Solve 4/15-(2-11/15):4/9+9/2

$$\frac { 4 } { 15 } - ( 2 - 1 \frac { 1 } { 15 } ) : \frac { 4 } { 9 } + \frac { 9 } { 2 }$$

Evaluate

$$\frac{8}{3}\approx 2.666666667$$

Solution Steps

Multiply 1 and 15 to get 15.

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

Add 15 and 1 to get 16.

$$\frac{4}{15}-\frac{2-\frac{16}{15}}{\frac{4}{9}}+\frac{9}{2}$$

Convert 2 to fraction \frac{30}{15}.

$$\frac{4}{15}-\frac{\frac{30}{15}-\frac{16}{15}}{\frac{4}{9}}+\frac{9}{2}$$

Since \frac{30}{15} and \frac{16}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4}{15}-\frac{\frac{30-16}{15}}{\frac{4}{9}}+\frac{9}{2}$$

Subtract 16 from 30 to get 14.

$$\frac{4}{15}-\frac{\frac{14}{15}}{\frac{4}{9}}+\frac{9}{2}$$

Divide \frac{14}{15} by \frac{4}{9} by multiplying \frac{14}{15} by the reciprocal of \frac{4}{9}.

$$\frac{4}{15}-\frac{14}{15}\times \frac{9}{4}+\frac{9}{2}$$

Multiply \frac{14}{15} times \frac{9}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4}{15}-\frac{14\times 9}{15\times 4}+\frac{9}{2}$$

Do the multiplications in the fraction \frac{14\times 9}{15\times 4}.

$$\frac{4}{15}-\frac{126}{60}+\frac{9}{2}$$

Reduce the fraction \frac{126}{60} to lowest terms by extracting and canceling out 6.

$$\frac{4}{15}-\frac{21}{10}+\frac{9}{2}$$

Least common multiple of 15 and 10 is 30. Convert \frac{4}{15} and \frac{21}{10} to fractions with denominator 30.

$$\frac{8}{30}-\frac{63}{30}+\frac{9}{2}$$

Since \frac{8}{30} and \frac{63}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{8-63}{30}+\frac{9}{2}$$

Subtract 63 from 8 to get -55.

$$\frac{-55}{30}+\frac{9}{2}$$

Reduce the fraction \frac{-55}{30} to lowest terms by extracting and canceling out 5.

$$-\frac{11}{6}+\frac{9}{2}$$

Least common multiple of 6 and 2 is 6. Convert -\frac{11}{6} and \frac{9}{2} to fractions with denominator 6.

$$-\frac{11}{6}+\frac{27}{6}$$

Since -\frac{11}{6} and \frac{27}{6} have the same denominator, add them by adding their numerators.

$$\frac{-11+27}{6}$$

Add -11 and 27 to get 16.

$$\frac{16}{6}$$

Reduce the fraction \frac{16}{6} to lowest terms by extracting and canceling out 2.

$$\frac{8}{3}$$

Factor

$$\frac{2 ^ {3}}{3} = 2\frac{2}{3} = 2.6666666666666665$$