Solve (14/5-33/8)div(-3/4)^2

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

Evaluate

$$-\frac{14}{5}=-2.8$$

Solution Steps

Multiply 1 and 5 to get 5.

$$\frac{\frac{5+4}{5}-\frac{3\times 8+3}{8}}{\left(-\frac{3}{4}\right)^{2}}$$

Add 5 and 4 to get 9.

$$\frac{\frac{9}{5}-\frac{3\times 8+3}{8}}{\left(-\frac{3}{4}\right)^{2}}$$

Multiply 3 and 8 to get 24.

$$\frac{\frac{9}{5}-\frac{24+3}{8}}{\left(-\frac{3}{4}\right)^{2}}$$

Add 24 and 3 to get 27.

$$\frac{\frac{9}{5}-\frac{27}{8}}{\left(-\frac{3}{4}\right)^{2}}$$

Least common multiple of 5 and 8 is 40. Convert \frac{9}{5} and \frac{27}{8} to fractions with denominator 40.

$$\frac{\frac{72}{40}-\frac{135}{40}}{\left(-\frac{3}{4}\right)^{2}}$$

Since \frac{72}{40} and \frac{135}{40} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{72-135}{40}}{\left(-\frac{3}{4}\right)^{2}}$$

Subtract 135 from 72 to get -63.

$$\frac{-\frac{63}{40}}{\left(-\frac{3}{4}\right)^{2}}$$

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

$$\frac{-\frac{63}{40}}{\frac{9}{16}}$$

Divide -\frac{63}{40} by \frac{9}{16} by multiplying -\frac{63}{40} by the reciprocal of \frac{9}{16}.

$$-\frac{63}{40}\times \frac{16}{9}$$

Multiply -\frac{63}{40} times \frac{16}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-63\times 16}{40\times 9}$$

Do the multiplications in the fraction \frac{-63\times 16}{40\times 9}.

$$\frac{-1008}{360}$$

Reduce the fraction \frac{-1008}{360} to lowest terms by extracting and canceling out 72.

$$-\frac{14}{5}$$

Factor

$$-\frac{14}{5} = -2\frac{4}{5} = -2.8$$