Expressions and equations

• Expressions


  Math phrases, part of a full math sentence, no equal sign, variable can change values
• Equations


  Full math sentence, have an equal sign, variable has a defined or set answer
• Expressions


  • a
  • b
• If x equals 5

  Answer is 12
• If x equals 13

  Answer is 20
• Multiplication


  When a number is right next to a variable
• If d equals 20

  Answer is 60
• Equations


  • c
  • d
• Solving equation c


  1. Isolate variable N

  2. Subtract 9 from both sides
• N can only equal 2
• Solving equation d


  1. Isolate variable R

  2. Multiply both sides by 3
• R can only equal 15
• Variable


  A symbol used to represent an unknown value
• Variables


  • Usually represented by a letter
  • Their value can change or be defined depending on the context or situation
• Expression


  A math phrase with no equal sign, where the variable can change values
• Equation


  A full math sentence with an equal sign, where variables have a defined or set answer
• Expressions


  • x + 7
  • 3d
• Equations


  • x = 11
  • 3d = 39
• Expressions


  Part of a math sentence
• Equations


  Full math sentence
• In expressions, the variable can change values
• In equations, the variable has a defined or set answer
• Equations have an equal sign, expressions do not
• Combining like terms


  Rewriting an algebraic expression by combining terms that have the same variables and exponents
• Steps to simplify an algebraic expression by combining like terms

  1. Identify any like terms

  2. Rewrite the expression with like terms next to each other

  3. Combine the coefficients of the like terms
• Combining like terms examples

  • 9x + 3x = 12x
  • 8g + 5g = 13g
  • 6y^2 + 2y^2 = 8y^2
  • 7x - 4x = 3x
  • 9c + 8c = 17c
  • -10a + 9a + 9a = 8a
• Distributive property


  A mathematical property that allows an expression to be rewritten by distributing a number or variable to the terms inside parentheses or brackets
• Steps to use the distributive property

  1. Identify the expression to be distributed

  2. Multiply each term inside the parentheses/brackets by the expression outside

  3. Simplify the resulting expression
• Simplifying expressions using combining like terms and the distributive property

  1. Identify any like terms and combine them

  2. Identify any expressions that can be distributed

  3. Apply the distributive property

  4. Combine any resulting like terms
• Like terms


  Terms that have the same variable(s) raised to the same power
• Identifying like terms


  1. Check if terms have the same variable(s) raised to the same power

  2. If so, they are like terms
• Combining like terms


  1. Add the coefficients of the like terms

  2. Keep the common variable(s) and exponent
• Rewriting expression with only addition separating terms
• When writing expressions
• Distributive property


  Allows removing parentheses by distributing the term outside the parentheses to the terms inside
• Using distributive property


  Distribute the term outside the parentheses to each term inside the parentheses
• Distributive property does not change the value of the expression
• When subtracting a negative, it's the same as adding the positive
• Simplifying algebraic expressions


  1. Distribute to remove parentheses

  2. Combine like terms
• Simplifying algebraic expressions involves using the distributive property and combining like terms