Solve 1/2left(47/512+23/256right)

$$\frac{ 1 }{ 2 } \left( \frac{ 47 }{ 512 } + \frac{ 23 }{ 256 } \right)$$

Evaluate

$$\frac{93}{1024}=0.090820312$$

Solution Steps

Least common multiple of 512 and 256 is 512. Convert \frac{47}{512} and \frac{23}{256} to fractions with denominator 512.

$$\frac{1}{2}\left(\frac{47}{512}+\frac{46}{512}\right)$$

Since \frac{47}{512} and \frac{46}{512} have the same denominator, add them by adding their numerators.

$$\frac{1}{2}\times \frac{47+46}{512}$$

Add 47 and 46 to get 93.

$$\frac{1}{2}\times \frac{93}{512}$$

Multiply \frac{1}{2} times \frac{93}{512} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 93}{2\times 512}$$

Do the multiplications in the fraction \frac{1\times 93}{2\times 512}.

$$\frac{93}{1024}$$

Factor

$$\frac{3 \cdot 31}{2 ^ {10}} = 0.0908203125$$