How to interpret mathematical problems

Did you know that Portuguese is directly linked to solving mathematical problems? Exactly! If you cannot interpret the wording of a question, it is difficult to convert the problem information to mathematical language.

Thinking about it, the Just Math has prepared some tips to help you interpret certain information that is common in the wording of quizzes, college entrance exams, or even that simple homework assignment.

What's the number… ?

You may have already seen the above question. When it appears, it means we need to find the value of a number, so let's just call it x. So already write:

x =?

By the way, whenever questions arise that involve interrogative pronouns (such as "what" and "how much"), we need to find the x of the question.

And when do prepositions appear?

Watch out for prepositions like "de", "da" and "do" as they often indicate a multiplication operation.

For example, if a problem asks of x, we have the expression:

which is equivalent to .

See another case:

Lucas is 21 years old. How much gives your age?
(see that we use multiplication)

Follow one more example:

How much ?

Another preposition that appears a lot in mathematical problems is the "by", which usually indicates a division operation. Note that this preposition is also "hidden" within the% ("per percent "). See examples:

2 by 3 =

How much is 1/5 of 10% of 500 worth?

Double, triple, half…

You can also find the words below, which are translated as follows in math.

Double a number? 2x

The triple of a no? 3x

The quadruple of a no? 4x

Half a no?

The third part of a no?

The fourth part of a paragraph?

And so on.


In the statement of the question, verbs like "is", "have" and "equals" mean equality. Follow the statements below and their translations into mathematical language.

Carlos and João has together 50 years.
C + J = 50

Rodrigo has 10 years longer than Marcelo.
R = M + 10

In 5 years, Luiz's age it will be half Peter's age.

Note that, when it comes to forming the equation, when we add five years at Luiz's age, we must also add 5 years at Pedro's age, as time passes in the same way for both.

Double a number increased by 6 equals to the fifth part of this number decreased by 7.

Notice now these two questions, which appear to be the same but have a difference:

What is half five plus five?
What is the half of: five plus five?

The sentence break caused by the colon (:) indicates that we must first calculate the expression that comes after this sign (5 + 5), then find its half. Already in the first sentence, where there are no pauses, reading from left to right, we calculate first half of 5, then add the other 5. In short, the two expressions would be:

Which half of five plus five?

Which half of: five plus five?

Sum, difference, product and quotient

These terms indicate, respectively, the result of the addition, subtraction, multiplication and division operations. Therefore:

Sum of x and y means: x + y

Difference between a and b means: a-b

Product of x and y means: x.y or xy

Quotient between a and b means:

Here are some examples of expressions:

The quadruple of the sum of a and b:
4. (a + b)

The eighth part of the difference of x and y:

Predecessor and consecutive

Other terms are very common in mathematical questions:

The predecessor of a number means x-1
The consecutive number means x + 1

Notice how important it is to analyze the wording of the question well. These expressions of yours are totally different:

Triple of a number consecutive
The consecutive triple of a number

The first one represents the mathematical expression 3 (x + 1), while the second one represents the 3x + 1 expression.

If the statement has the expression "two consecutive numbers", you can represent them as:
x and x + 1

Similarly, if it's three consecutive numbers, we would have:
x, x + 1 and x + 2

Opposite and inverse

Lastly, you may also find the following terms:

Opposite of a number means -x
Inverse of a number means

For example:

The opposite of the inverse of a number is 5.

Did you like this article? Wait, soon we will have more tips on other subjects!