Equations with Fractions on Both Sides

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Solving Equations with Fractions on Both Sides

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Equations with Fractions on Both Sides

  1. 1. Image Source: http://www.blogspot.com
  2. 2. Solve the Equation : n-3 = n+6 2 3 We cannot solve this Equation using “Onion Skins” or “Back-Tracking”, because our Equation has Fractions and the Variable letter “n” is on both sides of the Equation. WE NEED TO DO SOME EXTRA STEPS BEFORE WE CAN SOLVE THE EQUATION
  3. 3. Solve the Equation : n-3 = n+6 2 3 The Extra Steps are: 1. Cross Multiply using Brackets (to remove fractions) 2. Identify the smaller letter term (letters both sides step) 3. Apply the Opposite Operation ( + or - ) to this smaller item on both sides. 4. Simplify and Solve the Equation as normal.
  4. 4. Solve the Equation : 1a. Cross Multiply : 1b. Use Brackets : 1c. Expand Out : n-3 = n+6 2 3 n-3 = n+6 2 3 3 (n - 3) = 2 (n + 6) 3n - 9 = 2n + 12 Now solve as letter both sides (see next slide)
  5. 5. Finish off our previous question as a variable both sides type question (Eg.Apply Opposites) 3n - 9 - 2n n–9 +9 n = 2n + 12 - 2n = 12 +9 = 21
  6. 6. Solve the Equation : 8h + 7 = 3h - 4 2 1a. Cross Multiply : 8h + 7 = 3h -4 2 1b. Use Brackets : 1 (8h + 7) 1c. Expand Out : 8h + 7 1 = 2 (3h - 4) = 6h - 8 Now solve as letter both sides (see next slide)
  7. 7. Finish off our previous question as a variable both sides type question (Eg.Apply Opposites) 8h + 7 - 6h 2h + 7 -7 2h /2 h = 6h - 8 - 6h = -8 -7 = -15 /2 = -7.5 or -7 ½
  8. 8. http://passyworldofmathematics.com/ All Images and Diagrams are Copyright by Passy’s World of Mathematics

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