Least Common Denominator LCD and Simplifying Fractions

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Least Common Denominator(LCD) and Simplifying
Fractions

• Created by
• Brooke Thomas
• brothoma_at_nmu.edu

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What is the LCD?

• The LCD (Least Common Denominator) is the Least
  Common Multiple of two or more denominators.
• The LCD is what must be found when adding or
  subtracting fractions with different
  denominators.

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Finding the LCD

• Find the LCD for the denominators by first
  multiplying the denominators together to have a
  new common denominator.
• Then divide the product of the denominators by
  the GCF (Greatest Common Factor).
• The GCF is found by finding the greatest number
  that can be divided evenly by both denominators.
• Finally divide the new common denominator by the
  GCF to get the LCD.

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Example7/12 2/8

• Multiply the two denominators together .
• 12 8 96
• Rename the fraction with the new common
  denominators.
• 7/96 2/96
• Find the GCF or Greatest Common Factor of the
  denominators, which is 4. This is found by
  figuring out what is the same greatest number
  that is divisible by 12, and 8. The number 2 is
  divisible, but 4 works too and it is greater than
  2.
• Divide the new common denominator by the GCF to
  find the LCD.
• 96 / 4 24

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Solving the Problem 7/12 2/8

• Since the LCD is known, we can now work out the
  rest of the problem to solve.
• Divide the new common denominator of 96 by the
  original denominators.
• 96 / 12 8 and 96 / 8 12
• Multiply the numerators by their quotients.
• 7 8 56 and 2 12 24
• Rename the fractions
• 56/96 and 24/96
• Solve the problem
• 56/96 24/96
• 32/96

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Simplifying Fractions

• Simplifying fractions is a way to reduce the
  fraction while keeping the same value.
• Recall the answer from the example problem,
  32/96. This fraction has a numerator and a
  denominator that are both composite numbers.
• Composite numbers are numbers that have more than
  one factor and itself, and therefore can be
  reduced to a simpler form.

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How to Simplify 32/96

• Find the GCF of 32 and 96.
• 16 can go into 32 and 96.
• Divide the numerator and the denominator by the
  GCF.
• 32 / 16 2 and 96 / 16 6
• Rename the fraction
• 2/6
• The value of 32/96 and 2/6 are the same. Both
  fractions are .333 when the numerator is divided
  by the denominator.

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Resources

• Least Common Denominator
• http//www.aaamath.com/fra66j-lcd.html
• Simplifying Fractions
• http//www.aaamath.com/fra66h-simpfrac.html