Adding & Subtracting Fractions - Part 1

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  • 1. *
  • 2. * Remember from the previous section, that in order to add or subtract fractions, they need to be the same size pieces of the whole * This section will demonstrate how to add/subtract fractions that don’t have a common denominator (or aren’t same size pieces) *
  • 3. * So + =
  • 4. * So + =
  • 5. * So - =
  • 6. * So + = or
  • 7. *Notice that we need the WHOLE to be separated into the same number of same area pieces. *This allows us to have a common denominator *We then use the equivalent fraction that has that same denominator (remember talking about equivalent fractions earlier?) *So instead of drawing a picture each time, we can just use equivalent fractions to cut the whole into the same number of pieces  COMMON DENOMINATOR
  • 8. * *The Least Common Denominator(LCD) is the smallest number that both denominators will divide into *The smallest number that you can cut both rectangles into so that the pieces are all the same size *We will be using the Least Common Multiple (LCM) of the given denominators to determine the LCD *There are a couple of ways to determine the LCM, but I’m only going to show one way here (google/youtube it if you want to know the other way)
  • 9. * 1. 2. list the multiples of each number 3. That number is the LCM Locate the smallest number that is a multiple of both numbers Example: Determine the LCM of 6 & 9 Multiples of 6: 6, 12, 18, 24, 30, 36, … Multiples of 9: 9, 18, 27, 36, 45, … The LCM of 6 & 9 is 18
  • 10. * Example: Determine the LCM of 3 & 7 Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, … Multiples of 7: 7, 14, 21, 28, 35, … The LCM of 3 & 7 is 21 Example: Determine the LCM of 12 & 15 Multiples of 12: 12, 24, 36, 48, 60, 72, 84, … Multiples of 15: 15, 30, 45, 60, 75, 90, … The LCM of 12 & 15 is 60
  • 11. *Now let’s get some practice determining the LCM by playing a quick game, then we’ll continue with adding & subtracting fractions with uncommon denominators!