A recipe for a batch of blueberry muffins calls for [tex]\frac{3}{5}[/tex] cup of blueberries. If Riley wants to make [tex]\frac{1}{2}[/tex] a batch of muffins for herself and her tennis partner, how many cups of blueberries will she need?

Riley will need [tex]\square[/tex] cups of blueberries.



Answer :

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.