Solve 1-[(3/5div2/15-1)^2+1div(-1/2)^2]div1/4

$$1 - [ ( \frac { 3 } { 5 } \div \frac { 2 } { 15 } - 1 ) ^ { 2 } + 1 \div ( - \frac { 1 } { 2 } ) ^ { 2 } ] \div \frac { 1 } { 4 }$$

Evaluate

$$-64$$

Solution Steps

Divide \frac{3}{5} by \frac{2}{15} by multiplying \frac{3}{5} by the reciprocal of \frac{2}{15}.

$$1-\frac{\left(\frac{3}{5}\times \frac{15}{2}-1\right)^{2}+\frac{1}{\left(-\frac{1}{2}\right)^{2}}}{\frac{1}{4}}$$

Multiply \frac{3}{5} and \frac{15}{2} to get \frac{9}{2}.

$$1-\frac{\left(\frac{9}{2}-1\right)^{2}+\frac{1}{\left(-\frac{1}{2}\right)^{2}}}{\frac{1}{4}}$$

Subtract 1 from \frac{9}{2} to get \frac{7}{2}.

$$1-\frac{\left(\frac{7}{2}\right)^{2}+\frac{1}{\left(-\frac{1}{2}\right)^{2}}}{\frac{1}{4}}$$

Calculate \frac{7}{2} to the power of 2 and get \frac{49}{4}.

$$1-\frac{\frac{49}{4}+\frac{1}{\left(-\frac{1}{2}\right)^{2}}}{\frac{1}{4}}$$

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

$$1-\frac{\frac{49}{4}+\frac{1}{\frac{1}{4}}}{\frac{1}{4}}$$

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

$$1-\frac{\frac{49}{4}+1\times 4}{\frac{1}{4}}$$

Multiply 1 and 4 to get 4.

$$1-\frac{\frac{49}{4}+4}{\frac{1}{4}}$$

Add \frac{49}{4} and 4 to get \frac{65}{4}.

$$1-\frac{\frac{65}{4}}{\frac{1}{4}}$$

Divide \frac{65}{4} by \frac{1}{4} by multiplying \frac{65}{4} by the reciprocal of \frac{1}{4}.

$$1-\frac{65}{4}\times 4$$

Multiply \frac{65}{4} and 4 to get 65.

$$1-65$$

Subtract 65 from 1 to get -64.

$$-64$$

Factor

$$-64$$