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

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

Evaluate

$$\frac{44}{15}\approx 2.933333333$$

Solution Steps

Express 2\times \frac{4}{15} as a single fraction.

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

Multiply 2 and 4 to get 8.

$$\frac{8}{15}-\frac{2-\frac{1\times 15+1}{15}}{\frac{4}{9}}+\frac{9}{2}$$

Multiply 1 and 15 to get 15.

$$\frac{8}{15}-\frac{2-\frac{15+1}{15}}{\frac{4}{9}}+\frac{9}{2}$$

Add 15 and 1 to get 16.

$$\frac{8}{15}-\frac{2-\frac{16}{15}}{\frac{4}{9}}+\frac{9}{2}$$

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

$$\frac{8}{15}-\frac{\frac{30}{15}-\frac{16}{15}}{\frac{4}{9}}+\frac{9}{2}$$

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

$$\frac{8}{15}-\frac{\frac{30-16}{15}}{\frac{4}{9}}+\frac{9}{2}$$

Subtract 16 from 30 to get 14.

$$\frac{8}{15}-\frac{\frac{14}{15}}{\frac{4}{9}}+\frac{9}{2}$$

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

$$\frac{8}{15}-\frac{14}{15}\times \frac{9}{4}+\frac{9}{2}$$

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

$$\frac{8}{15}-\frac{14\times 9}{15\times 4}+\frac{9}{2}$$

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

$$\frac{8}{15}-\frac{126}{60}+\frac{9}{2}$$

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

$$\frac{8}{15}-\frac{21}{10}+\frac{9}{2}$$

Least common multiple of 15 and 10 is 30. Convert \frac{8}{15} and \frac{21}{10} to fractions with denominator 30.

$$\frac{16}{30}-\frac{63}{30}+\frac{9}{2}$$

Since \frac{16}{30} and \frac{63}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{16-63}{30}+\frac{9}{2}$$

Subtract 63 from 16 to get -47.

$$-\frac{47}{30}+\frac{9}{2}$$

Least common multiple of 30 and 2 is 30. Convert -\frac{47}{30} and \frac{9}{2} to fractions with denominator 30.

$$-\frac{47}{30}+\frac{135}{30}$$

Since -\frac{47}{30} and \frac{135}{30} have the same denominator, add them by adding their numerators.

$$\frac{-47+135}{30}$$

Add -47 and 135 to get 88.

$$\frac{88}{30}$$

Reduce the fraction \frac{88}{30} to lowest terms by extracting and canceling out 2.

$$\frac{44}{15}$$

Factor

$$\frac{2 ^ {2} \cdot 11}{3 \cdot 5} = 2\frac{14}{15} = 2.933333333333333$$