Solve 22/3-(-5/8)-11/2*8/9

$$2 \frac { 2 } { 3 } - ( - \frac { 5 } { 8 } ) - 1 \frac { 1 } { 2 } \times \frac { 8 } { 9 }$$

Evaluate

$$\frac{47}{24}\approx 1.958333333$$

Solution Steps

Multiply 2 and 3 to get 6.

$$\frac{6+2}{3}-\left(-\frac{5}{8}\right)-\frac{1\times 2+1}{2}\times \frac{8}{9}$$

Add 6 and 2 to get 8.

$$\frac{8}{3}-\left(-\frac{5}{8}\right)-\frac{1\times 2+1}{2}\times \frac{8}{9}$$

The opposite of -\frac{5}{8} is \frac{5}{8}.

$$\frac{8}{3}+\frac{5}{8}-\frac{1\times 2+1}{2}\times \frac{8}{9}$$

Least common multiple of 3 and 8 is 24. Convert \frac{8}{3} and \frac{5}{8} to fractions with denominator 24.

$$\frac{64}{24}+\frac{15}{24}-\frac{1\times 2+1}{2}\times \frac{8}{9}$$

Since \frac{64}{24} and \frac{15}{24} have the same denominator, add them by adding their numerators.

$$\frac{64+15}{24}-\frac{1\times 2+1}{2}\times \frac{8}{9}$$

Add 64 and 15 to get 79.

$$\frac{79}{24}-\frac{1\times 2+1}{2}\times \frac{8}{9}$$

Multiply 1 and 2 to get 2.

$$\frac{79}{24}-\frac{2+1}{2}\times \frac{8}{9}$$

Add 2 and 1 to get 3.

$$\frac{79}{24}-\frac{3}{2}\times \frac{8}{9}$$

Multiply \frac{3}{2} times \frac{8}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{79}{24}-\frac{3\times 8}{2\times 9}$$

Do the multiplications in the fraction \frac{3\times 8}{2\times 9}.

$$\frac{79}{24}-\frac{24}{18}$$

Reduce the fraction \frac{24}{18} to lowest terms by extracting and canceling out 6.

$$\frac{79}{24}-\frac{4}{3}$$

Least common multiple of 24 and 3 is 24. Convert \frac{79}{24} and \frac{4}{3} to fractions with denominator 24.

$$\frac{79}{24}-\frac{32}{24}$$

Since \frac{79}{24} and \frac{32}{24} have the same denominator, subtract them by subtracting their numerators.

$$\frac{79-32}{24}$$

Subtract 32 from 79 to get 47.

$$\frac{47}{24}$$

Factor

$$\frac{47}{2 ^ {3} \cdot 3} = 1\frac{23}{24} = 1.9583333333333333$$