Math Help: Basic Pre-Algebra

The word 'algebra' can sound intimidating, but you've probably been doing math problems that qualify as algebra for years without even knowing it. Read on to learn the vocabulary used in pre-algebra, then try out a couple of sample problems to test your knowledge.

Find available tutors

Pre-Algebra Terms Defined

A mathematical phrase that does not include an equal sign. Examples: 3 X 5, 6+8, 5x + 7
A mathematical sentence with an equal sign. Examples: 3 X 5 = 15, 6 + 8 = 14, 5x + 7 = 27
An unknown number in an algebraic expression or equation. It's usually represented by an x, but it can be any letter.
A number that's multiplied by a variable in an algebraic equation or expression. The coefficient will almost always come just before the variable. For example, in the expression 5x + 7, the number 5 is the coefficient because it's next to the variable, x.
A number in an equation or expression that doesn't change. In the expression 5x +7, the number 7 is the constant because it isn't attached to any variable.
Positive and negative whole numbers, including zero. These numbers can be written without a decimal or fraction. Examples: -1, 500, -1987
Negative numbers
Any number that's less than zero. A negative number will always be expressed with a - sign in front of it. You can express any negative number as 0 -x. For example: -7 is really just 0 - 7.
Order of operations
Also known as the precedence rule, the order of operations determines which actions will be performed in which order in an algebraic expression or equation. It's important to have an established order of operations for complex expressions and equations, otherwise you may not always get the same answer. For example: 6 X 3 + 2 could equal either 20 or 30 depending on whether you start with the multiplication of 6 X 3 or the addition of 3 + 2.
The order of operations states that first you solve anything that's inside parentheses. It also states that multiplication and division will always be performed before addition and subtraction, so the correct answer to 6 X 3 + 2 would be 20. Because parentheses come first, 6 X (3+2) would equal 30, but (6 X 3) +2 would still equal 20.

Sample Problems

Using your knowledge of basic pre-algebra terms, try solving the following example problems:

  1. Write 'six times x plus four' as an algebraic expression.
  2. Write 'twelve times x minus 3 equals nine' as an algebraic equation.
  3. Identify the variable, coefficient and constant in the following equation: 3x + 1 = 13
  4. Solve this expression with the order of operations: 14/2 + 3 X 5 - 8
  5. Use the order of operations to solve this expression: 6 + 4 X 9 -8/2
  6. Write 'nine times x equals 5 times x plus 8' as an algebraic equation.
  7. What's another way to express the integer -18?
Did you find this useful? If so, please let others know!

Other Articles You May Be Interested In

  • More Blog Articles
    Not Your Father's Algebra As 45 States Look to Math Reform

    One plus one will always equal two...but just how students are taught math is going to change. Nearly every state in the country has adopted the Common Core Standards; for math, this means new and more in-depth approaches to teaching the subject. Have we seen the last of traditional algebra and geometry classes?

  • More Blog Articles
    Elementary Math: Learning the Order of Operations

    Before you can advance to more complex levels of math (like algebra) you have to master the order of operations. Read on to learn the simple steps involved in completing ordered operations math problems. This article provides tips for working your way through math problems with several steps.

We Found 7 Tutors You Might Be Interested In

Huntington Learning

  • What Huntington Learning offers:
  • Online and in-center tutoring
  • One on one tutoring
  • Every Huntington tutor is certified and trained extensively on the most effective teaching methods
In-Center and Online


  • What K12 offers:
  • Online tutoring
  • Has a strong and effective partnership with public and private schools
  • AdvancED-accredited corporation meeting the highest standards of educational management
Online Only

Kaplan Kids

  • What Kaplan Kids offers:
  • Online tutoring
  • Customized learning plans
  • Real-Time Progress Reports track your child's progress
Online Only


  • What Kumon offers:
  • In-center tutoring
  • Individualized programs for your child
  • Helps your child develop the skills and study habits needed to improve their academic performance
In-Center and Online

Sylvan Learning

  • What Sylvan Learning offers:
  • Online and in-center tutoring
  • Sylvan tutors are certified teachers who provide personalized instruction
  • Regular assessment and progress reports
In-Home, In-Center and Online

Tutor Doctor

  • What Tutor Doctor offers:
  • In-Home tutoring
  • One on one attention by the tutor
  • Develops personlized programs by working with your child's existing homework
In-Home Only


  • What TutorVista offers:
  • Online tutoring
  • Student works one-on-one with a professional tutor
  • Using the virtual whiteboard workspace to share problems, solutions and explanations
Online Only

Our Commitment to You

  • Free Help from Teachers

  • Free Learning Materials

  • Helping Disadvantaged Youth