Solve 0,27*(-5/11*14/33*0,3*(2sqrt{3}*5/7-8/3)

$$0,27 \cdot ( - \frac { 5 } { 11 } \cdot \frac { 14 } { 33 } \cdot 0,3 \cdot ( 2 \sqrt { 3 } \cdot \frac { 5 } { 7 } - \frac { 8 } { 3 } )$$

Evaluate

$$-\frac{27\sqrt{3}}{1210}+\frac{126}{3025}\approx 0.003003825$$

Solution Steps

Multiply 0,27 and 0,3 to get 0,081.

$$0,081\left(-\frac{5}{11}\right)\times \frac{14}{33}\left(2\sqrt{3}\times \frac{5}{7}-\frac{8}{3}\right)$$

Convert decimal number 0,081 to fraction \frac{81}{1000}.

$$\frac{81}{1000}\left(-\frac{5}{11}\right)\times \frac{14}{33}\left(2\sqrt{3}\times \frac{5}{7}-\frac{8}{3}\right)$$

Multiply \frac{81}{1000} times -\frac{5}{11} by multiplying numerator times numerator and denominator times denominator.

$$\frac{81\left(-5\right)}{1000\times 11}\times \frac{14}{33}\left(2\sqrt{3}\times \frac{5}{7}-\frac{8}{3}\right)$$

Do the multiplications in the fraction \frac{81\left(-5\right)}{1000\times 11}.

$$\frac{-405}{11000}\times \frac{14}{33}\left(2\sqrt{3}\times \frac{5}{7}-\frac{8}{3}\right)$$

Reduce the fraction \frac{-405}{11000} to lowest terms by extracting and canceling out 5.

$$-\frac{81}{2200}\times \frac{14}{33}\left(2\sqrt{3}\times \frac{5}{7}-\frac{8}{3}\right)$$

Multiply -\frac{81}{2200} times \frac{14}{33} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-81\times 14}{2200\times 33}\left(2\sqrt{3}\times \frac{5}{7}-\frac{8}{3}\right)$$

Do the multiplications in the fraction \frac{-81\times 14}{2200\times 33}.

$$\frac{-1134}{72600}\left(2\sqrt{3}\times \frac{5}{7}-\frac{8}{3}\right)$$

Reduce the fraction \frac{-1134}{72600} to lowest terms by extracting and canceling out 6.

$$-\frac{189}{12100}\left(2\sqrt{3}\times \frac{5}{7}-\frac{8}{3}\right)$$

Express 2\times \frac{5}{7} as a single fraction.

$$-\frac{189}{12100}\left(\frac{2\times 5}{7}\sqrt{3}-\frac{8}{3}\right)$$

Multiply 2 and 5 to get 10.

$$-\frac{189}{12100}\left(\frac{10}{7}\sqrt{3}-\frac{8}{3}\right)$$

Use the distributive property to multiply -\frac{189}{12100} by \frac{10}{7}\sqrt{3}-\frac{8}{3}.

$$-\frac{189}{12100}\times \frac{10}{7}\sqrt{3}-\frac{189}{12100}\left(-\frac{8}{3}\right)$$

Multiply -\frac{189}{12100} times \frac{10}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-189\times 10}{12100\times 7}\sqrt{3}-\frac{189}{12100}\left(-\frac{8}{3}\right)$$

Do the multiplications in the fraction \frac{-189\times 10}{12100\times 7}.

$$\frac{-1890}{84700}\sqrt{3}-\frac{189}{12100}\left(-\frac{8}{3}\right)$$

Reduce the fraction \frac{-1890}{84700} to lowest terms by extracting and canceling out 70.

$$-\frac{27}{1210}\sqrt{3}-\frac{189}{12100}\left(-\frac{8}{3}\right)$$

Multiply -\frac{189}{12100} times -\frac{8}{3} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{27}{1210}\sqrt{3}+\frac{-189\left(-8\right)}{12100\times 3}$$

Do the multiplications in the fraction \frac{-189\left(-8\right)}{12100\times 3}.

$$-\frac{27}{1210}\sqrt{3}+\frac{1512}{36300}$$

Reduce the fraction \frac{1512}{36300} to lowest terms by extracting and canceling out 12.

$$-\frac{27}{1210}\sqrt{3}+\frac{126}{3025}$$

Factor

$$\frac{9 {(28 - 15 \sqrt{3})}}{6050} = 0.003003824955074643$$