Section 1.7: Adding and Subtracting Fractions
Essential Ideas

• Procedure for Adding Or Subtracting Fractions With Common Denominators
  To add or subtract fractions with common denominators, add or subtract the numerators. The denominator of the sum or difference is the same as the common denominator.

• Procedure for Finding the Lowest Common Denominator (LCD)
  Step 1. Factor all given denominators into prime factors; write this factorization using exponents.
  Step 2. List each different prime factor you found in the prime factorization of the denominators.
  Step 3. On each prime in the list from Step 2, place the largest exponent that appears on that prime factor anywhere in the factorization of the denominators.
  Step 4. The LCD is the product of the prime factors with the exponents found in Step 3.

  Extended Order-of-Operations Agreement
  Step 1. First, perform any operations enclosed in parentheses.
  Step 2. Next, perform any operations that involve raising to a power.
  Step 3. Perform multiplication and division, reading from left to right.
  Step 4. Do addition and subtraction, reading from left to right.

• PROCEDURE FOR ADDING OR SUBTRACTING FRACTIONS THAT DO NOT HAVE COMMON DENOMINATORS
  Step 1. Find the LCD.
  Step 2. Change the forms of the fractions to obtain forms with common denominators.
  Step 3. Add or subtract the numerators of the fractions with common denominators.