Solve 24/15-(2-11/15):4/9+9/2

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

Evaluate

$$\frac{14}{3}\approx 4.666666667$$

Solution Steps

Multiply 2 and 15 to get 30.

$$\frac{30+4}{15}-\frac{2-\frac{1\times 15+1}{15}}{\frac{4}{9}}+\frac{9}{2}$$

Add 30 and 4 to get 34.

$$\frac{34}{15}-\frac{2-\frac{1\times 15+1}{15}}{\frac{4}{9}}+\frac{9}{2}$$

Multiply 1 and 15 to get 15.

$$\frac{34}{15}-\frac{2-\frac{15+1}{15}}{\frac{4}{9}}+\frac{9}{2}$$

Add 15 and 1 to get 16.

$$\frac{34}{15}-\frac{2-\frac{16}{15}}{\frac{4}{9}}+\frac{9}{2}$$

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

$$\frac{34}{15}-\frac{\frac{30}{15}-\frac{16}{15}}{\frac{4}{9}}+\frac{9}{2}$$

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

$$\frac{34}{15}-\frac{\frac{30-16}{15}}{\frac{4}{9}}+\frac{9}{2}$$

Subtract 16 from 30 to get 14.

$$\frac{34}{15}-\frac{\frac{14}{15}}{\frac{4}{9}}+\frac{9}{2}$$

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

$$\frac{34}{15}-\frac{14}{15}\times \frac{9}{4}+\frac{9}{2}$$

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

$$\frac{34}{15}-\frac{14\times 9}{15\times 4}+\frac{9}{2}$$

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

$$\frac{34}{15}-\frac{126}{60}+\frac{9}{2}$$

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

$$\frac{34}{15}-\frac{21}{10}+\frac{9}{2}$$

Least common multiple of 15 and 10 is 30. Convert \frac{34}{15} and \frac{21}{10} to fractions with denominator 30.

$$\frac{68}{30}-\frac{63}{30}+\frac{9}{2}$$

Since \frac{68}{30} and \frac{63}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{68-63}{30}+\frac{9}{2}$$

Subtract 63 from 68 to get 5.

$$\frac{5}{30}+\frac{9}{2}$$

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

$$\frac{1}{6}+\frac{9}{2}$$

Least common multiple of 6 and 2 is 6. Convert \frac{1}{6} and \frac{9}{2} to fractions with denominator 6.

$$\frac{1}{6}+\frac{27}{6}$$

Since \frac{1}{6} and \frac{27}{6} have the same denominator, add them by adding their numerators.

$$\frac{1+27}{6}$$

Add 1 and 27 to get 28.

$$\frac{28}{6}$$

Reduce the fraction \frac{28}{6} to lowest terms by extracting and canceling out 2.

$$\frac{14}{3}$$

Factor

$$\frac{2 \cdot 7}{3} = 4\frac{2}{3} = 4.666666666666667$$