Solve 3/4+(-8/9)+5/8

$$\frac { 3 } { 4 } + ( \frac { - 8 } { 9 } ) + \frac { 5 } { 8 }$$

Evaluate

$$\frac{35}{72}\approx 0.486111111$$

Solution Steps

Fraction \frac{-8}{9} can be rewritten as -\frac{8}{9} by extracting the negative sign.

$$\frac{3}{4}-\frac{8}{9}+\frac{5}{8}$$

Least common multiple of 4 and 9 is 36. Convert \frac{3}{4} and \frac{8}{9} to fractions with denominator 36.

$$\frac{27}{36}-\frac{32}{36}+\frac{5}{8}$$

Since \frac{27}{36} and \frac{32}{36} have the same denominator, subtract them by subtracting their numerators.

$$\frac{27-32}{36}+\frac{5}{8}$$

Subtract 32 from 27 to get -5.

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

Least common multiple of 36 and 8 is 72. Convert -\frac{5}{36} and \frac{5}{8} to fractions with denominator 72.

$$-\frac{10}{72}+\frac{45}{72}$$

Since -\frac{10}{72} and \frac{45}{72} have the same denominator, add them by adding their numerators.

$$\frac{-10+45}{72}$$

Add -10 and 45 to get 35.

$$\frac{35}{72}$$

Factor

$$\frac{5 \cdot 7}{2 ^ {3} \cdot 3 ^ {2}} = 0.4861111111111111$$