To express the ratio of 36 social media posts to 16 social media posts in fractional notation, we write it as a fraction:
\[ \frac{36}{16} \]
Next, we simplify this fraction. To do that, we find the greatest common divisor (GCD) of 36 and 16.
The prime factorization of 36 is:
\[ 36 = 2^2 \times 3^2 \]
The prime factorization of 16 is:
\[ 16 = 2^4 \]
The GCD of 36 and 16 is the product of the lowest powers of the common prime factors. The only common prime factor is 2, and its lowest power between the two factorizations is \(2^2 = 4\).
Now we divide both the numerator and denominator of the fraction by their GCD:
\[ \frac{36 \div 4}{16 \div 4} = \frac{9}{4} \]
Thus, the simplified ratio of 36 social media posts to 16 social media posts is:
\[ \frac{9}{4} \]
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