To maintain the ratio of salt to flour, we start with the given amounts from the recipe, which are \( \frac{13}{1} \) teaspoons of salt to \( \frac{3}{4} \) cup of flour.
First, we convert \( \frac{3}{4} \) cup of flour to a decimal:
\[ \frac{3}{4} = 0.75 \text{ cups of flour.} \]
Now we can express the ratio of salt to flour:
\[ \text{Ratio} = \frac{13 \text{ teaspoons of salt}}{0.75 \text{ cups of flour}}. \]
To find out how many cups of flour correspond to 1 teaspoon of salt, we set up a proportion based on the existing ratio:
Let \( x \) be the amount of flour (in cups) that corresponds to 1 teaspoon of salt. The ratio can be set up as follows:
\[ \frac{13}{0.75} = \frac{1}{x}. \]
Cross multiplying gives:
\[ 13x = 0.75. \]
Now, solving for \( x \):
\[ x = \frac{0.75}{13}. \]
Calculating \( \frac{0.75}{13} \):
First, convert \( 0.75 \) to a fraction: \[ 0.75 = \frac{3}{4}. \]
Now substitute: \[ x = \frac{3/4}{13} = \frac{3}{4 \times 13} = \frac{3}{52}. \]
Now, converting \( \frac{3}{52} \) to decimal format:
\[ 3 \div 52 \approx 0.0576923077. \]
Rounding to an appropriate number of significant figures (as needed), we find:
\[ x \approx 0.0577. \]
Thus, the exact decimal form of cups of flour to mix with 1 teaspoon of salt is:
\[ \boxed{0.0576923077}. \]
Or approximately \( 0.058 \) if rounding to three decimal places.
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