To determine a ratio that forms a proportion with \( \frac{4}{5} \), we can set up a proportion as follows:
\[ \frac{4}{5} = \frac{a}{b} \]
For a proportion to hold, the cross products must be equal, meaning:
\[ 4 \times b = 5 \times a \]
This means that for any values of \( a \) and \( b \) that satisfy this equation, the ratios will form a proportion with \( \frac{4}{5} \).
To find a specific ratio, we can simply choose a value for \( a \) and solve for \( b \).
For example, if we let \( a = 8 \):
\[ 4b = 5(8) \] \[ 4b = 40 \] \[ b = 10 \]
So \( \frac{8}{10} \) forms a proportion with \( \frac{4}{5} \) since \( \frac{4}{5} = \frac{8}{10} \).
You can choose many different pairs of \( (a, b) \). Any equivalent fraction of \( \frac{4}{5} \), like \( \frac{12}{15}, \frac{16}{20}, \frac{20}{25} \), and so on, will also form a proportion with \( \frac{4}{5} \).
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