To determine the fraction of barbecued items that are mushroom caps, follow these steps:
1. Identify the given fractions:
- The fraction of items that are veggie burgers is [tex]\(\frac{3}{8}\)[/tex].
- The fraction of items that are corn cobs is [tex]\(\frac{1}{3}\)[/tex].
2. Find a common denominator for the fractions:
- The denominators are 8 and 3. The least common denominator (LCD) for 8 and 3 is 24.
3. Convert the fractions to the common denominator of 24:
- For the veggie burgers fraction:
[tex]\[
\frac{3}{8} = \frac{3 \times 3}{8 \times 3} = \frac{9}{24}
\][/tex]
- For the corn cobs fraction:
[tex]\[
\frac{1}{3} = \frac{1 \times 8}{3 \times 8} = \frac{8}{24}
\][/tex]
4. Add the fractions of veggie burgers and corn cobs:
- The total fraction of items that are either veggie burgers or corn cobs is:
[tex]\[
\frac{9}{24} + \frac{8}{24} = \frac{17}{24}
\][/tex]
5. Determine the fraction of items that are mushroom caps:
- Since the total of all items barbecued is 1 (or [tex]\(\frac{24}{24}\)[/tex]), the fraction of items that are mushroom caps is the remainder after accounting for the veggie burgers and corn cobs.
[tex]\[
1 - \frac{17}{24} = \frac{24}{24} - \frac{17}{24} = \frac{7}{24}
\][/tex]
Thus, the fraction of barbecued items that are mushroom caps is [tex]\(\frac{7}{24}\)[/tex].
