Improve the bracketed part of the sentence by choosing the best option: If you come across new words, you should look (them up) in the dictionary.

Introduction / Context:
This question is about phrasal verbs and sentence improvement. In English, many verbs combine with small particles like up, down, for, or at to form phrasal verbs with specific meanings. The sentence given describes what a learner should do when they meet new vocabulary items. The phrase look them up in the dictionary is already a standard and correct phrasal verb. The exam tests whether candidates recognise this and avoid making an unnecessary change.

Given Data / Assumptions:

• Base sentence: If you come across new words, you should look (them up) in the dictionary.
• The bracketed part them up is the segment we may or may not change.
• Options: for them, at them, them down, no improvement.
• We must select the option that produces the most natural and grammatically correct sentence in standard English.

Concept / Approach:
The phrasal verb look up, when used with words or information, means to search for the meaning, spelling, or details in a reference book or database. The correct structure is look something up or look up something. Expressions like look for them and look at them have different meanings. Look for means search for, often in a physical sense or in a wide area, while look at means direct your eyes toward something. Look them down is not a standard phrasal verb. The given sentence already uses the correct phrasal verb look them up, so no change is needed.

Step-by-Step Solution:
Step 1: Read the sentence carefully and focus on the phrase look them up in the dictionary. Step 2: Recall that the normal expression used when consulting a dictionary is look up a word or look a word up. Step 3: Test option a, for them. The sentence would read you should look for them in the dictionary, which sounds as if the words themselves are physically lost, which is not the intended meaning. Step 4: Test option b, at them. The sentence would read you should look at them in the dictionary, which simply suggests viewing them, not specifically searching for their meanings. Step 5: Test option c, them down. This does not form a recognised phrasal verb in this context and is incorrect. Step 6: Recognise that the original phrase look them up is the correct idiomatic usage and select no improvement.

Verification / Alternative check:
Consider typical dictionary related advice in textbooks: Students are often told, You should look new words up in a dictionary or Look up unfamiliar terms when you read. These instructions clearly show that look up is the accepted phrasal verb. Replacing it with look for or look at changes the sense or makes the sentence less precise. Therefore, the original construction them up is fully correct and does not require any change.

Why Other Options Are Wrong:
for them: Changes the meaning to searching for the physical presence of words, which is not the intended academic action of consulting a dictionary entry.
at them: Suggests only viewing words, not actively checking their meanings or usage.
them down: Does not create a correct phrasal verb in this context and is grammatically odd.

Common Pitfalls:
Many candidates assume that an improvement question must always contain an error and therefore try to change the bracketed part even when it is correct. This leads them to choose a weaker or incorrect option. To avoid this, learners should first check whether the original phrase is a recognised collocation or idiom. If it already matches common standard usage, they should confidently select no improvement rather than forcing a change.

Final Answer:
The phrase them up is already correct, so the best choice is no improvement, and option d is correct.