Solve {[(1/2+2/3-1/8)+(3/4+frac{1}{3}+1)]*frac{16}{9}}:frac{50}{9}

$$\{ [ ( \frac { 1 } { 2 } + \frac { 2 } { 3 } - \frac { 1 } { 8 } ) + ( \frac { 3 } { 4 } + \frac { 1 } { 3 } + 1 ) ] \cdot \frac { 16 } { 9 } \} : \frac { 50 } { 9 }$$

Evaluate

$$1$$

Solution Steps

Least common multiple of 2 and 3 is 6. Convert \frac{1}{2} and \frac{2}{3} to fractions with denominator 6.

$$\frac{\left(\frac{3}{6}+\frac{4}{6}-\frac{1}{8}+\frac{3}{4}+\frac{1}{3}+1\right)\times \frac{16}{9}}{\frac{50}{9}}$$

Since \frac{3}{6} and \frac{4}{6} have the same denominator, add them by adding their numerators.

$$\frac{\left(\frac{3+4}{6}-\frac{1}{8}+\frac{3}{4}+\frac{1}{3}+1\right)\times \frac{16}{9}}{\frac{50}{9}}$$

Add 3 and 4 to get 7.

$$\frac{\left(\frac{7}{6}-\frac{1}{8}+\frac{3}{4}+\frac{1}{3}+1\right)\times \frac{16}{9}}{\frac{50}{9}}$$

Least common multiple of 6 and 8 is 24. Convert \frac{7}{6} and \frac{1}{8} to fractions with denominator 24.

$$\frac{\left(\frac{28}{24}-\frac{3}{24}+\frac{3}{4}+\frac{1}{3}+1\right)\times \frac{16}{9}}{\frac{50}{9}}$$

Since \frac{28}{24} and \frac{3}{24} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\left(\frac{28-3}{24}+\frac{3}{4}+\frac{1}{3}+1\right)\times \frac{16}{9}}{\frac{50}{9}}$$

Subtract 3 from 28 to get 25.

$$\frac{\left(\frac{25}{24}+\frac{3}{4}+\frac{1}{3}+1\right)\times \frac{16}{9}}{\frac{50}{9}}$$

Least common multiple of 24 and 4 is 24. Convert \frac{25}{24} and \frac{3}{4} to fractions with denominator 24.

$$\frac{\left(\frac{25}{24}+\frac{18}{24}+\frac{1}{3}+1\right)\times \frac{16}{9}}{\frac{50}{9}}$$

Since \frac{25}{24} and \frac{18}{24} have the same denominator, add them by adding their numerators.

$$\frac{\left(\frac{25+18}{24}+\frac{1}{3}+1\right)\times \frac{16}{9}}{\frac{50}{9}}$$

Add 25 and 18 to get 43.

$$\frac{\left(\frac{43}{24}+\frac{1}{3}+1\right)\times \frac{16}{9}}{\frac{50}{9}}$$

Least common multiple of 24 and 3 is 24. Convert \frac{43}{24} and \frac{1}{3} to fractions with denominator 24.

$$\frac{\left(\frac{43}{24}+\frac{8}{24}+1\right)\times \frac{16}{9}}{\frac{50}{9}}$$

Since \frac{43}{24} and \frac{8}{24} have the same denominator, add them by adding their numerators.

$$\frac{\left(\frac{43+8}{24}+1\right)\times \frac{16}{9}}{\frac{50}{9}}$$

Add 43 and 8 to get 51.

$$\frac{\left(\frac{51}{24}+1\right)\times \frac{16}{9}}{\frac{50}{9}}$$

Reduce the fraction \frac{51}{24} to lowest terms by extracting and canceling out 3.

$$\frac{\left(\frac{17}{8}+1\right)\times \frac{16}{9}}{\frac{50}{9}}$$

Convert 1 to fraction \frac{8}{8}.

$$\frac{\left(\frac{17}{8}+\frac{8}{8}\right)\times \frac{16}{9}}{\frac{50}{9}}$$

Since \frac{17}{8} and \frac{8}{8} have the same denominator, add them by adding their numerators.

$$\frac{\frac{17+8}{8}\times \frac{16}{9}}{\frac{50}{9}}$$

Add 17 and 8 to get 25.

$$\frac{\frac{25}{8}\times \frac{16}{9}}{\frac{50}{9}}$$

Multiply \frac{25}{8} times \frac{16}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{25\times 16}{8\times 9}}{\frac{50}{9}}$$

Do the multiplications in the fraction \frac{25\times 16}{8\times 9}.

$$\frac{\frac{400}{72}}{\frac{50}{9}}$$

Reduce the fraction \frac{400}{72} to lowest terms by extracting and canceling out 8.

$$\frac{\frac{50}{9}}{\frac{50}{9}}$$

Divide \frac{50}{9} by \frac{50}{9} to get 1.

$$1$$

Factor

$$1$$