Solve 1/2+1/23:(6-7/4:2)-1/41=

$$\frac { 1 } { 2 } + \frac { 1 } { 23 } : ( 6 - \frac { 7 } { 4 } : 2 ) - \frac { 1 } { 41 } =$$

Evaluate

$$\frac{913}{1886}\approx 0.484093319$$

Solution Steps

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

$$\frac{1}{2}+\frac{\frac{1}{23}}{6-\frac{7}{4\times 2}}-\frac{1}{41}$$

Multiply 4 and 2 to get 8.

$$\frac{1}{2}+\frac{\frac{1}{23}}{6-\frac{7}{8}}-\frac{1}{41}$$

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

$$\frac{1}{2}+\frac{\frac{1}{23}}{\frac{48}{8}-\frac{7}{8}}-\frac{1}{41}$$

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

$$\frac{1}{2}+\frac{\frac{1}{23}}{\frac{48-7}{8}}-\frac{1}{41}$$

Subtract 7 from 48 to get 41.

$$\frac{1}{2}+\frac{\frac{1}{23}}{\frac{41}{8}}-\frac{1}{41}$$

Divide \frac{1}{23} by \frac{41}{8} by multiplying \frac{1}{23} by the reciprocal of \frac{41}{8}.

$$\frac{1}{2}+\frac{1}{23}\times \frac{8}{41}-\frac{1}{41}$$

Multiply \frac{1}{23} times \frac{8}{41} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{2}+\frac{1\times 8}{23\times 41}-\frac{1}{41}$$

Do the multiplications in the fraction \frac{1\times 8}{23\times 41}.

$$\frac{1}{2}+\frac{8}{943}-\frac{1}{41}$$

Least common multiple of 2 and 943 is 1886. Convert \frac{1}{2} and \frac{8}{943} to fractions with denominator 1886.

$$\frac{943}{1886}+\frac{16}{1886}-\frac{1}{41}$$

Since \frac{943}{1886} and \frac{16}{1886} have the same denominator, add them by adding their numerators.

$$\frac{943+16}{1886}-\frac{1}{41}$$

Add 943 and 16 to get 959.

$$\frac{959}{1886}-\frac{1}{41}$$

Least common multiple of 1886 and 41 is 1886. Convert \frac{959}{1886} and \frac{1}{41} to fractions with denominator 1886.

$$\frac{959}{1886}-\frac{46}{1886}$$

Since \frac{959}{1886} and \frac{46}{1886} have the same denominator, subtract them by subtracting their numerators.

$$\frac{959-46}{1886}$$

Subtract 46 from 959 to get 913.

$$\frac{913}{1886}$$

Factor

$$\frac{11 \cdot 83}{2 \cdot 23 \cdot 41} = 0.4840933191940615$$