Solve -3/24/5+9/5-10/3-frac{1}{2}*frac{3}{4}

$$- \frac{ 3 }{ 2 } \frac{ 4 }{ 5 } + \frac{ 9 }{ 5 } \frac{ -10 }{ 3 } - \frac{ 1 }{ 2 } \times \frac{ 3 }{ 4 }$$

Evaluate

$$-\frac{303}{40}=-7.575$$

Solution Steps

Multiply -\frac{3}{2} times \frac{4}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-3\times 4}{2\times 5}+\frac{9}{5}\times \frac{-10}{3}-\frac{1}{2}\times \frac{3}{4}$$

Do the multiplications in the fraction \frac{-3\times 4}{2\times 5}.

$$\frac{-12}{10}+\frac{9}{5}\times \frac{-10}{3}-\frac{1}{2}\times \frac{3}{4}$$

Reduce the fraction \frac{-12}{10} to lowest terms by extracting and canceling out 2.

$$-\frac{6}{5}+\frac{9}{5}\times \frac{-10}{3}-\frac{1}{2}\times \frac{3}{4}$$

Fraction \frac{-10}{3} can be rewritten as -\frac{10}{3} by extracting the negative sign.

$$-\frac{6}{5}+\frac{9}{5}\left(-\frac{10}{3}\right)-\frac{1}{2}\times \frac{3}{4}$$

Multiply \frac{9}{5} times -\frac{10}{3} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{6}{5}+\frac{9\left(-10\right)}{5\times 3}-\frac{1}{2}\times \frac{3}{4}$$

Do the multiplications in the fraction \frac{9\left(-10\right)}{5\times 3}.

$$-\frac{6}{5}+\frac{-90}{15}-\frac{1}{2}\times \frac{3}{4}$$

Divide -90 by 15 to get -6.

$$-\frac{6}{5}-6-\frac{1}{2}\times \frac{3}{4}$$

Convert 6 to fraction \frac{30}{5}.

$$-\frac{6}{5}-\frac{30}{5}-\frac{1}{2}\times \frac{3}{4}$$

Since -\frac{6}{5} and \frac{30}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-6-30}{5}-\frac{1}{2}\times \frac{3}{4}$$

Subtract 30 from -6 to get -36.

$$-\frac{36}{5}-\frac{1}{2}\times \frac{3}{4}$$

Multiply \frac{1}{2} times \frac{3}{4} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{36}{5}-\frac{1\times 3}{2\times 4}$$

Do the multiplications in the fraction \frac{1\times 3}{2\times 4}.

$$-\frac{36}{5}-\frac{3}{8}$$

Least common multiple of 5 and 8 is 40. Convert -\frac{36}{5} and \frac{3}{8} to fractions with denominator 40.

$$-\frac{288}{40}-\frac{15}{40}$$

Since -\frac{288}{40} and \frac{15}{40} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-288-15}{40}$$

Subtract 15 from -288 to get -303.

$$-\frac{303}{40}$$

Factor

$$-\frac{303}{40} = -7\frac{23}{40} = -7.575$$