Solve (7/3-2/5:6/5)e(2+3/4*4)

$$( \frac { 7 } { 3 } - \frac { 2 } { 5 } : \frac { 6 } { 5 } ) e ( 2 + \frac { 3 } { 4 } \cdot 4 )$$

Evaluate

$$10e\approx 27.182818285$$

Solution Steps

Divide \frac{2}{5} by \frac{6}{5} by multiplying \frac{2}{5} by the reciprocal of \frac{6}{5}.

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

Multiply \frac{2}{5} times \frac{5}{6} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out 5 in both numerator and denominator.

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

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

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

Since \frac{7}{3} and \frac{1}{3} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 1 from 7 to get 6.

$$\frac{6}{3}e\left(2+\frac{3}{4}\times 4\right)$$

Divide 6 by 3 to get 2.

$$2e\left(2+\frac{3}{4}\times 4\right)$$

Cancel out 4 and 4.

$$2e\left(2+3\right)$$

Add 2 and 3 to get 5.

$$2e\times 5$$

Multiply 2 and 5 to get 10.

$$10e$$

Expand

$$10e$$

Solution Steps

Divide \frac{2}{5} by \frac{6}{5} by multiplying \frac{2}{5} by the reciprocal of \frac{6}{5}.

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

Multiply \frac{2}{5} times \frac{5}{6} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out 5 in both numerator and denominator.

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

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

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

Since \frac{7}{3} and \frac{1}{3} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 1 from 7 to get 6.

$$\frac{6}{3}e\left(2+\frac{3}{4}\times 4\right)$$

Divide 6 by 3 to get 2.

$$2e\left(2+\frac{3}{4}\times 4\right)$$

Cancel out 4 and 4.

$$2e\left(2+3\right)$$

Add 2 and 3 to get 5.

$$2e\times 5$$

Multiply 2 and 5 to get 10.

$$10e$$