Solve [3/4+2/3:(3/4-2)]*6/41*frac{1}{2}

$$[ \frac { 3 } { 4 } + \frac { 2 } { 3 } : ( \frac { 3 } { 4 } - 2 ) ] \cdot \frac { 6 } { 41 } \cdot \frac { 1 } { 2 }$$

Evaluate

$$\frac{13}{820}\approx 0.015853659$$

Solution Steps

Convert 2 to fraction \frac{8}{4}.

$$\left(\frac{3}{4}+\frac{\frac{2}{3}}{\frac{3}{4}-\frac{8}{4}}\right)\times \frac{6}{41}\times \frac{1}{2}$$

Since \frac{3}{4} and \frac{8}{4} have the same denominator, subtract them by subtracting their numerators.

$$\left(\frac{3}{4}+\frac{\frac{2}{3}}{\frac{3-8}{4}}\right)\times \frac{6}{41}\times \frac{1}{2}$$

Subtract 8 from 3 to get -5.

$$\left(\frac{3}{4}+\frac{\frac{2}{3}}{-\frac{5}{4}}\right)\times \frac{6}{41}\times \frac{1}{2}$$

Divide \frac{2}{3} by -\frac{5}{4} by multiplying \frac{2}{3} by the reciprocal of -\frac{5}{4}.

$$\left(\frac{3}{4}+\frac{2}{3}\left(-\frac{4}{5}\right)\right)\times \frac{6}{41}\times \frac{1}{2}$$

Multiply \frac{2}{3} times -\frac{4}{5} by multiplying numerator times numerator and denominator times denominator.

$$\left(\frac{3}{4}+\frac{2\left(-4\right)}{3\times 5}\right)\times \frac{6}{41}\times \frac{1}{2}$$

Do the multiplications in the fraction \frac{2\left(-4\right)}{3\times 5}.

$$\left(\frac{3}{4}+\frac{-8}{15}\right)\times \frac{6}{41}\times \frac{1}{2}$$

Fraction \frac{-8}{15} can be rewritten as -\frac{8}{15} by extracting the negative sign.

$$\left(\frac{3}{4}-\frac{8}{15}\right)\times \frac{6}{41}\times \frac{1}{2}$$

Least common multiple of 4 and 15 is 60. Convert \frac{3}{4} and \frac{8}{15} to fractions with denominator 60.

$$\left(\frac{45}{60}-\frac{32}{60}\right)\times \frac{6}{41}\times \frac{1}{2}$$

Since \frac{45}{60} and \frac{32}{60} have the same denominator, subtract them by subtracting their numerators.

$$\frac{45-32}{60}\times \frac{6}{41}\times \frac{1}{2}$$

Subtract 32 from 45 to get 13.

$$\frac{13}{60}\times \frac{6}{41}\times \frac{1}{2}$$

Multiply \frac{13}{60} times \frac{6}{41} by multiplying numerator times numerator and denominator times denominator.

$$\frac{13\times 6}{60\times 41}\times \frac{1}{2}$$

Do the multiplications in the fraction \frac{13\times 6}{60\times 41}.

$$\frac{78}{2460}\times \frac{1}{2}$$

Reduce the fraction \frac{78}{2460} to lowest terms by extracting and canceling out 6.

$$\frac{13}{410}\times \frac{1}{2}$$

Multiply \frac{13}{410} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{13\times 1}{410\times 2}$$

Do the multiplications in the fraction \frac{13\times 1}{410\times 2}.

$$\frac{13}{820}$$

Factor

$$\frac{13}{2 ^ {2} \cdot 5 \cdot 41} = 0.015853658536585366$$