Solve 1.732*1.6*3/380*(21.6*1+0.1476*0.31)

$$\frac{ 1.732 \times 1.6 \times 3 }{ 380 } \times (21.6 \times 1+0.1476 \times 0.31)$$

Evaluate

$$\frac{7029459261}{14843750000}\approx 0.473563571$$

Solution Steps

Multiply 1.732 and 1.6 to get 2.7712.

$$\frac{2.7712\times 3}{380}\left(21.6\times 1+0.1476\times 0.31\right)$$

Multiply 2.7712 and 3 to get 8.3136.

$$\frac{8.3136}{380}\left(21.6\times 1+0.1476\times 0.31\right)$$

Expand \frac{8.3136}{380} by multiplying both numerator and the denominator by 10000.

$$\frac{83136}{3800000}\left(21.6\times 1+0.1476\times 0.31\right)$$

Reduce the fraction \frac{83136}{3800000} to lowest terms by extracting and canceling out 64.

$$\frac{1299}{59375}\left(21.6\times 1+0.1476\times 0.31\right)$$

Multiply 21.6 and 1 to get 21.6.

$$\frac{1299}{59375}\left(21.6+0.1476\times 0.31\right)$$

Multiply 0.1476 and 0.31 to get 0.045756.

$$\frac{1299}{59375}\left(21.6+0.045756\right)$$

Add 21.6 and 0.045756 to get 21.645756.

$$\frac{1299}{59375}\times 21.645756$$

Convert decimal number 21.645756 to fraction \frac{21645756}{1000000}. Reduce the fraction \frac{21645756}{1000000} to lowest terms by extracting and canceling out 4.

$$\frac{1299}{59375}\times \frac{5411439}{250000}$$

Multiply \frac{1299}{59375} times \frac{5411439}{250000} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1299\times 5411439}{59375\times 250000}$$

Do the multiplications in the fraction \frac{1299\times 5411439}{59375\times 250000}.

$$\frac{7029459261}{14843750000}$$

Factor

$$\frac{11 \cdot 47 \cdot 433 \cdot 1163 \cdot 3 ^ {3}}{19 \cdot 2 ^ {4} \cdot 5 ^ {11}} = 0.4735635712673684$$