"I also eat rice."
They wanted us to get used to "吃饭" as the expression for "eat", but they had to translate by one word, I'll explain.
A lot of Chinese words consist of two hieroglyphs, while one should be enough. So while 吃 = eat, 饭 = rice, 吃饭 means more like "eat [food in general]".
They want us to learn the expression "I eat [food]", but is hard to explain for students why there is suddenly "rice" there
They can't ask for "I eat", because you need something to put after 吃, and in general case as in I ate [food], Chinese say literally "I ate rice" meaning food in general.
But out of context, your sentence is correct. If you want to say you eat specifically rice, you use two words that mean rice.
It can be either, depending on the context. As "food", it often implies a meal rather than food in general, rice being the traditional foundation of the meal.
"我也吃饭" would be interpreted as "I eat too" or "I'm eating too", though you could specify the progressive with "在".
You may be aware that it's a standard Chinese greeting to say "（你）吃饭了吗？", i.e. "Have you eaten?"
Whether or not you've just eaten, you answer this with "吃饭了", or some other polite alternative to reassure the other party that your previous or subsequent meal is taken care of.
"吃米饭" is how to specify "eat rice". (That's accepted now, by the way.)
I'm also of a mind that the translation really shouldn't equate "吃饭" with "eat rice." While technically correct, that doesn't really reflect the common useage of the phrase, which just means to eat.
I think this confusion arises from the fact that 吃 is a v-o verb in Chinese. As such it requires an object, for which 饭 is the generic word used to complete the verb. But to translate 我也吃饭 as "I also eat rice" would be like translating "我也散步" as "I also walk steps."
The fact that this does not mean "eat rice" is made clear if you were to try to make the negative statement "I don't like to eat rice." You would need to say 我不喜欢吃米饭. If you just said 我不喜欢吃饭 that would mean "I don't like eating food."
It's definitely right that 饭 means food in general (especially for lunch or dinner). When we want to emphasize rice, we use 米饭. Let me explain in a conversation with context. At noon time in a office: 老王：中午啦，我要去吃饭了。 小李：正好我也要去吃饭，一起吧。 At the table : 老王：我想吃炸酱面，你呢？ 小李：我早饭就吃的面，我还是吃米饭吧。
Regarding the real meaning and literal translation, why can't you just put as an answer and accept either half as correct: I eat (literally eat rice). This exercise is a waste of time because there is no indication of the correct answer to learn. I could do it by process of elimination. Also I am up early and want to make use of the time doing languages but the family are asleep so I can't play the audio. I need to be able to turn to silent or very quiet and there is no way of doing this on screen.
I was in a Chinese class before this so i know the basics. The sentences and grammer are so different from us in the U.S. My teacher taught me the basics and she taught me that not everything in their language is literal. In fact, for words that don't exist (many words) they plug it in with easier words. That is why pinyin is so hard to write these days. Hope I helped.