A despesa variável mudou este mês.

Because despesa is a feminine singular noun in Portuguese, so it takes the feminine singular definite article a.

• a despesa = the expense
• as despesas = the expenses

This is something you simply have to learn with the noun: in Portuguese, nouns have grammatical gender.

In Portuguese, adjectives often come after the noun, especially in neutral, factual language.

So:

• despesa variável = variable expense

This is the normal order in a financial or accounting context. Putting the adjective before the noun is usually less neutral and can sound literary, emphatic, or stylistically marked.

Yes. Adjectives in Portuguese agree with the noun they describe, mainly in number, and often in gender too.

In this case:

• despesa is singular
• variável is singular too

A useful detail: variável has the same form in the masculine and feminine singular.

Examples:

• a despesa variável
• o custo variável
• as despesas variáveis
• os custos variáveis

So the plural changes to variáveis.

Mudou is the 3rd person singular of the pretérito perfeito simples of mudar.

That means it refers to a completed change:

• eu mudei
• tu mudaste
• ele/ela mudou

In English, depending on context, this can correspond to:

• changed
• sometimes has changed

In this sentence, Portuguese uses the simple past form mudou, even though English might sometimes prefer has changed this month.

In European Portuguese, the distinction between este, esse, and aquele is important:

• este = this, near the speaker / current
• esse = that, near the listener or already mentioned
• aquele = that over there / more distant

So este mês means this month, the current month.

For a learner of European Portuguese, it is useful to keep this distinction clear, because Portugal Portuguese tends to preserve it more consistently than some other varieties.

Because Portuguese often uses a bare time expression without a preposition when talking about time adverbials.

So these are natural:

• este mês = this month
• esta semana = this week
• este ano = this year

You can also hear neste mês, but that usually feels more like in this month, often with a more contrastive or formal tone.

So in a simple sentence like this, este mês is the most natural choice.

In a normal full sentence, yes, it is the natural choice.

Portuguese uses definite articles more often than English does. With a specific subject like this, a despesa variável sounds complete and normal.

If you remove the article:

• Despesa variável mudou este mês

it sounds more like a headline, note, label, or very telegraphic style, not standard everyday sentence structure.

Here, mudar is being used intransitively, meaning to change.

• A despesa variável mudou. = The variable expense changed.

But mudar can also be transitive, meaning to change something:

• A empresa mudou a política. = The company changed the policy.

So the verb can work both ways. In your sentence, there is no direct object, so it means the expense itself changed.

Yes, but the meaning or emphasis may shift.

The neutral order is:

• A despesa variável mudou este mês.

You could also say:

• Este mês, a despesa variável mudou.

That puts more focus on this month.

What is not natural in this context is moving the adjective before the noun:

• a variável despesa

That sounds unusual here and not like normal financial Portuguese.

Both can relate to expense/spending, but they are not always identical.

• despesa is very common in formal, financial, accounting, and administrative language
• gasto is often more general and can refer to spending or money spent

So in a phrase like despesa variável, Portuguese speakers would strongly expect despesa, especially in a budgeting or accounting context.

A common contrast is:

• despesa fixa = fixed expense
• despesa variável = variable expense

That sounds standard and natural in European Portuguese.