Solve -1/4+1/3(-3/4+2/3)

$$- \frac { 1 } { 4 } + \frac { 1 } { 3 } ( - \frac { 3 } { 4 } + \frac { 2 } { 3 } )$$

Evaluate

$$-\frac{5}{18}\approx -0.277777778$$

Solution Steps

Least common multiple of 4 and 3 is 12. Convert -\frac{3}{4} and \frac{2}{3} to fractions with denominator 12.

$$-\frac{1}{4}+\frac{1}{3}\left(-\frac{9}{12}+\frac{8}{12}\right)$$

Since -\frac{9}{12} and \frac{8}{12} have the same denominator, add them by adding their numerators.

$$-\frac{1}{4}+\frac{1}{3}\times \frac{-9+8}{12}$$

Add -9 and 8 to get -1.

$$-\frac{1}{4}+\frac{1}{3}\left(-\frac{1}{12}\right)$$

Multiply \frac{1}{3} times -\frac{1}{12} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{1}{4}+\frac{1\left(-1\right)}{3\times 12}$$

Do the multiplications in the fraction \frac{1\left(-1\right)}{3\times 12}.

$$-\frac{1}{4}+\frac{-1}{36}$$

Fraction \frac{-1}{36} can be rewritten as -\frac{1}{36} by extracting the negative sign.

$$-\frac{1}{4}-\frac{1}{36}$$

Least common multiple of 4 and 36 is 36. Convert -\frac{1}{4} and \frac{1}{36} to fractions with denominator 36.

$$-\frac{9}{36}-\frac{1}{36}$$

Since -\frac{9}{36} and \frac{1}{36} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-9-1}{36}$$

Subtract 1 from -9 to get -10.

$$\frac{-10}{36}$$

Reduce the fraction \frac{-10}{36} to lowest terms by extracting and canceling out 2.

$$-\frac{5}{18}$$

Factor

$$-\frac{5}{18} = -0.2777777777777778$$