Solve 1.732*5.3*15/380*(21.6*0.75+0.1476*0.31)

$$\frac{ 1.732 \times 5.3 \times 15 }{ 380 } \times (21.6 \times 0.75+0.1476 \times 0.31)$$

Evaluate

$$\frac{279617890833}{47500000000}\approx 5.886692439$$

Solution Steps

Multiply 1.732 and 5.3 to get 9.1796.

$$\frac{9.1796\times 15}{380}\left(21.6\times 0.75+0.1476\times 0.31\right)$$

Multiply 9.1796 and 15 to get 137.694.

$$\frac{137.694}{380}\left(21.6\times 0.75+0.1476\times 0.31\right)$$

Expand \frac{137.694}{380} by multiplying both numerator and the denominator by 1000.

$$\frac{137694}{380000}\left(21.6\times 0.75+0.1476\times 0.31\right)$$

Reduce the fraction \frac{137694}{380000} to lowest terms by extracting and canceling out 2.

$$\frac{68847}{190000}\left(21.6\times 0.75+0.1476\times 0.31\right)$$

Multiply 21.6 and 0.75 to get 16.2.

$$\frac{68847}{190000}\left(16.2+0.1476\times 0.31\right)$$

Multiply 0.1476 and 0.31 to get 0.045756.

$$\frac{68847}{190000}\left(16.2+0.045756\right)$$

Add 16.2 and 0.045756 to get 16.245756.

$$\frac{68847}{190000}\times 16.245756$$

Convert decimal number 16.245756 to fraction \frac{16245756}{1000000}. Reduce the fraction \frac{16245756}{1000000} to lowest terms by extracting and canceling out 4.

$$\frac{68847}{190000}\times \frac{4061439}{250000}$$

Multiply \frac{68847}{190000} times \frac{4061439}{250000} by multiplying numerator times numerator and denominator times denominator.

$$\frac{68847\times 4061439}{190000\times 250000}$$

Do the multiplications in the fraction \frac{68847\times 4061439}{190000\times 250000}.

$$\frac{279617890833}{47500000000}$$

Factor

$$\frac{53 \cdot 83 \cdot 433 \cdot 5437 \cdot 3 ^ {3}}{19 \cdot 2 ^ {8} \cdot 5 ^ {10}} = 5\frac{42117890833}{47500000000} = 5.886692438589474$$