Solve 2/3*(2-51/2div24/4/15)

$$\frac { 2 } { 3 } \times ( 2 - 5 \frac { 1 } { 2 } \div 2 \frac { 4 / 4 } { 15 } )$$

Evaluate

$$\frac{109}{90}\approx 1.211111111$$

Solution Steps

Divide 4 by 4 to get 1.

$$\frac{2}{3}\left(2-\frac{\frac{5\times 2+1}{2}}{2}\times \frac{1}{15}\right)$$

Express \frac{\frac{5\times 2+1}{2}}{2} as a single fraction.

$$\frac{2}{3}\left(2-\frac{5\times 2+1}{2\times 2}\times \frac{1}{15}\right)$$

Multiply 5 and 2 to get 10.

$$\frac{2}{3}\left(2-\frac{10+1}{2\times 2}\times \frac{1}{15}\right)$$

Add 10 and 1 to get 11.

$$\frac{2}{3}\left(2-\frac{11}{2\times 2}\times \frac{1}{15}\right)$$

Multiply 2 and 2 to get 4.

$$\frac{2}{3}\left(2-\frac{11}{4}\times \frac{1}{15}\right)$$

Multiply \frac{11}{4} times \frac{1}{15} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2}{3}\left(2-\frac{11\times 1}{4\times 15}\right)$$

Do the multiplications in the fraction \frac{11\times 1}{4\times 15}.

$$\frac{2}{3}\left(2-\frac{11}{60}\right)$$

Convert 2 to fraction \frac{120}{60}.

$$\frac{2}{3}\left(\frac{120}{60}-\frac{11}{60}\right)$$

Since \frac{120}{60} and \frac{11}{60} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2}{3}\times \frac{120-11}{60}$$

Subtract 11 from 120 to get 109.

$$\frac{2}{3}\times \frac{109}{60}$$

Multiply \frac{2}{3} times \frac{109}{60} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2\times 109}{3\times 60}$$

Do the multiplications in the fraction \frac{2\times 109}{3\times 60}.

$$\frac{218}{180}$$

Reduce the fraction \frac{218}{180} to lowest terms by extracting and canceling out 2.

$$\frac{109}{90}$$

Factor

$$\frac{109}{2 \cdot 3 ^ {2} \cdot 5} = 1\frac{19}{90} = 1.211111111111111$$