac{3}{5} to fractions with denominator 45.

$$\frac{\frac{50}{45}-\frac{27}{45}-3}{4+\frac{3}{2}\times \frac{4}{5}-1}$$

Since \frac{50}{45} and \frac{27}{45} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{50-27}{45}-3}{4+\frac{3}{2}\times \frac{4}{5}-1}$$

Subtract 27 from 50 to get 23.

$$\frac{\frac{23}{45}-3}{4+\frac{3}{2}\times \frac{4}{5}-1}$$

Convert 3 to fraction \frac{135}{45}.

$$\frac{\frac{23}{45}-\frac{135}{45}}{4+\frac{3}{2}\times \frac{4}{5}-1}$$

Since \frac{23}{45} and \frac{135}{45} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{23-135}{45}}{4+\frac{3}{2}\times \frac{4}{5}-1}$$

Subtract 135 from 23 to get -112.

$$\frac{-\frac{112}{45}}{4+\frac{3}{2}\times \frac{4}{5}-1}$$

Multiply \frac{3}{2} times \frac{4}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-\frac{112}{45}}{4+\frac{3\times 4}{2\times 5}-1}$$

Do the multiplications in the fraction \frac{3\times 4}{2\times 5}.

$$\frac{-\frac{112}{45}}{4+\frac{12}{10}-1}$$

Reduce the fraction \frac{12}{10} to lowest terms by extracting and canceling out 2.

$$\frac{-\frac{112}{45}}{4+\frac{6}{5}-1}$$

Convert 4 to fraction \frac{20}{5}.

$$\frac{-\frac{112}{45}}{\frac{20}{5}+\frac{6}{5}-1}$$

Since \frac{20}{5} and \frac{6}{5} have the same denominator, add them by adding their numerators.

$$\frac{-\frac{112}{45}}{\frac{20+6}{5}-1}$$

Add 20 and 6 to get 26.

$$\frac{-\frac{112}{45}}{\frac{26}{5}-1}$$

Convert 1 to fraction \frac{5}{5}.

$$\frac{-\frac{112}{45}}{\frac{26}{5}-\frac{5}{5}}$$

Since \frac{26}{5} and \frac{5}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-\frac{112}{45}}{\frac{26-5}{5}}$$

Subtract 5 from 26 to get 21.

$$\frac{-\frac{112}{45}}{\frac{21}{5}}$$

Divide -\frac{112}{45} by \frac{21}{5} by multiplying -\frac{112}{45} by the reciprocal of \frac{21}{5}.

$$-\frac{112}{45}\times \frac{5}{21}$$

Multiply -\frac{112}{45} times \frac{5}{21} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-112\times 5}{45\times 21}$$

Do the multiplications in the fraction \frac{-112\times 5}{45\times 21}.

$$\frac{-560}{945}$$

Reduce the fraction \frac{-560}{945} to lowest terms by extracting and canceling out 35.

$$-\frac{16}{27}$$

Factor

$$-\frac{16}{27} = -0.5925925925925926$$