To solve the question of finding the equation that represents the product of [tex]\( 4 \times \frac{1}{9} \)[/tex], let’s examine each choice step-by-step to determine its validity:
1. Equation: [tex]\(\frac{4+1}{4+5} = \frac{5}{9}\)[/tex]
- The equation simplifies to [tex]\(\frac{5}{9}\)[/tex]. While this fraction is calculated correctly, it does not represent the product [tex]\( 4 \times \frac{1}{9} \)[/tex].
2. Equation: [tex]\(\frac{4 \times 9}{1} = 36\)[/tex]
- This equation simplifies to [tex]\( 36 \)[/tex]. Clearly, [tex]\( 36 \)[/tex] is not the product of [tex]\( 4 \times \frac{1}{9} \)[/tex], as it results in a much larger number.
3. Equation: [tex]\(\frac{4 \times 1}{9} = \frac{4}{9}\)[/tex]
- This equation simplifies to [tex]\(\frac{4}{9}\)[/tex]. This is the correct representation of the product [tex]\( 4 \times \frac{1}{9} \)[/tex].
4. Equation: [tex]\(\frac{4 \times 1}{4 \times 9} = \frac{4}{36} = \frac{1}{9}\)[/tex]
- While the simplification is correct, resulting in [tex]\(\frac{1}{9}\)[/tex], it does not represent the product [tex]\( 4 \times \frac{1}{9} \)[/tex], but rather [tex]\( 1 \times \frac{1}{9} \)[/tex].
Given the true results, the correct equation to represent the product [tex]\( 4 \times \frac{1}{9} \)[/tex] is:
[tex]\[ \boxed{\frac{4 \times 1}{9} = \frac{4}{9}} \][/tex]
