How to Solve an Equation With Different Denominators

Addition and Subtraction

• 1

  Multiply the denominators by each other to create a common denominator.

  Example: 4/5 + 2/3; 3 x 5 = 15. The common denominator is 15.

• 2

  Multiply the first numerator by the second denominator.

  Example: 4/5 + 2/3; 4 x 3 = 12.

• 3

  Multiply the second numerator by the first denominator.

  Example: 4/5 + 2/3; 2 x 5 = 10.

• 4

  Write the new equation.

  Example of new equation: 4/5 + 2/3 = 12/15 + 10/15.

• 5

  Add or subtract the numerators.

  Addition example: 12/15 + 10/15 = 22/15.

  Subtraction example: 12/15 - 10/15 = 2/15.

Multiplication

• 6

  Multiply the numerators.

  Example: 2/3 x 4/5; 4 x 2 = 8

• 7

  Multiply the denominators.

  Example: 3 x 5 = 15

• 8

  Write the solution.

  Example: 8/15

Division

• 9

  Invert the second fraction by flipping the numerator and denominator.

  Example: 4/5 ÷ 2/3; 2/3 changes to 3/2.

• 10

  Multiply the numerators.

  Example: 4 x 3 = 12.

• 11

  Multiply the denominators.

  Example: 5 x 2 = 10

• 12

  Write the solution.

  Example: 12/10; in lowest terms 12/10 is 6/5 or 1 1/5.