Solve 1/2+1/2/6-frac{frac{7{4}}{2}}-1/11

$$\frac{ 1 }{ 2 } + \frac{ \frac{ 1 }{ 2 } }{ 6- \frac{ \frac{ 7 }{ 4 } }{ 2 } } - \frac{ 1 }{ 11 }$$

Evaluate

$$\frac{457}{902}\approx 0.506651885$$

Solution Steps

Express \frac{\frac{7}{4}}{2} as a single fraction.

$$\frac{1}{2}+\frac{\frac{1}{2}}{6-\frac{7}{4\times 2}}-\frac{1}{11}$$

Multiply 4 and 2 to get 8.

$$\frac{1}{2}+\frac{\frac{1}{2}}{6-\frac{7}{8}}-\frac{1}{11}$$

Convert 6 to fraction \frac{48}{8}.

$$\frac{1}{2}+\frac{\frac{1}{2}}{\frac{48}{8}-\frac{7}{8}}-\frac{1}{11}$$

Since \frac{48}{8} and \frac{7}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{2}+\frac{\frac{1}{2}}{\frac{48-7}{8}}-\frac{1}{11}$$

Subtract 7 from 48 to get 41.

$$\frac{1}{2}+\frac{\frac{1}{2}}{\frac{41}{8}}-\frac{1}{11}$$

Divide \frac{1}{2} by \frac{41}{8} by multiplying \frac{1}{2} by the reciprocal of \frac{41}{8}.

$$\frac{1}{2}+\frac{1}{2}\times \frac{8}{41}-\frac{1}{11}$$

Multiply \frac{1}{2} times \frac{8}{41} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{2}+\frac{1\times 8}{2\times 41}-\frac{1}{11}$$

Do the multiplications in the fraction \frac{1\times 8}{2\times 41}.

$$\frac{1}{2}+\frac{8}{82}-\frac{1}{11}$$

Reduce the fraction \frac{8}{82} to lowest terms by extracting and canceling out 2.

$$\frac{1}{2}+\frac{4}{41}-\frac{1}{11}$$

Least common multiple of 2 and 41 is 82. Convert \frac{1}{2} and \frac{4}{41} to fractions with denominator 82.

$$\frac{41}{82}+\frac{8}{82}-\frac{1}{11}$$

Since \frac{41}{82} and \frac{8}{82} have the same denominator, add them by adding their numerators.

$$\frac{41+8}{82}-\frac{1}{11}$$

Add 41 and 8 to get 49.

$$\frac{49}{82}-\frac{1}{11}$$

Least common multiple of 82 and 11 is 902. Convert \frac{49}{82} and \frac{1}{11} to fractions with denominator 902.

$$\frac{539}{902}-\frac{82}{902}$$

Since \frac{539}{902} and \frac{82}{902} have the same denominator, subtract them by subtracting their numerators.

$$\frac{539-82}{902}$$

Subtract 82 from 539 to get 457.

$$\frac{457}{902}$$

Factor

$$\frac{457}{2 \cdot 11 \cdot 41} = 0.5066518847006651$$