Solve 13/40+1/16/frac{13{5}-8/15}

$$\frac { \frac { 13 } { 40 } + \frac { 1 } { 16 } } { \frac { 13 } { 5 } - \frac { 8 } { 15 } }$$

Evaluate

$$\frac{3}{16}=0.1875$$

Solution Steps

Least common multiple of 40 and 16 is 80. Convert \frac{13}{40} and \frac{1}{16} to fractions with denominator 80.

$$\frac{\frac{26}{80}+\frac{5}{80}}{\frac{13}{5}-\frac{8}{15}}$$

Since \frac{26}{80} and \frac{5}{80} have the same denominator, add them by adding their numerators.

$$\frac{\frac{26+5}{80}}{\frac{13}{5}-\frac{8}{15}}$$

Add 26 and 5 to get 31.

$$\frac{\frac{31}{80}}{\frac{13}{5}-\frac{8}{15}}$$

Least common multiple of 5 and 15 is 15. Convert \frac{13}{5} and \frac{8}{15} to fractions with denominator 15.

$$\frac{\frac{31}{80}}{\frac{39}{15}-\frac{8}{15}}$$

Since \frac{39}{15} and \frac{8}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{31}{80}}{\frac{39-8}{15}}$$

Subtract 8 from 39 to get 31.

$$\frac{\frac{31}{80}}{\frac{31}{15}}$$

Divide \frac{31}{80} by \frac{31}{15} by multiplying \frac{31}{80} by the reciprocal of \frac{31}{15}.

$$\frac{31}{80}\times \frac{15}{31}$$

Multiply \frac{31}{80} times \frac{15}{31} by multiplying numerator times numerator and denominator times denominator.

$$\frac{31\times 15}{80\times 31}$$

Cancel out 31 in both numerator and denominator.

$$\frac{15}{80}$$

Reduce the fraction \frac{15}{80} to lowest terms by extracting and canceling out 5.

$$\frac{3}{16}$$

Factor

$$\frac{3}{2 ^ {4}} = 0.1875$$