# Writing Algebraic Expressions from Word Problems

Algebraic expressions are a series of arithmetic operations consisting of the four operations, numbers, variables, parentheses and other mathematical symbols (square roots, powers, factors...).

These algebraic expressions are abstracted from physical concepts so that we can see their applications in all fields.

As we said earlier, algebraic expressions mainly consist of the four operations, numbers, variables, parentheses and various mathematical symbols that we will discuss as follows:

• Numbers: They are fixed values such as
• Operations Symbols: These are addition(+), subtraction(-), multiplication() and division()
• Variables: These are the unknowns that we usually express with letters such as
• Grouping Symbols: It contains other expressions such as
• Other Mathematical Symbols: such as square roots, exponents,

## Convert texts to algebraic expressions

Let's take some exemples:

#### Example1:

Sum of two unknown numbers.

#### Solution:

Let the first number be and the second number be .

So their sum is

#### Example2:

The sum of twice and

#### Solution:

Let the first number be , the twice of is .

So the sum is

#### Example3:

The difference of the number and the triple of the number .

#### Solution:

The variables are already defined and . the triple of is .

So the difference is

#### Example4:

The difference of the product of and , and the quotient of and

#### Solution:

The product of and is

The quotient of and is

So the difference is

#### Example5:

The product of two consecutive numbers.

#### Solution:

Let be the first number. then the second number is .

So, the product of this two numbers is

#### Example6:

The product of the sum of the numbers and and the sum of the numbers and twice of .

#### Solution:

The sum of and is

The sum of and the twice of is

The product is

#### Example7:

The sum of the square root of a number and the number next of it

#### Solution:

Let the unknown number. then the square root of is . The number next of is . The sum is