Solve 12.1*(-3/2)^2+15.4*(-3^2/4)-6.5*(-9/4)=

$$12.1 \times ( - \frac { 3 } { 2 } ) ^ { 2 } + 15.4 \times ( - \frac { 3 ^ { 2 } } { 4 } ) - 6.5 \times ( - \frac { 9 } { 4 } ) =$$

Evaluate

$$7.2$$

Solution Steps

Calculate -\frac{3}{2} to the power of 2 and get \frac{9}{4}.

$$12.1\times \frac{9}{4}+15.4\left(-\frac{3^{2}}{4}\right)-6.5\left(-\frac{9}{4}\right)$$

Convert decimal number 12.1 to fraction \frac{121}{10}.

$$\frac{121}{10}\times \frac{9}{4}+15.4\left(-\frac{3^{2}}{4}\right)-6.5\left(-\frac{9}{4}\right)$$

Multiply \frac{121}{10} times \frac{9}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{121\times 9}{10\times 4}+15.4\left(-\frac{3^{2}}{4}\right)-6.5\left(-\frac{9}{4}\right)$$

Do the multiplications in the fraction \frac{121\times 9}{10\times 4}.

$$\frac{1089}{40}+15.4\left(-\frac{3^{2}}{4}\right)-6.5\left(-\frac{9}{4}\right)$$

Calculate 3 to the power of 2 and get 9.

$$\frac{1089}{40}+15.4\left(-\frac{9}{4}\right)-6.5\left(-\frac{9}{4}\right)$$

Convert decimal number 15.4 to fraction \frac{154}{10}. Reduce the fraction \frac{154}{10} to lowest terms by extracting and canceling out 2.

$$\frac{1089}{40}+\frac{77}{5}\left(-\frac{9}{4}\right)-6.5\left(-\frac{9}{4}\right)$$

Multiply \frac{77}{5} times -\frac{9}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1089}{40}+\frac{77\left(-9\right)}{5\times 4}-6.5\left(-\frac{9}{4}\right)$$

Do the multiplications in the fraction \frac{77\left(-9\right)}{5\times 4}.

$$\frac{1089}{40}+\frac{-693}{20}-6.5\left(-\frac{9}{4}\right)$$

Fraction \frac{-693}{20} can be rewritten as -\frac{693}{20} by extracting the negative sign.

$$\frac{1089}{40}-\frac{693}{20}-6.5\left(-\frac{9}{4}\right)$$

Least common multiple of 40 and 20 is 40. Convert \frac{1089}{40} and \frac{693}{20} to fractions with denominator 40.

$$\frac{1089}{40}-\frac{1386}{40}-6.5\left(-\frac{9}{4}\right)$$

Since \frac{1089}{40} and \frac{1386}{40} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1089-1386}{40}-6.5\left(-\frac{9}{4}\right)$$

Subtract 1386 from 1089 to get -297.

$$-\frac{297}{40}-6.5\left(-\frac{9}{4}\right)$$

Convert decimal number 6.5 to fraction \frac{65}{10}. Reduce the fraction \frac{65}{10} to lowest terms by extracting and canceling out 5.

$$-\frac{297}{40}-\frac{13}{2}\left(-\frac{9}{4}\right)$$

Multiply \frac{13}{2} times -\frac{9}{4} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{297}{40}-\frac{13\left(-9\right)}{2\times 4}$$

Do the multiplications in the fraction \frac{13\left(-9\right)}{2\times 4}.

$$-\frac{297}{40}-\frac{-117}{8}$$

Fraction \frac{-117}{8} can be rewritten as -\frac{117}{8} by extracting the negative sign.

$$-\frac{297}{40}-\left(-\frac{117}{8}\right)$$

The opposite of -\frac{117}{8} is \frac{117}{8}.

$$-\frac{297}{40}+\frac{117}{8}$$

Least common multiple of 40 and 8 is 40. Convert -\frac{297}{40} and \frac{117}{8} to fractions with denominator 40.

$$-\frac{297}{40}+\frac{585}{40}$$

Since -\frac{297}{40} and \frac{585}{40} have the same denominator, add them by adding their numerators.

$$\frac{-297+585}{40}$$

Add -297 and 585 to get 288.

$$\frac{288}{40}$$

Reduce the fraction \frac{288}{40} to lowest terms by extracting and canceling out 8.

$$\frac{36}{5}$$

Factor

$$\frac{2 ^ {2} \cdot 3 ^ {2}}{5} = 7\frac{1}{5} = 7.2$$