To solve the word problem of determining the total amount of chopped onion and chopped celery needed for the soup, we first need to identify the fractions representing the given amounts of onion and celery.
The recipe calls for:
- [tex]\(\frac{2}{4}\)[/tex] cup of chopped onion
- [tex]\(\frac{1}{5}\)[/tex] cup of chopped celery
We need to add these two amounts to find the total amount required for the soup.
First, we note that [tex]\(\frac{2}{4}\)[/tex] can be simplified to [tex]\(\frac{1}{2}\)[/tex] since [tex]\(\frac{2}{4} = \frac{1}{2}\)[/tex].
Next, we sum the fractions [tex]\(\frac{1}{2}\)[/tex] and [tex]\(\frac{1}{5}\)[/tex].
To add these fractions, we need a common denominator. The least common multiple of 2 and 5 is 10.
We convert the fractions to have this common denominator:
[tex]\[
\frac{1}{2} = \frac{5}{10}
\][/tex]
[tex]\[
\frac{1}{5} = \frac{2}{10}
\][/tex]
Adding these together:
[tex]\[
\frac{5}{10} + \frac{2}{10} = \frac{7}{10}
\][/tex]
Thus, the total amount of onion and celery needed for the soup is [tex]\(\frac{7}{10}\)[/tex] cups.
So the final answer is:
[tex]\[
\boxed{\frac{7}{10}}
\][/tex]
