To determine how many cups of blueberries Riley will need, we'll follow a step-by-step approach:
1. Understand the given fractions:
- The recipe requires [tex]\(\frac{3}{5}\)[/tex] cup of blueberries for a full batch.
- Riley wants to make [tex]\(\frac{1}{2}\)[/tex] of a batch.
2. Calculate the fraction of blueberries needed for [tex]\(\frac{1}{2}\)[/tex] of a batch:
Since Riley is making [tex]\(\frac{1}{2}\)[/tex] of a batch, we need to find out what fraction of [tex]\(\frac{3}{5}\)[/tex] cup of blueberries [tex]\(\frac{1}{2}\)[/tex] of a batch will require. To do this, we multiply the fraction of a full batch ([tex]\(\frac{3}{5}\)[/tex]) by the fraction of the batch Riley wants to make ([tex]\(\frac{1}{2}\)[/tex]).
[tex]\[
\text{Blueberries needed} = \frac{3}{5} \times \frac{1}{2}
\][/tex]
3. Multiply the fractions:
To multiply these fractions, multiply the numerators together and the denominators together:
[tex]\[
\frac{3}{5} \times \frac{1}{2} = \frac{3 \times 1}{5 \times 2} = \frac{3}{10}
\][/tex]
4. Simplify the result:
The fraction [tex]\(\frac{3}{10}\)[/tex] is already in its simplest form.
Therefore, Riley will need [tex]\(\frac{3}{10}\)[/tex] cup of blueberries to make [tex]\(\frac{1}{2}\)[/tex] a batch of muffins.
In decimal form, [tex]\(\frac{3}{10}\)[/tex] is equivalent to 0.3.
So, Riley will need [tex]\(0.3\)[/tex] cups of blueberries.
