Solve 0-[4/5+5/4](20/41)+[(1/4)/(1/48)](5/6

$$0 - [ 4 / 5 + 5 / 4 ] ( 20 / 41 ) + [ ( 1 / 4 ) / ( 1 / 48 ) ] ( 5 / 6$$

Evaluate

$$-\frac{43}{48}\approx -0.895833333$$

Solution Steps

Least common multiple of 5 and 4 is 20. Convert \frac{4}{5} and \frac{5}{4} to fractions with denominator 20.

$$0-\left(\frac{16}{20}+\frac{25}{20}\right)\times \frac{20}{41}+\frac{\frac{1}{4}}{\frac{1}{4}\times 8}\times \frac{5}{6}$$

Since \frac{16}{20} and \frac{25}{20} have the same denominator, add them by adding their numerators.

$$0-\frac{16+25}{20}\times \frac{20}{41}+\frac{\frac{1}{4}}{\frac{1}{4}\times 8}\times \frac{5}{6}$$

Add 16 and 25 to get 41.

$$0-\frac{41}{20}\times \frac{20}{41}+\frac{\frac{1}{4}}{\frac{1}{4}\times 8}\times \frac{5}{6}$$

Cancel out \frac{41}{20} and its reciprocal \frac{20}{41}.

$$0-1+\frac{\frac{1}{4}}{\frac{1}{4}\times 8}\times \frac{5}{6}$$

Subtract 1 from 0 to get -1.

$$-1+\frac{\frac{1}{4}}{\frac{1}{4}\times 8}\times \frac{5}{6}$$

Multiply \frac{1}{4} and 8 to get \frac{8}{4}.

$$-1+\frac{\frac{1}{4}}{\frac{8}{4}}\times \frac{5}{6}$$

Divide 8 by 4 to get 2.

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

Express \frac{\frac{1}{4}}{2} as a single fraction.

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

Multiply 4 and 2 to get 8.

$$-1+\frac{1}{8}\times \frac{5}{6}$$

Multiply \frac{1}{8} times \frac{5}{6} by multiplying numerator times numerator and denominator times denominator.

$$-1+\frac{1\times 5}{8\times 6}$$

Do the multiplications in the fraction \frac{1\times 5}{8\times 6}.

$$-1+\frac{5}{48}$$

Convert -1 to fraction -\frac{48}{48}.

$$-\frac{48}{48}+\frac{5}{48}$$

Since -\frac{48}{48} and \frac{5}{48} have the same denominator, add them by adding their numerators.

$$\frac{-48+5}{48}$$

Add -48 and 5 to get -43.

$$-\frac{43}{48}$$

Factor

$$-\frac{43}{48} = -0.8958333333333334$$