Solve C=2-4/5+1/3/2+frac{4{5}+1/3}

$$C = \frac { 2 - \frac { 4 } { 5 } + \frac { 1 } { 3 } } { 2 + \frac { 4 } { 5 } + \frac { 1 } { 3 } }$$

Solve for C

$$C=\frac{23}{47}\approx 0.489361702$$

Steps for Solving Linear Equation

Convert 2 to fraction \frac{10}{5}.

$$C=\frac{\frac{10}{5}-\frac{4}{5}+\frac{1}{3}}{2+\frac{4}{5}+\frac{1}{3}}$$

Since \frac{10}{5} and \frac{4}{5} have the same denominator, subtract them by subtracting their numerators.

$$C=\frac{\frac{10-4}{5}+\frac{1}{3}}{2+\frac{4}{5}+\frac{1}{3}}$$

Subtract 4 from 10 to get 6.

$$C=\frac{\frac{6}{5}+\frac{1}{3}}{2+\frac{4}{5}+\frac{1}{3}}$$

Least common multiple of 5 and 3 is 15. Convert \frac{6}{5} and \frac{1}{3} to fractions with denominator 15.

$$C=\frac{\frac{18}{15}+\frac{5}{15}}{2+\frac{4}{5}+\frac{1}{3}}$$

Since \frac{18}{15} and \frac{5}{15} have the same denominator, add them by adding their numerators.

$$C=\frac{\frac{18+5}{15}}{2+\frac{4}{5}+\frac{1}{3}}$$

Add 18 and 5 to get 23.

$$C=\frac{\frac{23}{15}}{2+\frac{4}{5}+\frac{1}{3}}$$

Convert 2 to fraction \frac{10}{5}.

$$C=\frac{\frac{23}{15}}{\frac{10}{5}+\frac{4}{5}+\frac{1}{3}}$$

Since \frac{10}{5} and \frac{4}{5} have the same denominator, add them by adding their numerators.

$$C=\frac{\frac{23}{15}}{\frac{10+4}{5}+\frac{1}{3}}$$

Add 10 and 4 to get 14.

$$C=\frac{\frac{23}{15}}{\frac{14}{5}+\frac{1}{3}}$$

Least common multiple of 5 and 3 is 15. Convert \frac{14}{5} and \frac{1}{3} to fractions with denominator 15.

$$C=\frac{\frac{23}{15}}{\frac{42}{15}+\frac{5}{15}}$$

Since \frac{42}{15} and \frac{5}{15} have the same denominator, add them by adding their numerators.

$$C=\frac{\frac{23}{15}}{\frac{42+5}{15}}$$

Add 42 and 5 to get 47.

$$C=\frac{\frac{23}{15}}{\frac{47}{15}}$$

Divide \frac{23}{15} by \frac{47}{15} by multiplying \frac{23}{15} by the reciprocal of \frac{47}{15}.

$$C=\frac{23}{15}\times \frac{15}{47}$$

Multiply \frac{23}{15} times \frac{15}{47} by multiplying numerator times numerator and denominator times denominator.

$$C=\frac{23\times 15}{15\times 47}$$

Cancel out 15 in both numerator and denominator.

$$C=\frac{23}{47}$$

Assign C

$$C≔\frac{23}{47}$$