Interpret Expressions

These lessons, with videos, examples, and step-by-step solutions, help High School students learn to interpret expressions that represent a quantity in terms of its context.

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Common Core (Algebra)
Common Core for Mathematics

A. Interpret parts of an expression, such as terms, factors, and coefficients.

B. Interpret complicated expressions by viewing one or more of their parts as a single entity.  For example, interpret P(1+r)n as the product of P and a factor not depending on P.

Suggested Learning Targets

  • Identify the different parts of the expression, such as terms, factors, and coefficients, bases, exponents, and constant.

  • Explain the meaning of the part in relationship to the entire expression and to the context of the problem.

  • Decompose expressions and make sense of the multiple factors and terms by explaining the meaning of the individual parts.

  • Understand that the product of two binomials is the sum of monomial terms. For example the product of (3x + 2) and (x - 5) is the sum of 3x2 ,-13x, and -10.

Common Core: HSA-SSE.A.1

Parts of an Expression
Terms, Coefficients, Like Terms, Constants.

Parts of an Expression
An expression is a number sentence without an equal sign.
Each part of an expression is called a term.
The variable is the symbol that we use.
The coefficient is the number with the variable.
The constant is the number without the variable.

Interpret parts of an expression
Algebra: Learning the terminology that goes with algebra topics like polynomials and expressions.
Any algebraic expression can have the following parts: Numbers, Variables, Operations.
Parts that are combined using multiplication and/or division are called a Term. Terms are separated by addition or subtraction.
Expressions can be identified by their number of terms:
Monomial has one term.
Binomial has two terms.
Trinomial has three terms.

Expressions can also be identified by the highest exponent of any one term (called the Degree).
Degree 0 - Constant
Degree 1 - Linear
Degree 2 - Quadratic
Degree 3 - Cubic

Standard Form of an expression: When we write the terms of an expression starting with the term with the highest degree and work down to the constant term.
Leading Coefficient: The leading coefficient is the number multiplied by the variable with the highest exponent.

For the following expression, tell how many terms it has, write it in standard form, and identify the leading coefficient and constant.

Translate Word Phrases and Sentences Into Algebraic Expressions
How to translate words into algebraic expressions and how to translate algebraic expressions into words.

Translate Word Phrases and Sentences Into Inequalities and Vice Versa
Interpret expressions that represent a quantity in terms of its context.


  1. Write the following algebraic inequality as a written sentence:
    2x - 3 < 7
  2. Write “the sum of 3 and a number is less than or equal to -5” as an algebraic inequality.
  3. Write “the sum of twice a number and 15 is greater than or equal to 25” as an algebraic inequality.
  4. Write the following algebraic inequality as a written expression:
    6x + 1 < 30
  5. Kelly received 5 new MP3 songs as a gift. She plans to buy 3 new songs each week. When Kelly has more than 20 songs, she will need to buy a memory card. Write an algebraic inequality that represents how many weeks Kelly can continue to put new songs on her player without a memory card.
  6. Every month a company has expenses of $150,000 plus monthly salaries of $3,000 per employee(x). Write an inequality that shows how much the company will have to earn to make a profit. Let y equal revenue.

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.
Mathway Calculator Widget

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