Solve -1-3/2:(5/4)-2:(-3/4)

$$- 1 - 3 / 2 : ( 5 / 4 ) - 2 : ( - 3 / 4 )$$

Evaluate

$$\frac{7}{15}\approx 0.466666667$$

Solution Steps

Divide \frac{3}{2} by \frac{5}{4} by multiplying \frac{3}{2} by the reciprocal of \frac{5}{4}.

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

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

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

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

$$-1-\frac{12}{10}-\frac{2}{-\frac{3}{4}}$$

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

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

Convert -1 to fraction -\frac{5}{5}.

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

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

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

Subtract 6 from -5 to get -11.

$$-\frac{11}{5}-\frac{2}{-\frac{3}{4}}$$

Divide 2 by -\frac{3}{4} by multiplying 2 by the reciprocal of -\frac{3}{4}.

$$-\frac{11}{5}-2\left(-\frac{4}{3}\right)$$

Express 2\left(-\frac{4}{3}\right) as a single fraction.

$$-\frac{11}{5}-\frac{2\left(-4\right)}{3}$$

Multiply 2 and -4 to get -8.

$$-\frac{11}{5}-\frac{-8}{3}$$

Fraction \frac{-8}{3} can be rewritten as -\frac{8}{3} by extracting the negative sign.

$$-\frac{11}{5}-\left(-\frac{8}{3}\right)$$

The opposite of -\frac{8}{3} is \frac{8}{3}.

$$-\frac{11}{5}+\frac{8}{3}$$

Least common multiple of 5 and 3 is 15. Convert -\frac{11}{5} and \frac{8}{3} to fractions with denominator 15.

$$-\frac{33}{15}+\frac{40}{15}$$

Since -\frac{33}{15} and \frac{40}{15} have the same denominator, add them by adding their numerators.

$$\frac{-33+40}{15}$$

Add -33 and 40 to get 7.

$$\frac{7}{15}$$

Factor

$$\frac{7}{3 \cdot 5} = 0.4666666666666667$$