Solve -1.3/1.2*((63-217)+0.00203*(63^2-217^2))

$$- \frac{ 1.3 }{ 1.2 } \times ((63-217)+0.00203 \times ( { 63 }^{ 2 } - { 217 }^{ 2 } ))$$

Evaluate

$$261.6614$$

Solution Steps

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

$$-\frac{13}{12}\left(63-217+0.00203\left(63^{2}-217^{2}\right)\right)$$

Subtract 217 from 63 to get -154.

$$-\frac{13}{12}\left(-154+0.00203\left(63^{2}-217^{2}\right)\right)$$

Calculate 63 to the power of 2 and get 3969.

$$-\frac{13}{12}\left(-154+0.00203\left(3969-217^{2}\right)\right)$$

Calculate 217 to the power of 2 and get 47089.

$$-\frac{13}{12}\left(-154+0.00203\left(3969-47089\right)\right)$$

Subtract 47089 from 3969 to get -43120.

$$-\frac{13}{12}\left(-154+0.00203\left(-43120\right)\right)$$

Multiply 0.00203 and -43120 to get -87.5336.

$$-\frac{13}{12}\left(-154-87.5336\right)$$

Subtract 87.5336 from -154 to get -241.5336.

$$-\frac{13}{12}\left(-241.5336\right)$$

Convert decimal number -241.5336 to fraction -\frac{2415336}{10000}. Reduce the fraction -\frac{2415336}{10000} to lowest terms by extracting and canceling out 8.

$$-\frac{13}{12}\left(-\frac{301917}{1250}\right)$$

Multiply -\frac{13}{12} times -\frac{301917}{1250} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-13\left(-301917\right)}{12\times 1250}$$

Do the multiplications in the fraction \frac{-13\left(-301917\right)}{12\times 1250}.

$$\frac{3924921}{15000}$$

Reduce the fraction \frac{3924921}{15000} to lowest terms by extracting and canceling out 3.

$$\frac{1308307}{5000}$$

Factor

$$\frac{7 \cdot 11 \cdot 13 \cdot 1307}{2 ^ {3} \cdot 5 ^ {4}} = 261\frac{3307}{5000} = 261.6614$$