Solve 33/4:3/10-(-11/6):7/5

$$3 \frac { 3 } { 4 } : \frac { 3 } { 10 } - ( - 1 \frac { 1 } { 6 } ) : \frac { 7 } { 5 }$$

Evaluate

$$\frac{40}{3}\approx 13.333333333$$

Solution Steps

Divide \frac{3\times 4+3}{4} by \frac{3}{10} by multiplying \frac{3\times 4+3}{4} by the reciprocal of \frac{3}{10}.

$$\frac{\left(3\times 4+3\right)\times 10}{4\times 3}-\frac{-\frac{1\times 6+1}{6}}{\frac{7}{5}}$$

Cancel out 2 in both numerator and denominator.

$$\frac{5\left(3+3\times 4\right)}{2\times 3}-\frac{-\frac{1\times 6+1}{6}}{\frac{7}{5}}$$

Multiply 3 and 4 to get 12.

$$\frac{5\left(3+12\right)}{2\times 3}-\frac{-\frac{1\times 6+1}{6}}{\frac{7}{5}}$$

Add 3 and 12 to get 15.

$$\frac{5\times 15}{2\times 3}-\frac{-\frac{1\times 6+1}{6}}{\frac{7}{5}}$$

Multiply 5 and 15 to get 75.

$$\frac{75}{2\times 3}-\frac{-\frac{1\times 6+1}{6}}{\frac{7}{5}}$$

Multiply 2 and 3 to get 6.

$$\frac{75}{6}-\frac{-\frac{1\times 6+1}{6}}{\frac{7}{5}}$$

Reduce the fraction \frac{75}{6} to lowest terms by extracting and canceling out 3.

$$\frac{25}{2}-\frac{-\frac{1\times 6+1}{6}}{\frac{7}{5}}$$

Multiply 1 and 6 to get 6.

$$\frac{25}{2}-\frac{-\frac{6+1}{6}}{\frac{7}{5}}$$

Add 6 and 1 to get 7.

$$\frac{25}{2}-\frac{-\frac{7}{6}}{\frac{7}{5}}$$

Divide -\frac{7}{6} by \frac{7}{5} by multiplying -\frac{7}{6} by the reciprocal of \frac{7}{5}.

$$\frac{25}{2}-\left(-\frac{7}{6}\times \frac{5}{7}\right)$$

Multiply -\frac{7}{6} times \frac{5}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{25}{2}-\frac{-7\times 5}{6\times 7}$$

Do the multiplications in the fraction \frac{-7\times 5}{6\times 7}.

$$\frac{25}{2}-\frac{-35}{42}$$

Reduce the fraction \frac{-35}{42} to lowest terms by extracting and canceling out 7.

$$\frac{25}{2}-\left(-\frac{5}{6}\right)$$

The opposite of -\frac{5}{6} is \frac{5}{6}.

$$\frac{25}{2}+\frac{5}{6}$$

Least common multiple of 2 and 6 is 6. Convert \frac{25}{2} and \frac{5}{6} to fractions with denominator 6.

$$\frac{75}{6}+\frac{5}{6}$$

Since \frac{75}{6} and \frac{5}{6} have the same denominator, add them by adding their numerators.

$$\frac{75+5}{6}$$

Add 75 and 5 to get 80.

$$\frac{80}{6}$$

Reduce the fraction \frac{80}{6} to lowest terms by extracting and canceling out 2.

$$\frac{40}{3}$$

Factor

$$\frac{2 ^ {3} \cdot 5}{3} = 13\frac{1}{3} = 13.333333333333334$$