У моей сумочки сломался ремешок, поэтому я взяла другую сумочку.

Because the thing that actually broke is ремешок. In Russian, a very common way to say that one thing belongs to another is у + genitive.

So the structure is:

У моей сумочки сломался ремешок
literally something like: At my little bag, the strap broke

Natural English turns that into The strap on/of my bag broke.

If you said Моя сумочка сломалась, that would mean the whole bag broke, not specifically the strap.

Because у requires the genitive case.

The basic form is:

• моя сумочка = my little bag / my handbag

After у, it becomes:

• у моей сумочки

Both words change:

• моя → моей
• сумочка → сумочки

So this is just normal case agreement: adjective and noun both go into the genitive singular.

Сумочка is a diminutive form of сумка.

Very roughly:

• сумка = bag
• сумочка = little bag, handbag, purse-like bag

In many contexts, сумочка sounds more like a woman’s handbag or a smaller, personal bag. It can also sound a bit softer or more natural depending on the object being described.

So the choice of сумочка gives a slightly more specific feel than plain сумка.

Because the verb agrees with the subject, and the subject here is ремешок, not сумочка.

• ремешок is masculine singular
• so the past-tense verb is сломался

Russian past tense agrees in gender and number with the subject:

• masculine: сломался
• feminine: сломалась
• neuter: сломалось
• plural: сломались

So the sentence is built around ремешок сломался = the strap broke.

Here -ся is part of the verb сломаться, which means to break, to get broken, or to end up broken.

Compare:

• сломать = to break something
• сломаться = to break, to become broken

So:

• Я сломала ремешок = I broke the strap
• Ремешок сломался = The strap broke

In this sentence, the focus is on what happened to the strap, not on who caused it.

Ремешок usually means a small strap. It is the diminutive form of ремень.

Very roughly:

• ремень = belt / strap
• ремешок = little strap, small strap

For a bag, watch, sandal, or similar item, ремешок is often the natural choice when talking about a smaller attached strap. It sounds more specific and more idiomatic here than ремень.

Because in the past tense, Russian verbs agree with the gender of the speaker when the subject is я.

• я взял = I took, said by a man
• я взяла = I took, said by a woman

So this sentence tells you that the speaker is female.

Because взять / взяла is perfective, and it presents the action as a completed whole: she took another bag.

That fits the situation well:

• the strap broke
• so she took another bag

If you used брала from брать, that would be imperfective and would sound more like a process, repeated action, or something habitual, depending on context.

Here Russian wants a single completed action, so взяла is the natural choice.

It is in the accusative singular, because it is the direct object of взяла.

Basic form:

• другая сумочка

After взяла:

• взяла другую сумочку

Both words change to the feminine singular accusative:

• другая → другую
• сумочка → сумочку

As for meaning, другой can mean both another and different, depending on context. Here it naturally means another bag or a different bag.

Yes, я взяла другую is possible if the context is clear.

But repeating the noun is also very natural in Russian, especially when the speaker wants to be clear and explicit:

• я взяла другую = I took another one
• я взяла другую сумочку = I took another bag

The full version leaves no doubt about what другую refers to.

Поэтому means therefore, that’s why, or so.

It connects the two ideas logically:

• the strap broke
• therefore she took another bag

The comma is used because these are two separate clauses:

• У моей сумочки сломался ремешок
• поэтому я взяла другую сумочку

So the punctuation matches the sentence structure: first the cause/result setup, then the consequence.

The word order is fairly flexible, but different orders change the emphasis.

For example, these are all possible:

• У моей сумочки сломался ремешок
• Ремешок у моей сумочки сломался
• Сломался ремешок у моей сумочки

The original version is natural because it first sets the context with my bag, then tells you what happened the strap broke.

So the order is not completely fixed, but the chosen version sounds smooth and normal.