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Strategy for Adding or Subtracting Fractions
When adding or subtracting any two fractions — whether they already share a denominator or not — follow a three-step procedure:
- Determine whether the fractions share a common denominator.
- If yes, proceed directly to Step 2.
- If no, find the least common denominator (LCD) of the fractions. Rewrite each fraction as an equivalent fraction whose denominator equals the LCD by multiplying both its numerator and denominator by the appropriate factor.
- Add or subtract the numerators and place the result over the common denominator, using the rule or .
- Simplify the resulting fraction, if possible, by dividing out any common factors shared by the numerator and denominator.
An important reminder: an LCD is required only for addition and subtraction. Multiplication and division of fractions do not need a common denominator.
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