Let's solve the problem step-by-step:
1. Identify the initial amount of flour in the cupboard.
You have [tex]\(\frac{4}{6}\)[/tex] cup of flour. Simplify this fraction.
[tex]\[
\frac{4}{6} = \frac{2 \times 2}{2 \times 3} = \frac{2}{3}
\][/tex]
2. Identify the amount of flour required by the recipe.
The recipe calls for [tex]\(\frac{1}{5}\)[/tex] cup of flour.
3. Subtract the amount of flour required from the initial amount.
To subtract these two fractions, we need a common denominator. The common denominator for [tex]\(\frac{2}{3}\)[/tex] and [tex]\(\frac{1}{5}\)[/tex] is 15. Convert both fractions to have this common denominator:
[tex]\[
\frac{2}{3} = \frac{2 \times 5}{3 \times 5} = \frac{10}{15}
\][/tex]
[tex]\[
\frac{1}{5} = \frac{1 \times 3}{5 \times 3} = \frac{3}{15}
\][/tex]
4. Perform the subtraction.
[tex]\[
\frac{10}{15} - \frac{3}{15} = \frac{10 - 3}{15} = \frac{7}{15}
\][/tex]
Therefore, after making the bread, you would have [tex]\(\frac{7}{15}\)[/tex] cup of flour left in your cupboard.
