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The Freeman family is barbecuing veggie burgers, corn cobs, and mushroom caps in their local park. If [tex]\frac{3}{8}[/tex] of the items barbecued are veggie burgers, and [tex]\frac{1}{3}[/tex] of the items barbecued are corn cobs, what fraction of barbecued items are mushroom caps?



Answer :

GinnyAnswer
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].

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