Solve 1/8div2-3/4*(5/2)^2

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

Evaluate

$$-\frac{37}{8}=-4.625$$

Solution Steps

Express \frac{\frac{1}{8}}{2} as a single fraction.

$$\frac{1}{8\times 2}-\frac{3}{4}\times \left(\frac{5}{2}\right)^{2}$$

Multiply 8 and 2 to get 16.

$$\frac{1}{16}-\frac{3}{4}\times \left(\frac{5}{2}\right)^{2}$$

Calculate \frac{5}{2} to the power of 2 and get \frac{25}{4}.

$$\frac{1}{16}-\frac{3}{4}\times \frac{25}{4}$$

Multiply \frac{3}{4} times \frac{25}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{16}-\frac{3\times 25}{4\times 4}$$

Do the multiplications in the fraction \frac{3\times 25}{4\times 4}.

$$\frac{1}{16}-\frac{75}{16}$$

Since \frac{1}{16} and \frac{75}{16} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1-75}{16}$$

Subtract 75 from 1 to get -74.

$$\frac{-74}{16}$$

Reduce the fraction \frac{-74}{16} to lowest terms by extracting and canceling out 2.

$$-\frac{37}{8}$$

Factor

$$-\frac{37}{8} = -4\frac{5}{8} = -4.625$$