Solve 10-21/2/3frac{3{4}}+left(21/2-11/3right)6

$$10- \frac{ 2 \frac{ 1 }{ 2 } }{ 3 \frac{ 3 }{ 4 } } + \left( 2 \frac{ 1 }{ 2 } -1 \frac{ 1 }{ 3 } \right) 6$$

Evaluate

$$\frac{49}{3}\approx 16.333333333$$

Solution Steps

Divide \frac{2\times 2+1}{2} by \frac{3\times 4+3}{4} by multiplying \frac{2\times 2+1}{2} by the reciprocal of \frac{3\times 4+3}{4}.

$$10-\frac{\left(2\times 2+1\right)\times 4}{2\left(3\times 4+3\right)}+\left(\frac{2\times 2+1}{2}-\frac{1\times 3+1}{3}\right)\times 6$$

Cancel out 2 in both numerator and denominator.

$$10-\frac{2\left(1+2\times 2\right)}{3+3\times 4}+\left(\frac{2\times 2+1}{2}-\frac{1\times 3+1}{3}\right)\times 6$$

Multiply 2 and 2 to get 4.

$$10-\frac{2\left(1+4\right)}{3+3\times 4}+\left(\frac{2\times 2+1}{2}-\frac{1\times 3+1}{3}\right)\times 6$$

Add 1 and 4 to get 5.

$$10-\frac{2\times 5}{3+3\times 4}+\left(\frac{2\times 2+1}{2}-\frac{1\times 3+1}{3}\right)\times 6$$

Multiply 2 and 5 to get 10.

$$10-\frac{10}{3+3\times 4}+\left(\frac{2\times 2+1}{2}-\frac{1\times 3+1}{3}\right)\times 6$$

Multiply 3 and 4 to get 12.

$$10-\frac{10}{3+12}+\left(\frac{2\times 2+1}{2}-\frac{1\times 3+1}{3}\right)\times 6$$

Add 3 and 12 to get 15.

$$10-\frac{10}{15}+\left(\frac{2\times 2+1}{2}-\frac{1\times 3+1}{3}\right)\times 6$$

Reduce the fraction \frac{10}{15} to lowest terms by extracting and canceling out 5.

$$10-\frac{2}{3}+\left(\frac{2\times 2+1}{2}-\frac{1\times 3+1}{3}\right)\times 6$$

Convert 10 to fraction \frac{30}{3}.

$$\frac{30}{3}-\frac{2}{3}+\left(\frac{2\times 2+1}{2}-\frac{1\times 3+1}{3}\right)\times 6$$

Since \frac{30}{3} and \frac{2}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{30-2}{3}+\left(\frac{2\times 2+1}{2}-\frac{1\times 3+1}{3}\right)\times 6$$

Subtract 2 from 30 to get 28.

$$\frac{28}{3}+\left(\frac{2\times 2+1}{2}-\frac{1\times 3+1}{3}\right)\times 6$$

Multiply 2 and 2 to get 4.

$$\frac{28}{3}+\left(\frac{4+1}{2}-\frac{1\times 3+1}{3}\right)\times 6$$

Add 4 and 1 to get 5.

$$\frac{28}{3}+\left(\frac{5}{2}-\frac{1\times 3+1}{3}\right)\times 6$$

Multiply 1 and 3 to get 3.

$$\frac{28}{3}+\left(\frac{5}{2}-\frac{3+1}{3}\right)\times 6$$

Add 3 and 1 to get 4.

$$\frac{28}{3}+\left(\frac{5}{2}-\frac{4}{3}\right)\times 6$$

Least common multiple of 2 and 3 is 6. Convert \frac{5}{2} and \frac{4}{3} to fractions with denominator 6.

$$\frac{28}{3}+\left(\frac{15}{6}-\frac{8}{6}\right)\times 6$$

Since \frac{15}{6} and \frac{8}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{28}{3}+\frac{15-8}{6}\times 6$$

Subtract 8 from 15 to get 7.

$$\frac{28}{3}+\frac{7}{6}\times 6$$

Cancel out 6 and 6.

$$\frac{28}{3}+7$$

Convert 7 to fraction \frac{21}{3}.

$$\frac{28}{3}+\frac{21}{3}$$

Since \frac{28}{3} and \frac{21}{3} have the same denominator, add them by adding their numerators.

$$\frac{28+21}{3}$$

Add 28 and 21 to get 49.

$$\frac{49}{3}$$

Factor

$$\frac{7 ^ {2}}{3} = 16\frac{1}{3} = 16.333333333333332$$