Solve 1/21=(1/2)^2-4/(frac{1{3})^3-(1/2)^2-6(frac{1}{2})}

$$\frac { 1 } { 2 } 1 = \frac { ( \frac { 1 } { 2 } ) ^ { 2 } - 4 } { ( \frac { 1 } { 3 } ) ^ { 3 } - ( \frac { 1 } { 2 } ) ^ { 2 } - 6 ( \frac { 1 } { 2 } ) }$$

Verify

Solution Steps

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

$$\frac{1}{2}=\frac{\left(\frac{1}{2}\right)^{2}-4}{\left(\frac{1}{3}\right)^{3}-\left(\frac{1}{2}\right)^{2}-6\times \frac{1}{2}}$$

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

$$\frac{1}{2}=\frac{\frac{1}{4}-4}{\left(\frac{1}{3}\right)^{3}-\left(\frac{1}{2}\right)^{2}-6\times \frac{1}{2}}$$

Convert 4 to fraction \frac{16}{4}.

$$\frac{1}{2}=\frac{\frac{1}{4}-\frac{16}{4}}{\left(\frac{1}{3}\right)^{3}-\left(\frac{1}{2}\right)^{2}-6\times \frac{1}{2}}$$

Since \frac{1}{4} and \frac{16}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{2}=\frac{\frac{1-16}{4}}{\left(\frac{1}{3}\right)^{3}-\left(\frac{1}{2}\right)^{2}-6\times \frac{1}{2}}$$

Subtract 16 from 1 to get -15.

$$\frac{1}{2}=\frac{-\frac{15}{4}}{\left(\frac{1}{3}\right)^{3}-\left(\frac{1}{2}\right)^{2}-6\times \frac{1}{2}}$$

Calculate \frac{1}{3} to the power of 3 and get \frac{1}{27}.

$$\frac{1}{2}=\frac{-\frac{15}{4}}{\frac{1}{27}-\left(\frac{1}{2}\right)^{2}-6\times \frac{1}{2}}$$

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

$$\frac{1}{2}=\frac{-\frac{15}{4}}{\frac{1}{27}-\frac{1}{4}-6\times \frac{1}{2}}$$

Least common multiple of 27 and 4 is 108. Convert \frac{1}{27} and \frac{1}{4} to fractions with denominator 108.

$$\frac{1}{2}=\frac{-\frac{15}{4}}{\frac{4}{108}-\frac{27}{108}-6\times \frac{1}{2}}$$

Since \frac{4}{108} and \frac{27}{108} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{2}=\frac{-\frac{15}{4}}{\frac{4-27}{108}-6\times \frac{1}{2}}$$

Subtract 27 from 4 to get -23.

$$\frac{1}{2}=\frac{-\frac{15}{4}}{-\frac{23}{108}-6\times \frac{1}{2}}$$

Multiply 6 and \frac{1}{2} to get \frac{6}{2}.

$$\frac{1}{2}=\frac{-\frac{15}{4}}{-\frac{23}{108}-\frac{6}{2}}$$

Divide 6 by 2 to get 3.

$$\frac{1}{2}=\frac{-\frac{15}{4}}{-\frac{23}{108}-3}$$

Convert 3 to fraction \frac{324}{108}.

$$\frac{1}{2}=\frac{-\frac{15}{4}}{-\frac{23}{108}-\frac{324}{108}}$$

Since -\frac{23}{108} and \frac{324}{108} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{2}=\frac{-\frac{15}{4}}{\frac{-23-324}{108}}$$

Subtract 324 from -23 to get -347.

$$\frac{1}{2}=\frac{-\frac{15}{4}}{-\frac{347}{108}}$$

Divide -\frac{15}{4} by -\frac{347}{108} by multiplying -\frac{15}{4} by the reciprocal of -\frac{347}{108}.

$$\frac{1}{2}=-\frac{15}{4}\left(-\frac{108}{347}\right)$$

Multiply -\frac{15}{4} times -\frac{108}{347} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{2}=\frac{-15\left(-108\right)}{4\times 347}$$

Do the multiplications in the fraction \frac{-15\left(-108\right)}{4\times 347}.

$$\frac{1}{2}=\frac{1620}{1388}$$

Reduce the fraction \frac{1620}{1388} to lowest terms by extracting and canceling out 4.

$$\frac{1}{2}=\frac{405}{347}$$

Least common multiple of 2 and 347 is 694. Convert \frac{1}{2} and \frac{405}{347} to fractions with denominator 694.

$$\frac{347}{694}=\frac{810}{694}$$

Compare \frac{347}{694} and \frac{810}{694}.

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