In this sentence improvement item, choose the best replacement for the bracketed word "(numbered)" in the sentence about ant communities sometimes having up to five hundred individuals.

Introduction / Context:
This question deals with choosing the correct non finite verb form to describe a characteristic of a subject. The sentence explains that communities of ants can sometimes be very large, with as many as five hundred individuals, and then comments on their peaceful behaviour. The bracketed word "numbered" does not fit smoothly into the descriptive structure, so you need to select a better form that links the number information to the subject "communities of ants".

Given Data / Assumptions:

• Subject: "The communities of ants".
• Bracketed word: "numbered".
• The phrase is "sometimes very large, numbered even up to 500 individuals".
• Options: "number", "numerous", "numbering", and "No improvement".

Concept / Approach:
When we want to add extra information about the size of a group, we often use the present participle "numbering" after a comma, for example "the crowd, numbering nearly ten thousand" or "a team, numbering twelve players". This form functions like a reduced relative clause "which numbers". The past form "numbered" would be used in a full clause such as "the communities were numbered up to 500", which is not the intended structure. The adjective "numerous" does not directly introduce the specific figure "500 individuals". Therefore, "numbering" is the correct choice here.

Step-by-Step Solution:
Step 1: Observe that the phrase after the comma provides extra descriptive information about the subject. Step 2: Recall the common pattern "subject, numbering X individuals", which summarises group size. Step 3: Replace "numbered" with "numbering" so the sentence reads "communities of ants are sometimes very large, numbering even up to 500 individuals". Step 4: Check that the new structure flows naturally and correctly associates the number with the subject. Step 5: Verify that other options do not fit the grammatical pattern or the intended meaning.

Verification / Alternative check:
Read the improved sentence: "The communities of ants are sometimes very large, numbering even up to 500 individuals, and it is a lesson to us that no one has ever yet seen a quarrel between any two ants belonging to the same community." This flows like a standard descriptive sentence. "Number even up to 500 individuals" would require a different structure, such as "may number up to 500 individuals". "Numerous even up to 500 individuals" is ungrammatical. Leaving "numbered" keeps an awkward, incomplete form after the comma. So "numbering" is the only option that creates a smooth, correct participial phrase.

Why Other Options Are Wrong:
"Number" as a base verb form would generally need an auxiliary, and "are sometimes very large, number even up to 500" does not work.

"Numerous" is an adjective meaning "many", used directly before a noun, as in "numerous individuals", not before "even up to 500 individuals".

"No improvement" would retain "numbered even up to 500 individuals", which is clumsy and incomplete in this context.

Common Pitfalls:
Learners often hesitate between "-ed" and "-ing" forms after a comma when giving additional information. A helpful rule is that if the phrase describes an ongoing characteristic of the subject, the "-ing" form is usually more appropriate, as in "standing at the corner", "consisting of three parts", or "numbering five hundred". The "-ed" form is more often used in passive constructions with explicit auxiliaries, such as "was numbered", "was painted", or "was closed".

Final Answer:
The correct improvement is "numbering", giving the phrase "numbering even up to 500 individuals".