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Online Algebra Tutoring: Variable Expressions

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Learn Variable Expressions from Certified Online Algebra Tutor

variable is a symbol or an alphabetical letter used to represent an unknown number in an expression or an equation. The value of this number can vary. A variable expression is a math expression that consists of variables, numbers and operations (like add,subtract, multiply, and divide)

To translate verbal phrases into variable expressions. Look for key words that indicate additionsubtractionmultiplicationdivision.

Key Words:

Addition: plus, the sum of, increased by, total, more than, added to.
Subtraction: minus, the difference of, decreased by, fewer than, less than, subtracted from.
Multiplication: times, the product of, multiplied by, of.
Division: divided by, the quotient of.

Let’s understand with an example

The product of  two and a number increased by nineteen.

The product of two and a number increased by nineteen. (LOOK FOR KEYWORDS)

Product of indicates multiplication
Increased by indicates addition

To write variable expression, assign a variable to represent the unknown number. You can take any alphabetical letter of your choice!

The product of two and a number increased by nineteen.


Check Point

Directions: Choose the algebraic expression that correctly represents the phrase provided. Select your answer.


  1. Twenty less than twice a number
  1. 20 – 2x
  2. 2x+20
  3. 2x – 20
  4. None of the above
  1. Three times a number increased by sixteen
  1. 3(a + 16)
  2. 3a + 16
  3. (16 + 3)a
  4. None of the above.
  1. The product of eight and a number decreased by five.
  1. 8(m – 5)
  2. 5(8 – m)
  3. 8m – 5
  4. None of the above
  1.  Sixty divided by nine times a number
  1. 60 + 9n
  2. 9n/60
  3. 60/9n
  4. None of the above
  1. Sarah earns $10 a day working part time at a supermarket. Write a variable expression to represent the amount of money she will earn in p days.
  1. 10p
  2. 10/p
  3. 10 + p
  4. None of the above
Answer Key
  1. 2x -20
  2. 3a +16
  3. 8m-5
  4. 60/9n
  5. 10p

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