An Easy Way of Translating Words into Algebraic Expressions

Translating Words into Algebraic Expressions

As a math teacher, I frequently meet students who tend to have difficulties converting words into algebraic expressions. This may be a challenging exercise to most people, but it is an important concept in algebra. In this article, I will give you a clear procedure of translating words into algebraic expressions. I will also elaborate on some frequently used phrases in this process, provide illustrations and exercises along with tips to master it.

Understand the Language of Algebra.

The simplest way to convert words into algebraic formulas is understanding the language of algebra. Symbols and characters are used to represent numbers and variables in algebra.

An algebraic expression is a set of variables, constants and operations. Fixed numbers are constants, while unknowable values are variables. Operations include addition, subtraction, multiplication and division.

For example, $$2x + 3$$ is an algebraic expression. $$2$$  and  $$3$$  are constants, while  $$x$$  is a variable. The $$+$$ symbol represents addition. When we substitute a value for $$x$$ , we can evaluate the expression.

Algebraic expressions definition and examples: Translating Words into Algebraic Expressions

Once you understand these basic concepts, you can begin to translate words into algebraic expressions with ease.

Step #1: Identify the Variables and Constants.​

First, variables and constants must be located when words are transformed into algebraic expressions.

Variables are denoted by letters or symbols and can have different values. Constants, however, are values that never change.

Algebraic expressions  examples displaying coefficients, variables constant Translating Words into Algebraic Expressions

Identify keywords or word phrases in the problem which imply a variable or constant. Such as the variable x or a constant 5. After you have defined the variables and constants, you can start to form your algebraic expression.

Step #2: Determine the Operations and Order of Operations.​

After determining the variables and constants in a word problem, it is necessary to find out what operations are involved, as well as their order.
Look for terms that convey mathematical operations, including “add,” “subtract,” multiply” or divide.

The order of operations, starting with exponents followed by brackets, multiplication and division (left to right) alongside addition and subtraction from left to also be kept in mind. If needed, use brackets to further clarify the chain of events.

Translating Words into Algebraic Expressions :order of operations , PEDMAS rule

Step #3 Use Parentheses to Clarify Meaning.

Use brackets to define the expression when converting a word problem into an algebraic expression.

Translating Words into Algebraic Expressions: Use parenthesis to clarify the meaning

For example, if the problem states “Multiply $$3$$ by the sum of $$x$$ and $$y$$ ” the expression would be $$3(x+y)$$


Translating Words into Algebraic Expressions: the sum of sixteen and three times a number minus 4

Without the parentheses, the expression could be misinterpreted as $$3x+y$$ or $$3x+3y$$ . Always use parentheses to ensure the correct order of operations and to avoid confusion.

Example to translate words into algebraic expressions.

Let’s apply these steps to an example:

Five times a number increased by twelve.


Identify the variable(s)

a number” represents an unknown value. Let’s use $$x$$ to represent this value.


Identify the operations

Five times a number” represents multiplication, while “increased by twelve” represents addition.


Write the expression

$$5x + 12$$

Common Phrases Used in Translating Words into Algebraic Expressions

There are several common phrases used in translating words into algebraic expressions. Here are some examples:

More thanAddition
Less thanSubtraction
Product ofMultiplication
Quotient ofDivision
Increased byAddition
Decreased by 


Examples of Translating Words into Algebraic Expressions

Let’s look at some more examples:

The sum of twice a number and three$$2x + 3$$
Seven less than a number$$x – 7$$
The difference between a number and four$$x – 4$$
The product of three and a number$$3x$$
The quotient of a number and two$$\frac{x}{2}$$

Practice Problems for Translating Words into Algebraic Expressions

Now it’s time for you to practice! Try translating the following phrases into algebraic expressions:

  1. “The sum of a number and six.”
  2. “Ten less than twice a number.”
  3. “The product of five and a number, decreased by two.”
  4. “The quotient of a number and three, increased by four.”
  5. “The difference between eight and three times a number.”

Tips for Mastering

  1. Practice, practice, practice: The repetition will make it easier.
  2. Identify keywords: Search for such words as variables and operations.
  3. Break down the problem: The problem could be broken down one step at a time to determine the variable and operation for each step.
  4. Check your work: You should check if you have adequately translated the words into an algebraic expression.
  5. Use real-life examples: Applying this concept to real-life events makes it more applicable and familiar.

Practice understanding translating Words into Algebraic Expressions

Practice is the key to becoming proficient at converting words into algebraic expressions. Work your way up to increasingly difficult word problems by starting with the simpler ones.

Practice Problems: Translating Words into Algebraic Expressions

Use the internet or textbook resources to get practice problems, and don’t be afraid to ask for help if you need it. You’ll become more comfortable with the process and better able to tackle any word problems that you encounter with more practice.



Practice Problems: Translating Words into Algebraic Expressions

How to Translate Phrases into an Algebraic expressions?

Converting phrases into algebraic expressions requires an understanding of mathematical concepts and algebraic symbols. The following steps need to be taken:

1. Determine the variable: Identifying the variable or variables that the phrase or problem comprises should be your first step. The letters x, y, z, and so on are corresponding letters that represent variables.

2. Choose the operation: The next step requires you to choose the operation that will be applied to the variable. Common operations include division (/), multiplication (*), subtraction (-), and addition (+).

3. Write the expression: Now that the variable and operation have been determined, you may write the algebraic expression.

You can use the addition symbol (+) to denote “increased by 5” and the multiplication sign (*) to denote “twice a number increased by $$5$$” in the phrase “Twice a number increased by $$5$$.” In algebra, that would be $$2x + 5.$$.

Another example might be “the sum of $$3$$ times a number and $$7$$”. Here, “3 times” can be represented by the multiplication symbol (*), “sum” and “$$7$$” by the addition sign ($$+$$), and y can be used to indicate the variable. In algebraic notation, this would be $$3y + 7$$.

In conclusion, choosing the variable, the operation, and the right symbol placement while constructing the expression are the steps involved in turning words into algebraic expressions.

How to know which operation symbol to use?

In order to accurately transform a given collection of words into an algebraic equation comprising both numbers and variables, it’s vital to recognise and use key information, in the form of words and phrases. Here are some guidelines to help you choose the appropriate operation symbol when translating:

  • Look for keywords that indicate which operation symbol to use. For example, the word “sum” indicates addition, “difference” indicates subtraction, “product” indicates multiplication, and “quotient” indicates division.

  • Look for phrases that indicate which operation symbol to use. For example, the phrase “five times” indicates multiplication.

  • Look for parentheses that indicate the order of operations. For example, the phrase “the sum of $$3$$ and $$4$$ times $$5$$ ” should be translated as “ $$(3 + (4 \times 5))$$ ”.


Translating words into algebraic expressions is not complicated. Simply comprehends the essential terms, writes the operations, and transforms it into algebraic formulas.

Although it may seem difficult at first to translate words into algebraic expressions, anyone can become proficient in this skill with patience and practice. Don’t forget to define the variables and operations, deconstruct the issue, and double-check your work. With any luck, after reading this essay, you will be able to convert words into algebraic formulas with confidence.

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