Solve (32/5*31/3-55/6)div11/2=3frac{2}{3}

$$( 3 \frac { 2 } { 5 } \times 3 \frac { 1 } { 3 } - 5 \frac { 5 } { 6 } ) \div 1 \frac { 1 } { 2 } = 3 \frac { 2 } { 3 }$$

Verify

Solution Steps

Multiply both sides of the equation by 3.

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

Multiply 3 and 5 to get 15.

$$2\left(\frac{15+2}{5}\times \frac{3\times 3+1}{3}-\frac{5\times 6+5}{6}\right)=3\times 3+2$$

Add 15 and 2 to get 17.

$$2\left(\frac{17}{5}\times \frac{3\times 3+1}{3}-\frac{5\times 6+5}{6}\right)=3\times 3+2$$

Multiply 3 and 3 to get 9.

$$2\left(\frac{17}{5}\times \frac{9+1}{3}-\frac{5\times 6+5}{6}\right)=3\times 3+2$$

Add 9 and 1 to get 10.

$$2\left(\frac{17}{5}\times \frac{10}{3}-\frac{5\times 6+5}{6}\right)=3\times 3+2$$

Multiply \frac{17}{5} times \frac{10}{3} by multiplying numerator times numerator and denominator times denominator.

$$2\left(\frac{17\times 10}{5\times 3}-\frac{5\times 6+5}{6}\right)=3\times 3+2$$

Do the multiplications in the fraction \frac{17\times 10}{5\times 3}.

$$2\left(\frac{170}{15}-\frac{5\times 6+5}{6}\right)=3\times 3+2$$

Reduce the fraction \frac{170}{15} to lowest terms by extracting and canceling out 5.

$$2\left(\frac{34}{3}-\frac{5\times 6+5}{6}\right)=3\times 3+2$$

Multiply 5 and 6 to get 30.

$$2\left(\frac{34}{3}-\frac{30+5}{6}\right)=3\times 3+2$$

Add 30 and 5 to get 35.

$$2\left(\frac{34}{3}-\frac{35}{6}\right)=3\times 3+2$$

Least common multiple of 3 and 6 is 6. Convert \frac{34}{3} and \frac{35}{6} to fractions with denominator 6.

$$2\left(\frac{68}{6}-\frac{35}{6}\right)=3\times 3+2$$

Since \frac{68}{6} and \frac{35}{6} have the same denominator, subtract them by subtracting their numerators.

$$2\times \frac{68-35}{6}=3\times 3+2$$

Subtract 35 from 68 to get 33.

$$2\times \frac{33}{6}=3\times 3+2$$

Reduce the fraction \frac{33}{6} to lowest terms by extracting and canceling out 3.

$$2\times \frac{11}{2}=3\times 3+2$$

Cancel out 2 and 2.

$$11=3\times 3+2$$

Multiply 3 and 3 to get 9.

$$11=9+2$$

Add 9 and 2 to get 11.

$$11=11$$

Compare 11 and 11.

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