Solve -1.3/1.2left(67-217+0.00203left(67^2-217^2right)right)

$$- \frac{ 1.3 }{ 1.2 } \left( 67-217+0.00203 \left( { 67 }^{ 2 } - { 217 }^{ 2 } \right) \right)$$

Evaluate

$$256.1845$$

Solution Steps

Expand \frac{1.3}{1.2} by multiplying both numerator and the denominator by 10.

$$-\frac{13}{12}\left(67-217+0.00203\left(67^{2}-217^{2}\right)\right)$$

Subtract 217 from 67 to get -150.

$$-\frac{13}{12}\left(-150+0.00203\left(67^{2}-217^{2}\right)\right)$$

Calculate 67 to the power of 2 and get 4489.

$$-\frac{13}{12}\left(-150+0.00203\left(4489-217^{2}\right)\right)$$

Calculate 217 to the power of 2 and get 47089.

$$-\frac{13}{12}\left(-150+0.00203\left(4489-47089\right)\right)$$

Subtract 47089 from 4489 to get -42600.

$$-\frac{13}{12}\left(-150+0.00203\left(-42600\right)\right)$$

Multiply 0.00203 and -42600 to get -86.478.

$$-\frac{13}{12}\left(-150-86.478\right)$$

Subtract 86.478 from -150 to get -236.478.

$$-\frac{13}{12}\left(-236.478\right)$$

Convert decimal number -236.478 to fraction -\frac{236478}{1000}. Reduce the fraction -\frac{236478}{1000} to lowest terms by extracting and canceling out 2.

$$-\frac{13}{12}\left(-\frac{118239}{500}\right)$$

Multiply -\frac{13}{12} times -\frac{118239}{500} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-13\left(-118239\right)}{12\times 500}$$

Do the multiplications in the fraction \frac{-13\left(-118239\right)}{12\times 500}.

$$\frac{1537107}{6000}$$

Reduce the fraction \frac{1537107}{6000} to lowest terms by extracting and canceling out 3.

$$\frac{512369}{2000}$$

Factor

$$\frac{11 \cdot 13 \cdot 3583}{2 ^ {4} \cdot 5 ^ {3}} = 256\frac{369}{2000} = 256.1845$$