Common Core Math Vocabulary

Expression - Definition with Examples

What is an expression?

In math, an expression is defined as a mathematical phrase that comprises numbers with at least one arithmetic operation. 
A mathematical expression is a representation of a value.
Arithmetic operations include addition, subtraction, multiplication and division. The symbols that show the operations, “+”, “−”, “×”, “÷” are called operators. 
Examples of arithmetic expressions are 15 + 6, 58 − 19, 41 × 10 and 84 ÷ 7.
What is an algebraic expression?
An algebraic expression is  defined as an expression that comprises variables and/or constants that appear alone or in combination with operators.

An algebraic expression can be represented as: 

Parts of an algebraic expression

The parts of an algebraic expression can be described as:

  • Variable - A variable is represented by an alphabet such as x, y or z, in an algebraic expression.The value of the variable varies basis the coefficients and constants in the expression.
  • Constant - A constant can be a whole number, a decimal number or any fraction that has no variable attached to it. It stands alone in an algebraic expression.
  • Coefficient - A coefficient of any variable is a number attached to a variable. If the variable exists without a coefficient,  then its coefficient is 1.
  • Terms - Terms are the values on which the mathematical operations take place in an expression. A term can be a constant or a variable or both in an expression.
  • Examples of algebraic expressions are 3a + 8, 9x − 6y, 7pq², fraction .

   Fun Facts

  • An expression does not contain equal to sign or any inequalities signs.
  • When we add inequality or equality sign to an expression, it becomes an equation.
  • Both sides of an equation are an expression.

When changing verbal phrases and sentences into expressions, look for words that indicate operations and assign a meaningful variable to represent what is to be calculated. 

 Verbal phrase/sentence  Algebraic Expression
 Five added to four times of a number  5 + 4x
 Two times a number reduced by 9  2y − 9
 Twice a number subtracted from 8  8  − 2z
 Sum of 8 and a number divided by 4  (8 + t) / 4

let's sing Let's sing!

Expression’s all about terms on a mission,
constants, variables and an operation!
Here’s an algebraic expression, 2x + 9,
2x and 9 are the TERMS that combine.
Coefficient 2, variable ‘x’,  and a “+” sign.
9 is the constant to be added, next in line.

let's do it Let's do it!

Children can develop an understanding of how we form expressions mentally to compute everyday calculations.
Take your child out for grocery shopping and have them pick out multiple quantities of the same items like 2 boxes of cereal or 4 packets of cookies. Ask them to form expression by assigning meaningful variables to calculate the total price of all the items.

You can ask your child to follow a recipe and form expressions for computing the increased or decreased quantity of ingredients required as per the number of people. 

Expressions Real life activity

related math vocabulary  Related math vocabulary


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