Solve (1/3)^2*(1-1/4)/frac{8{9}+11/3-2/3}

$$\frac { ( 1 / 3 ) ^ { 2 } \times ( 1 - \frac { 1 } { 4 } ) } { \frac { 8 } { 9 } + \frac { 11 } { 3 } - \frac { 2 } { 3 } }$$

Evaluate

$$\frac{3}{140}\approx 0.021428571$$

Solution Steps

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

$$\frac{\frac{1}{9}\left(1-\frac{1}{4}\right)}{\frac{8}{9}+\frac{11}{3}-\frac{2}{3}}$$

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

$$\frac{\frac{1}{9}\left(\frac{4}{4}-\frac{1}{4}\right)}{\frac{8}{9}+\frac{11}{3}-\frac{2}{3}}$$

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

$$\frac{\frac{1}{9}\times \frac{4-1}{4}}{\frac{8}{9}+\frac{11}{3}-\frac{2}{3}}$$

Subtract 1 from 4 to get 3.

$$\frac{\frac{1}{9}\times \frac{3}{4}}{\frac{8}{9}+\frac{11}{3}-\frac{2}{3}}$$

Multiply \frac{1}{9} times \frac{3}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{1\times 3}{9\times 4}}{\frac{8}{9}+\frac{11}{3}-\frac{2}{3}}$$

Do the multiplications in the fraction \frac{1\times 3}{9\times 4}.

$$\frac{\frac{3}{36}}{\frac{8}{9}+\frac{11}{3}-\frac{2}{3}}$$

Reduce the fraction \frac{3}{36} to lowest terms by extracting and canceling out 3.

$$\frac{\frac{1}{12}}{\frac{8}{9}+\frac{11}{3}-\frac{2}{3}}$$

Least common multiple of 9 and 3 is 9. Convert \frac{8}{9} and \frac{11}{3} to fractions with denominator 9.

$$\frac{\frac{1}{12}}{\frac{8}{9}+\frac{33}{9}-\frac{2}{3}}$$

Since \frac{8}{9} and \frac{33}{9} have the same denominator, add them by adding their numerators.

$$\frac{\frac{1}{12}}{\frac{8+33}{9}-\frac{2}{3}}$$

Add 8 and 33 to get 41.

$$\frac{\frac{1}{12}}{\frac{41}{9}-\frac{2}{3}}$$

Least common multiple of 9 and 3 is 9. Convert \frac{41}{9} and \frac{2}{3} to fractions with denominator 9.

$$\frac{\frac{1}{12}}{\frac{41}{9}-\frac{6}{9}}$$

Since \frac{41}{9} and \frac{6}{9} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{1}{12}}{\frac{41-6}{9}}$$

Subtract 6 from 41 to get 35.

$$\frac{\frac{1}{12}}{\frac{35}{9}}$$

Divide \frac{1}{12} by \frac{35}{9} by multiplying \frac{1}{12} by the reciprocal of \frac{35}{9}.

$$\frac{1}{12}\times \frac{9}{35}$$

Multiply \frac{1}{12} times \frac{9}{35} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 9}{12\times 35}$$

Do the multiplications in the fraction \frac{1\times 9}{12\times 35}.

$$\frac{9}{420}$$

Reduce the fraction \frac{9}{420} to lowest terms by extracting and canceling out 3.

$$\frac{3}{140}$$

Factor

$$\frac{3}{2 ^ {2} \cdot 5 \cdot 7} = 0.02142857142857143$$