Solve 15((1/2)^2-1)/frac{2{3}-1}

$$\frac { 15 ( ( \frac { 1 } { 2 } ) ^ { 2 } - 1 ) } { \frac { 2 } { 3 } - 1 }$$

Evaluate

$$\frac{135}{4}=33.75$$

Solution Steps

Calculate \frac{1}{2} to the power of 2 and get \frac{1}{4}.

$$\frac{15\left(\frac{1}{4}-1\right)}{\frac{2}{3}-1}$$

Convert 1 to fraction \frac{4}{4}.

$$\frac{15\left(\frac{1}{4}-\frac{4}{4}\right)}{\frac{2}{3}-1}$$

Since \frac{1}{4} and \frac{4}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{15\times \frac{1-4}{4}}{\frac{2}{3}-1}$$

Subtract 4 from 1 to get -3.

$$\frac{15\left(-\frac{3}{4}\right)}{\frac{2}{3}-1}$$

Express 15\left(-\frac{3}{4}\right) as a single fraction.

$$\frac{\frac{15\left(-3\right)}{4}}{\frac{2}{3}-1}$$

Multiply 15 and -3 to get -45.

$$\frac{\frac{-45}{4}}{\frac{2}{3}-1}$$

Fraction \frac{-45}{4} can be rewritten as -\frac{45}{4} by extracting the negative sign.

$$\frac{-\frac{45}{4}}{\frac{2}{3}-1}$$

Convert 1 to fraction \frac{3}{3}.

$$\frac{-\frac{45}{4}}{\frac{2}{3}-\frac{3}{3}}$$

Since \frac{2}{3} and \frac{3}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-\frac{45}{4}}{\frac{2-3}{3}}$$

Subtract 3 from 2 to get -1.

$$\frac{-\frac{45}{4}}{-\frac{1}{3}}$$

Divide -\frac{45}{4} by -\frac{1}{3} by multiplying -\frac{45}{4} by the reciprocal of -\frac{1}{3}.

$$-\frac{45}{4}\left(-3\right)$$

Express -\frac{45}{4}\left(-3\right) as a single fraction.

$$\frac{-45\left(-3\right)}{4}$$

Multiply -45 and -3 to get 135.

$$\frac{135}{4}$$

Factor

$$\frac{3 ^ {3} \cdot 5}{2 ^ {2}} = 33\frac{3}{4} = 33.75$$