Solve A=(5-2/3)div(2/3+1/4)+4/9

$$A = ( 5 - \frac { 2 } { 3 } ) \div ( \frac { 2 } { 3 } + \frac { 1 } { 4 } ) + \frac { 4 } { 9 }$$

Solve for A

$$A = \frac{512}{99} = 5\frac{17}{99} \approx 5.171717172$$

Steps for Solving Linear Equation

Convert 5 to fraction \frac{15}{3}.

$$A=\frac{\frac{15}{3}-\frac{2}{3}}{\frac{2}{3}+\frac{1}{4}}+\frac{4}{9}$$

Since \frac{15}{3} and \frac{2}{3} have the same denominator, subtract them by subtracting their numerators.

$$A=\frac{\frac{15-2}{3}}{\frac{2}{3}+\frac{1}{4}}+\frac{4}{9}$$

Subtract 2 from 15 to get 13.

$$A=\frac{\frac{13}{3}}{\frac{2}{3}+\frac{1}{4}}+\frac{4}{9}$$

Least common multiple of 3 and 4 is 12. Convert \frac{2}{3} and \frac{1}{4} to fractions with denominator 12.

$$A=\frac{\frac{13}{3}}{\frac{8}{12}+\frac{3}{12}}+\frac{4}{9}$$

Since \frac{8}{12} and \frac{3}{12} have the same denominator, add them by adding their numerators.

$$A=\frac{\frac{13}{3}}{\frac{8+3}{12}}+\frac{4}{9}$$

Add 8 and 3 to get 11.

$$A=\frac{\frac{13}{3}}{\frac{11}{12}}+\frac{4}{9}$$

Divide \frac{13}{3} by \frac{11}{12} by multiplying \frac{13}{3} by the reciprocal of \frac{11}{12}.

$$A=\frac{13}{3}\times \frac{12}{11}+\frac{4}{9}$$

Multiply \frac{13}{3} times \frac{12}{11} by multiplying numerator times numerator and denominator times denominator.

$$A=\frac{13\times 12}{3\times 11}+\frac{4}{9}$$

Do the multiplications in the fraction \frac{13\times 12}{3\times 11}.

$$A=\frac{156}{33}+\frac{4}{9}$$

Reduce the fraction \frac{156}{33} to lowest terms by extracting and canceling out 3.

$$A=\frac{52}{11}+\frac{4}{9}$$

Least common multiple of 11 and 9 is 99. Convert \frac{52}{11} and \frac{4}{9} to fractions with denominator 99.

$$A=\frac{468}{99}+\frac{44}{99}$$

Since \frac{468}{99} and \frac{44}{99} have the same denominator, add them by adding their numerators.

$$A=\frac{468+44}{99}$$

Add 468 and 44 to get 512.

$$A=\frac{512}{99}$$

Assign A

$$A≔\frac{512}{99}$$