Solve 1.732*10.3*9/380left(21.6*0.84+0.1476*0.31right)

$$\frac{ 1.732 \times 10.3 \cdot 9 }{ 380 } \left( 21.6 \cdot 0.84+0.1476 \cdot 0.31 \right)$$

Evaluate

$$\frac{1825301087649}{237500000000}\approx 7.685478264$$

Solution Steps

Multiply 1.732 and 10.3 to get 17.8396.

$$\frac{17.8396\times 9}{380}\left(21.6\times 0.84+0.1476\times 0.31\right)$$

Multiply 17.8396 and 9 to get 160.5564.

$$\frac{160.5564}{380}\left(21.6\times 0.84+0.1476\times 0.31\right)$$

Expand \frac{160.5564}{380} by multiplying both numerator and the denominator by 10000.

$$\frac{1605564}{3800000}\left(21.6\times 0.84+0.1476\times 0.31\right)$$

Reduce the fraction \frac{1605564}{3800000} to lowest terms by extracting and canceling out 4.

$$\frac{401391}{950000}\left(21.6\times 0.84+0.1476\times 0.31\right)$$

Multiply 21.6 and 0.84 to get 18.144.

$$\frac{401391}{950000}\left(18.144+0.1476\times 0.31\right)$$

Multiply 0.1476 and 0.31 to get 0.045756.

$$\frac{401391}{950000}\left(18.144+0.045756\right)$$

Add 18.144 and 0.045756 to get 18.189756.

$$\frac{401391}{950000}\times 18.189756$$

Convert decimal number 18.189756 to fraction \frac{18189756}{1000000}. Reduce the fraction \frac{18189756}{1000000} to lowest terms by extracting and canceling out 4.

$$\frac{401391}{950000}\times \frac{4547439}{250000}$$

Multiply \frac{401391}{950000} times \frac{4547439}{250000} by multiplying numerator times numerator and denominator times denominator.

$$\frac{401391\times 4547439}{950000\times 250000}$$

Do the multiplications in the fraction \frac{401391\times 4547439}{950000\times 250000}.

$$\frac{1825301087649}{237500000000}$$

Factor

$$\frac{13 \cdot 103 \cdot 433 \cdot 38867 \cdot 3 ^ {4}}{19 \cdot 2 ^ {8} \cdot 5 ^ {11}} = 7\frac{162801087649}{237500000000} = 7.685478263785263$$