Solve 3{left(1/2right)}^2-22{left(1/3right)}^2-221/3

$$3 { \left( \frac{ 1 }{ 2 } \right) }^{ 2 } -22 { \left( \frac{ 1 }{ 3 } \right) }^{ 2 } -22 \frac{ 1 }{ 3 }$$

Evaluate

$$-\frac{865}{36}\approx -24.027777778$$

Solution Steps

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

$$3\times \frac{1}{4}-22\times \left(\frac{1}{3}\right)^{2}-\frac{22\times 3+1}{3}$$

Multiply 3 and \frac{1}{4} to get \frac{3}{4}.

$$\frac{3}{4}-22\times \left(\frac{1}{3}\right)^{2}-\frac{22\times 3+1}{3}$$

Calculate \frac{1}{3} to the power of 2 and get \frac{1}{9}.

$$\frac{3}{4}-22\times \frac{1}{9}-\frac{22\times 3+1}{3}$$

Multiply 22 and \frac{1}{9} to get \frac{22}{9}.

$$\frac{3}{4}-\frac{22}{9}-\frac{22\times 3+1}{3}$$

Least common multiple of 4 and 9 is 36. Convert \frac{3}{4} and \frac{22}{9} to fractions with denominator 36.

$$\frac{27}{36}-\frac{88}{36}-\frac{22\times 3+1}{3}$$

Since \frac{27}{36} and \frac{88}{36} have the same denominator, subtract them by subtracting their numerators.

$$\frac{27-88}{36}-\frac{22\times 3+1}{3}$$

Subtract 88 from 27 to get -61.

$$-\frac{61}{36}-\frac{22\times 3+1}{3}$$

Multiply 22 and 3 to get 66.

$$-\frac{61}{36}-\frac{66+1}{3}$$

Add 66 and 1 to get 67.

$$-\frac{61}{36}-\frac{67}{3}$$

Least common multiple of 36 and 3 is 36. Convert -\frac{61}{36} and \frac{67}{3} to fractions with denominator 36.

$$-\frac{61}{36}-\frac{804}{36}$$

Since -\frac{61}{36} and \frac{804}{36} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-61-804}{36}$$

Subtract 804 from -61 to get -865.

$$-\frac{865}{36}$$

Factor

$$-\frac{865}{36} = -24\frac{1}{36} = -24.02777777777778$$