Solve (42/3+13/4)*13/7-21/2:frac{3}{5}

$$( 4 \frac { 2 } { 3 } + 1 \frac { 3 } { 4 } ) \cdot 1 \frac { 3 } { 7 } - 2 \frac { 1 } { 2 } : \frac { 3 } { 5 }$$

Evaluate

$$5$$

Solution Steps

Multiply 4 and 3 to get 12.

$$\left(\frac{12+2}{3}+\frac{1\times 4+3}{4}\right)\times \frac{1\times 7+3}{7}-\frac{\frac{2\times 2+1}{2}}{\frac{3}{5}}$$

Add 12 and 2 to get 14.

$$\left(\frac{14}{3}+\frac{1\times 4+3}{4}\right)\times \frac{1\times 7+3}{7}-\frac{\frac{2\times 2+1}{2}}{\frac{3}{5}}$$

Multiply 1 and 4 to get 4.

$$\left(\frac{14}{3}+\frac{4+3}{4}\right)\times \frac{1\times 7+3}{7}-\frac{\frac{2\times 2+1}{2}}{\frac{3}{5}}$$

Add 4 and 3 to get 7.

$$\left(\frac{14}{3}+\frac{7}{4}\right)\times \frac{1\times 7+3}{7}-\frac{\frac{2\times 2+1}{2}}{\frac{3}{5}}$$

Least common multiple of 3 and 4 is 12. Convert \frac{14}{3} and \frac{7}{4} to fractions with denominator 12.

$$\left(\frac{56}{12}+\frac{21}{12}\right)\times \frac{1\times 7+3}{7}-\frac{\frac{2\times 2+1}{2}}{\frac{3}{5}}$$

Since \frac{56}{12} and \frac{21}{12} have the same denominator, add them by adding their numerators.

$$\frac{56+21}{12}\times \frac{1\times 7+3}{7}-\frac{\frac{2\times 2+1}{2}}{\frac{3}{5}}$$

Add 56 and 21 to get 77.

$$\frac{77}{12}\times \frac{1\times 7+3}{7}-\frac{\frac{2\times 2+1}{2}}{\frac{3}{5}}$$

Multiply 1 and 7 to get 7.

$$\frac{77}{12}\times \frac{7+3}{7}-\frac{\frac{2\times 2+1}{2}}{\frac{3}{5}}$$

Add 7 and 3 to get 10.

$$\frac{77}{12}\times \frac{10}{7}-\frac{\frac{2\times 2+1}{2}}{\frac{3}{5}}$$

Multiply \frac{77}{12} times \frac{10}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{77\times 10}{12\times 7}-\frac{\frac{2\times 2+1}{2}}{\frac{3}{5}}$$

Do the multiplications in the fraction \frac{77\times 10}{12\times 7}.

$$\frac{770}{84}-\frac{\frac{2\times 2+1}{2}}{\frac{3}{5}}$$

Reduce the fraction \frac{770}{84} to lowest terms by extracting and canceling out 14.

$$\frac{55}{6}-\frac{\frac{2\times 2+1}{2}}{\frac{3}{5}}$$

Divide \frac{2\times 2+1}{2} by \frac{3}{5} by multiplying \frac{2\times 2+1}{2} by the reciprocal of \frac{3}{5}.

$$\frac{55}{6}-\frac{\left(2\times 2+1\right)\times 5}{2\times 3}$$

Multiply 2 and 2 to get 4.

$$\frac{55}{6}-\frac{\left(4+1\right)\times 5}{2\times 3}$$

Add 4 and 1 to get 5.

$$\frac{55}{6}-\frac{5\times 5}{2\times 3}$$

Multiply 5 and 5 to get 25.

$$\frac{55}{6}-\frac{25}{2\times 3}$$

Multiply 2 and 3 to get 6.

$$\frac{55}{6}-\frac{25}{6}$$

Since \frac{55}{6} and \frac{25}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{55-25}{6}$$

Subtract 25 from 55 to get 30.

$$\frac{30}{6}$$

Divide 30 by 6 to get 5.

$$5$$

Factor

$$5$$