Mathematics » Introducing Fractions » Solve Equations with Fractions

Key Concepts

Key Concepts

  • Determine whether a number is a solution to an equation.
    1. Substitute the number for the variable in the equation.
    2. Simplify the expressions on both sides of the equation.
    3. Determine whether the resulting equation is true. If it is true, the number is a solution. If it is not true, the number is not a solution.
  • Addition, Subtraction, and Division Properties of Equality
    • For any numbers a, b, and c,
       

      if \(a=b\), then \(a+c=b+c\). Addition Property of Equality

    • if \(a=b\), then \(a-c=b-c\). Subtraction Property of Equality
    • if \(a=b\), then \(\frac{a}{c}=\frac{b}{c}\), \(c\ne 0\). Division Property of Equality
  • The Multiplication Property of Equality
    • For any numbers \(ab\) and \(c,a=b\), then \(ac=bc\).
    • If you multiply both sides of an equation by the same quantity, you still have equality.

 

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