okonomiyaki wo kiriwakeru tuide ni, aonori wo hurikaketa.

ついでに means while I was at it, on the occasion of doing that, or as a side thing.

In this sentence, the speaker is saying that while cutting up the okonomiyaki, they also sprinkled aonori on it.

The nuance is not just two actions in sequence. It suggests:

• one action was the main thing
• the second action was done conveniently at the same time or on that occasion

So it feels like:

• Since I was already cutting up the okonomiyaki, I went ahead and sprinkled aonori on it too.

With ついでに, the verb usually comes in its dictionary form when you mean on the occasion of doing X:

• Vる + ついでに
• Nの + ついでに

So:

• 切り分けるついでに = while/when cutting it up
• 買い物のついでに = while out shopping

Using て-form before ついでに is generally not the normal pattern here.

切る just means to cut.

切り分ける means to cut something into portions/pieces and distribute or separate them.

For food, 切り分ける often implies cutting it so people can eat it more easily or share it. That fits well with お好み焼き, since you often cut it into bite-sized or shareable pieces.

So 切り分ける is more specific than just cut.

The particle を marks the direct object of the verb.

Here:

• お好み焼きを切り分ける = to cut up the okonomiyaki

So お好み焼き is the thing being cut up.

Because 青のり is also the direct object of the second verb:

• 青のりを振りかけた = sprinkled aonori

In Japanese, each verb can have its own object, and each object can be marked with を.

So the sentence has two verb phrases:

• お好み焼きを切り分ける
• 青のりを振りかけた

振りかける means to sprinkle something over something.

So:

• 青のりを振りかけた = sprinkled aonori on it

It is more specific than just put on. It suggests a shaking or sprinkling motion, which is exactly how aonori is typically added to food.

This is because 切り分ける is inside the grammar pattern Vる + ついでに, where the dictionary form is used as part of the structure.

The main action of the whole sentence is expressed by 振りかけた, which is in the past tense.

So the sentence structure is roughly:

• On the occasion of cutting up the okonomiyaki, I sprinkled aonori.

Even though both actions happened in the past, only the main clause needs the past tense here.

No, the subject is omitted.

This is very common in Japanese when the subject is obvious from context. In a sentence like this, the implied subject is usually something like:

• I
• we
• or sometimes someone specific already understood from context

So the sentence does not explicitly say who cut it up and sprinkled the aonori.

青のり is a type of green seaweed powder/flakes often used as a topping in Japanese cooking.

It is commonly sprinkled on foods like:

• お好み焼き
• たこ焼き
• 焼きそば

So in this sentence, it is a food topping.

No. ついでに can be used more broadly for any additional action done on the same occasion.

Examples:

• コンビニに行くついでに、飲み物を買った。
  While I was going to the convenience store, I bought a drink too.

• 掃除のついでに、古い本も捨てた。
  While I was cleaning, I threw out some old books too.

So it does not have to be physical movement. The key idea is doing something extra while already doing something else.

Not necessarily at the exact same second.

ついでに usually means the second action was done in connection with or on the occasion of the first action. It often means the actions happened in the same general situation, not literally simultaneously.

So here the idea is:

• the speaker was cutting up the okonomiyaki
• and as part of that opportunity, they also sprinkled aonori

It is more like while I was at it than at the exact same moment.

Japanese often puts the background or setup first, then the main action later.

So here:

• お好み焼きを切り分けるついでに = background/context
• 青のりを振りかけた = main action

This is a very natural Japanese way to organize information: first explain the circumstance, then say what happened.

ながら usually means doing two actions simultaneously, and it often focuses on one person doing both actions at the same time.

But ついでに means doing something as an extra action on the occasion of another action.

So:

• ついでに = while I was at it / since I was doing that anyway
• ながら = while doing X, doing Y at the same time

In this sentence, ついでに is better because sprinkling aonori is presented as an extra thing done conveniently while cutting up the okonomiyaki.