Question
If a three-vegetable soup contains 3/4 tomatoes and 1/8 squash, what fraction of onions are
in the soup?
in the soup?
Answers
GPT-4o mini
To find the fraction of onions in the soup, we first need to determine the total fraction of vegetables already accounted for (tomatoes and squash) and then calculate the fraction of onions.
The fraction of tomatoes in the soup is \( \frac{3}{4} \) and the fraction of squash is \( \frac{1}{8} \).
To add these two fractions, we first need a common denominator. The least common multiple of 4 and 8 is 8.
Now, we can convert \( \frac{3}{4} \) to a fraction with a denominator of 8:
\[
\frac{3}{4} = \frac{3 \times 2}{4 \times 2} = \frac{6}{8}
\]
Now we can add the fractions for tomatoes and squash:
\[
\frac{6}{8} + \frac{1}{8} = \frac{6 + 1}{8} = \frac{7}{8}
\]
The total fraction of tomatoes and squash in the soup is \( \frac{7}{8} \). To find the fraction of onions, we subtract this from the whole (which is represented as 1):
\[
1 - \frac{7}{8} = \frac{8}{8} - \frac{7}{8} = \frac{1}{8}
\]
Thus, the fraction of onions in the soup is \( \frac{1}{8} \).
The fraction of tomatoes in the soup is \( \frac{3}{4} \) and the fraction of squash is \( \frac{1}{8} \).
To add these two fractions, we first need a common denominator. The least common multiple of 4 and 8 is 8.
Now, we can convert \( \frac{3}{4} \) to a fraction with a denominator of 8:
\[
\frac{3}{4} = \frac{3 \times 2}{4 \times 2} = \frac{6}{8}
\]
Now we can add the fractions for tomatoes and squash:
\[
\frac{6}{8} + \frac{1}{8} = \frac{6 + 1}{8} = \frac{7}{8}
\]
The total fraction of tomatoes and squash in the soup is \( \frac{7}{8} \). To find the fraction of onions, we subtract this from the whole (which is represented as 1):
\[
1 - \frac{7}{8} = \frac{8}{8} - \frac{7}{8} = \frac{1}{8}
\]
Thus, the fraction of onions in the soup is \( \frac{1}{8} \).