Solve 5/8+(-7/15)+(3/32)+11/75

$$\frac { 5 } { 8 } + ( - \frac { 7 } { 15 } ) + ( \frac { 3 } { 32 } ) + \frac { 11 } { 75 }$$

Evaluate

$$\frac{319}{800}=0.39875$$

Solution Steps

Least common multiple of 8 and 15 is 120. Convert \frac{5}{8} and \frac{7}{15} to fractions with denominator 120.

$$\frac{75}{120}-\frac{56}{120}+\frac{3}{32}+\frac{11}{75}$$

Since \frac{75}{120} and \frac{56}{120} have the same denominator, subtract them by subtracting their numerators.

$$\frac{75-56}{120}+\frac{3}{32}+\frac{11}{75}$$

Subtract 56 from 75 to get 19.

$$\frac{19}{120}+\frac{3}{32}+\frac{11}{75}$$

Least common multiple of 120 and 32 is 480. Convert \frac{19}{120} and \frac{3}{32} to fractions with denominator 480.

$$\frac{76}{480}+\frac{45}{480}+\frac{11}{75}$$

Since \frac{76}{480} and \frac{45}{480} have the same denominator, add them by adding their numerators.

$$\frac{76+45}{480}+\frac{11}{75}$$

Add 76 and 45 to get 121.

$$\frac{121}{480}+\frac{11}{75}$$

Least common multiple of 480 and 75 is 2400. Convert \frac{121}{480} and \frac{11}{75} to fractions with denominator 2400.

$$\frac{605}{2400}+\frac{352}{2400}$$

Since \frac{605}{2400} and \frac{352}{2400} have the same denominator, add them by adding their numerators.

$$\frac{605+352}{2400}$$

Add 605 and 352 to get 957.

$$\frac{957}{2400}$$

Reduce the fraction \frac{957}{2400} to lowest terms by extracting and canceling out 3.

$$\frac{319}{800}$$

Factor

$$\frac{11 \cdot 29}{2 ^ {5} \cdot 5 ^ {2}} = 0.39875$$