To find the total amount of ingredients Jesse needs for her smoothie, you can add the amount of milk and the amount of bananas together.
She needs \( \frac{1}{5} \) cup of milk and \( \frac{3}{4} \) cup of bananas.
To add these fractions, we first need a common denominator. The least common multiple of 5 and 4 is 20.
Now convert each fraction:
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Convert \( \frac{1}{5} \) to a fraction with a denominator of 20: \[ \frac{1}{5} = \frac{1 \times 4}{5 \times 4} = \frac{4}{20} \]
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Convert \( \frac{3}{4} \) to a fraction with a denominator of 20: \[ \frac{3}{4} = \frac{3 \times 5}{4 \times 5} = \frac{15}{20} \]
Now, add the two fractions: \[ \frac{4}{20} + \frac{15}{20} = \frac{4 + 15}{20} = \frac{19}{20} \]
So, the total amount of ingredients Jesse needs is \( \frac{19}{20} \) of a cup.
The answer is: \[ \frac{19}{20} \text{ of a cup.} \]