Solve 1/4div(3-5/13+8/13)

$$\frac { 1 } { 4 } \div ( 3 - \frac { 5 } { 13 } + \frac { 8 } { 13 } )$$

Evaluate

$$\frac{13}{168}\approx 0.077380952$$

Solution Steps

Convert 3 to fraction \frac{39}{13}.

$$\frac{\frac{1}{4}}{\frac{39}{13}-\frac{5}{13}+\frac{8}{13}}$$

Since \frac{39}{13} and \frac{5}{13} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{1}{4}}{\frac{39-5}{13}+\frac{8}{13}}$$

Subtract 5 from 39 to get 34.

$$\frac{\frac{1}{4}}{\frac{34}{13}+\frac{8}{13}}$$

Since \frac{34}{13} and \frac{8}{13} have the same denominator, add them by adding their numerators.

$$\frac{\frac{1}{4}}{\frac{34+8}{13}}$$

Add 34 and 8 to get 42.

$$\frac{\frac{1}{4}}{\frac{42}{13}}$$

Divide \frac{1}{4} by \frac{42}{13} by multiplying \frac{1}{4} by the reciprocal of \frac{42}{13}.

$$\frac{1}{4}\times \frac{13}{42}$$

Multiply \frac{1}{4} times \frac{13}{42} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 13}{4\times 42}$$

Do the multiplications in the fraction \frac{1\times 13}{4\times 42}.

$$\frac{13}{168}$$

Factor

$$\frac{13}{2 ^ {3} \cdot 3 \cdot 7} = 0.07738095238095238$$