Solve [5/2-(1-1/3)]*1/4:121/12

$$[ \frac { 5 } { 2 } - ( 1 - \frac { 1 } { 3 } ) ] \times \frac { 1 } { 4 } : \frac { 121 } { 12 }$$

Evaluate

$$\frac{1}{22}\approx 0.045454545$$

Solution Steps

Convert 1 to fraction \frac{3}{3}.

$$\frac{\left(\frac{5}{2}-\left(\frac{3}{3}-\frac{1}{3}\right)\right)\times \frac{1}{4}}{\frac{121}{12}}$$

Since \frac{3}{3} and \frac{1}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\left(\frac{5}{2}-\frac{3-1}{3}\right)\times \frac{1}{4}}{\frac{121}{12}}$$

Subtract 1 from 3 to get 2.

$$\frac{\left(\frac{5}{2}-\frac{2}{3}\right)\times \frac{1}{4}}{\frac{121}{12}}$$

Least common multiple of 2 and 3 is 6. Convert \frac{5}{2} and \frac{2}{3} to fractions with denominator 6.

$$\frac{\left(\frac{15}{6}-\frac{4}{6}\right)\times \frac{1}{4}}{\frac{121}{12}}$$

Since \frac{15}{6} and \frac{4}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{15-4}{6}\times \frac{1}{4}}{\frac{121}{12}}$$

Subtract 4 from 15 to get 11.

$$\frac{\frac{11}{6}\times \frac{1}{4}}{\frac{121}{12}}$$

Multiply \frac{11}{6} times \frac{1}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{11\times 1}{6\times 4}}{\frac{121}{12}}$$

Do the multiplications in the fraction \frac{11\times 1}{6\times 4}.

$$\frac{\frac{11}{24}}{\frac{121}{12}}$$

Divide \frac{11}{24} by \frac{121}{12} by multiplying \frac{11}{24} by the reciprocal of \frac{121}{12}.

$$\frac{11}{24}\times \frac{12}{121}$$

Multiply \frac{11}{24} times \frac{12}{121} by multiplying numerator times numerator and denominator times denominator.

$$\frac{11\times 12}{24\times 121}$$

Do the multiplications in the fraction \frac{11\times 12}{24\times 121}.

$$\frac{132}{2904}$$

Reduce the fraction \frac{132}{2904} to lowest terms by extracting and canceling out 132.

$$\frac{1}{22}$$

Factor

$$\frac{1}{2 \cdot 11} = 0.045454545454545456$$