Solve 1/32(1/4)^2-1/4-4

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

Evaluate

$$-\frac{101}{24}\approx -4.208333333$$

Solution Steps

Multiply \frac{1}{3} and 2 to get \frac{2}{3}.

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

Calculate \frac{1}{4} to the power of 2 and get \frac{1}{16}.

$$\frac{2}{3}\times \frac{1}{16}-\frac{1}{4}-4$$

Multiply \frac{2}{3} times \frac{1}{16} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2\times 1}{3\times 16}-\frac{1}{4}-4$$

Do the multiplications in the fraction \frac{2\times 1}{3\times 16}.

$$\frac{2}{48}-\frac{1}{4}-4$$

Reduce the fraction \frac{2}{48} to lowest terms by extracting and canceling out 2.

$$\frac{1}{24}-\frac{1}{4}-4$$

Least common multiple of 24 and 4 is 24. Convert \frac{1}{24} and \frac{1}{4} to fractions with denominator 24.

$$\frac{1}{24}-\frac{6}{24}-4$$

Since \frac{1}{24} and \frac{6}{24} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1-6}{24}-4$$

Subtract 6 from 1 to get -5.

$$-\frac{5}{24}-4$$

Convert 4 to fraction \frac{96}{24}.

$$-\frac{5}{24}-\frac{96}{24}$$

Since -\frac{5}{24} and \frac{96}{24} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-5-96}{24}$$

Subtract 96 from -5 to get -101.

$$-\frac{101}{24}$$

Factor

$$-\frac{101}{24} = -4\frac{5}{24} = -4.208333333333333$$