In the statements of algebraic problems you find **expressions in the usual language or common language**, in which one or more quantities are unknown and you need to **translate them into algebraic language,** in order to solve the problem. The unknown amounts are the unknown amounts, are the **unknowns**.

The algebraic expressions allow translating from common language to algebraic language and write the corresponding equation to solve it and calculate the unknown required.

An **algebraic expression** is a combination of unknowns with numbers, related by mathematical operations. These are first-degree expressions, second-degree expressions, with one or more unknowns, etc.

Examples of algebraic expressions may be:

Índice de Contenidos

- 1 Translation of common language algebraic expressions into algebraic language
- 1.1 How to translate numerical or quantitative expressions into algebraic language
- 1.2 How to translate expressions related to operations with numbers into algebraic language
- 1.3 How to translate percentage-related expressions into algebraic language
- 1.4 How to translate age-related expressions into algebraic language
- 1.5 How to translate expressions related to geometry into algebraic language

## Translation of common language algebraic expressions into algebraic language

We will translate into algebraic language the expressions that appear most frequently in math problems.

### How to translate numerical or quantitative expressions into algebraic language

- Any number:
**x** - Twice as many numbers:
**2x** - Twice the first by the second:
**2ab**(used in special products formulas) - Triple of a number:
**3x** - Half a number:
**x/2** - A number divided by 3:
**x/3** - Part five of a number:
**x/5**

- An increased number by 1 or a plus number by 1:
**x+1** - A number decreased by 20:
**x-20** - 15 less than half a number:
**x/2-15** - An even number:
**2x** - An odd number:
**2x+1**or**2x-1** - Two consecutive numbers:
**x, x+1** - Two consecutive even numbers:
**2x, 2x+2** - Two consecutive odd numbers:
**2x+1,2x+3** - The square of a number:
**x²** - The cube of a number:
**x³** - The excess of one number over another:
**x-y** - The excess of a number over 150:
**x-150** - The excess of 200 over a number:
**200-x**

- The sum of a number plus its half:
**x+x/2** - The sum of two consecutive numbers:
**x+ (x+1)** - The sum of two consecutive even numbers:
**2x+ (2x+2)**

- One-quarter of a number less one-fifth of what remains:
**x/4 – (3x/4)/5**- Quarter of a number:
**x/4** - What’s left:
**x-x/4=3x/4**

- Quarter of a number:
- Double the sum of two numbers:
**2 (a+b)**

- 23% of a number:
**0.23x** - Reduced number 25%:
**0,75x** - Number increased by 30%:
**1,30x** - The 7% increase of a number:
**1.07x (careful! 1.7 would be an increase of 70%)**

- The age of a person:
**x** - The age of a person 4 years ago:
**x-4** - The age of a person within 5 years:
**x+5** - Double the age:
**2x** - 6 years older than triple his age:
**3x+6**

- The area of a square side x:
**x²** - The perimeter of a square side x:
**4x** - The area of a rectangle of base x and height x+2:
**x (x+2)** - The perimeter of a rectangle of base x and height x+2:
**2x + 2 (x+2)**

With all these expressions, you can already translate many problems from common language to algebraic language and you can only begin to solve them.