﻿ How to translate the statement of problems into algebraic language

# How to translate the statement of problems into algebraic language. Examples.

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: ## 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:
• The cube of a number:
• 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

### How to translate expressions related to operations with numbers into algebraic language

• 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
• Double the sum of two numbers: 2 (a+b)

### How to translate percentage-related expressions into algebraic language

• 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%)

### How to translate age-related expressions into algebraic language

• 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

### How to translate expressions related to geometry into algebraic language

• The area of a square side x:
• 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.