To determine how much water you would need to make only [tex]\(\frac{1}{8}\)[/tex] of the recipe, we need to compute a fraction of the original amount of water.
Given:
- The original recipe calls for [tex]\(\frac{4}{5}\)[/tex] cup of water.
- You want to make [tex]\(\frac{1}{8}\)[/tex] of the recipe.
We need to find [tex]\(\frac{1}{8}\)[/tex] of [tex]\(\frac{4}{5}\)[/tex] cup of water.
To find a fraction of another fraction, you multiply the two fractions together:
[tex]\[
\frac{4}{5} \times \frac{1}{8}
\][/tex]
Now, multiply the numerators (the top numbers) together and the denominators (the bottom numbers) together:
[tex]\[
\frac{4 \times 1}{5 \times 8} = \frac{4}{40}
\][/tex]
Next, simplify the fraction [tex]\(\frac{4}{40}\)[/tex]. Both the numerator and the denominator can be divided by their greatest common divisor, which is 4:
[tex]\[
\frac{4 \div 4}{40 \div 4} = \frac{1}{10}
\][/tex]
Therefore, to make [tex]\(\frac{1}{8}\)[/tex] of the recipe, you need [tex]\(\frac{1}{10}\)[/tex] cup of water.
The final answer is:
[tex]\(\frac{1}{10}\)[/tex] cups
