Solve (3/2div4/9)+2/3-3/2+(frac{5}{9}+frac{2}{3})

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

Evaluate

$$\frac{271}{72}\approx 3.763888889$$

Solution Steps

Divide \frac{3}{2} by \frac{4}{9} by multiplying \frac{3}{2} by the reciprocal of \frac{4}{9}.

$$\frac{3}{2}\times \frac{9}{4}+\frac{2}{3}-\frac{3}{2}+\frac{5}{9}+\frac{2}{3}$$

Multiply \frac{3}{2} times \frac{9}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\times 9}{2\times 4}+\frac{2}{3}-\frac{3}{2}+\frac{5}{9}+\frac{2}{3}$$

Do the multiplications in the fraction \frac{3\times 9}{2\times 4}.

$$\frac{27}{8}+\frac{2}{3}-\frac{3}{2}+\frac{5}{9}+\frac{2}{3}$$

Least common multiple of 8 and 3 is 24. Convert \frac{27}{8} and \frac{2}{3} to fractions with denominator 24.

$$\frac{81}{24}+\frac{16}{24}-\frac{3}{2}+\frac{5}{9}+\frac{2}{3}$$

Since \frac{81}{24} and \frac{16}{24} have the same denominator, add them by adding their numerators.

$$\frac{81+16}{24}-\frac{3}{2}+\frac{5}{9}+\frac{2}{3}$$

Add 81 and 16 to get 97.

$$\frac{97}{24}-\frac{3}{2}+\frac{5}{9}+\frac{2}{3}$$

Least common multiple of 24 and 2 is 24. Convert \frac{97}{24} and \frac{3}{2} to fractions with denominator 24.

$$\frac{97}{24}-\frac{36}{24}+\frac{5}{9}+\frac{2}{3}$$

Since \frac{97}{24} and \frac{36}{24} have the same denominator, subtract them by subtracting their numerators.

$$\frac{97-36}{24}+\frac{5}{9}+\frac{2}{3}$$

Subtract 36 from 97 to get 61.

$$\frac{61}{24}+\frac{5}{9}+\frac{2}{3}$$

Least common multiple of 24 and 9 is 72. Convert \frac{61}{24} and \frac{5}{9} to fractions with denominator 72.

$$\frac{183}{72}+\frac{40}{72}+\frac{2}{3}$$

Since \frac{183}{72} and \frac{40}{72} have the same denominator, add them by adding their numerators.

$$\frac{183+40}{72}+\frac{2}{3}$$

Add 183 and 40 to get 223.

$$\frac{223}{72}+\frac{2}{3}$$

Least common multiple of 72 and 3 is 72. Convert \frac{223}{72} and \frac{2}{3} to fractions with denominator 72.

$$\frac{223}{72}+\frac{48}{72}$$

Since \frac{223}{72} and \frac{48}{72} have the same denominator, add them by adding their numerators.

$$\frac{223+48}{72}$$

Add 223 and 48 to get 271.

$$\frac{271}{72}$$

Factor

$$\frac{271}{2 ^ {3} \cdot 3 ^ {2}} = 3\frac{55}{72} = 3.763888888888889$$