From everyday language to algebraic expression

Why translate words in maths?

A maths problem is often described using sentences. To solve it, you first need to transform these sentences into algebraic expressions – that is, calculations involving letters and numbers. It’s like translating from one language to another: the meaning doesn’t change, only the form does.

Vocabulary to know

Certain words come up often and always correspond to the same operation.

French expression	Algebraic translation
the sum of x and 5	x + 5
twice x	2 * x
three times a number	3 * x
half of x	x / 2
a number minus 7	x - 7
the square of a number	x²
3 more than twice x	2 × x + 3

Guided example

Problem: “A number increased by 4 equals 15.”

Let x be the unknown number. “Increases by 4” means +4. “Equals 15” means that the result is equal to 15. We therefore get:

x + 4 = 15

Common pitfall to avoid

Pay attention to the word order! “7 decreases by x” is not written as x – 7 but as 7 – x, because it is 7 that is decreasing. Similarly, “half of x plus 3” is written as x/2 + 3, whereas “half of x plus 3” in the sense of “half of (x plus 3)” would be written as (x + 3)/2. Brackets make all the difference: always read the question very carefully before writing out your calculation.