3 Chapter Chapter 2 Fractions and Mixed Numbers

Section 3.4 Adding and Subtracting Like Fractions, Least Common Denominator, and Equivalent Fractions

Add or Subtract Like Fractions. Objective A Add or Subtract Like Fractions.

Adding Like Fractions Fractions with the same denominator are called like fractions. Fractions that have different denominators are called unlike fractions. Objective A

Adding or Subtracting Like Fractions Adding or Subtracting Like Fractions (Fractions with the Same Denominator) If a, b, and c are numbers and b is not 0, then Objective A Continued

Examples Add and simplify. a. b. c. Objective B

Examples Subtract and simplify. a. b. Objective B

Examples Add: Objective B

Example Subtract:

Add or Subtract Given Fractional Replacement Values. Objective B Add or Subtract Given Fractional Replacement Values.

Example Evaluate x + y if x = –10/12 and y = 5/12. Objective B

Solve Problems by Adding or Subtracting Like Fractions. Objective C Solve Problems by Adding or Subtracting Like Fractions.

Solving Problems by Adding or Subtracting Like Fractions Find the perimeter of the following rectangle. Rectangle Perimeter Objective B

Example A recipe calls for 1/3 of a cup of brown sugar and 2/3 of a cup of white sugar. How much total sugar is in the recipe? Total sugar = brown sugar + white sugar The total amount of sugar needed in the recipe is 1 cup. Objective B

Find the Least Common Denominator of a List of Fractions. Objective D Find the Least Common Denominator of a List of Fractions.

Finding the Least Common Multiple Using Multiples Method 1: Find the LCM of a List of Numbers Using Multiples of the Largest Number Step 1: Write the multiples of the largest number (starting with the number itself) until a multiple common to all numbers in the list is found. Step 2: The multiple found in Step 1 is the LCM. Objective A

Example Find the LCM of 9 and 12. Write the multiples of 12 until we find a number that is also a multiple of 9. 12  1 = 12 Not a multiple of 9. 12  2 = 24 Not a multiple of 9. 12  3 = 36 A multiple of 9. The LCM of 9 and 12 is 36. Objective A Continued

Finding the Least Common Multiple Using Multiples Method 2: Find the LCM of a List of Numbers Using Prime Factorization Step 1: Write the prime factorization of each number. Step 2: For each different prime factor in step 1, circle the greatest number of times that factor occurs in any one factorization. Step 3: The LCM is the product of the circle factors. Objective A

Example Find the LCM of 72 and 60. Circle the greatest number of prime factors found in either factorization. Objective B The LCM is the product of the circle factors.

Example Find the LCM of 15, 18, and 54. Objective B

Example Find the LCD of

Write Equivalent Fractions. Objective E Write Equivalent Fractions.

Writing Equivalent Fractions To add or subtract unlike fractions, we first write equivalent fractions with the LCM as the denominator. To write an equivalent fraction, where a, b, and c are nonzero numbers. Objective A

Example Write an equivalent fraction with the indicated denominator. Objective B

Example Write an equivalent fraction with the indicated denominator. Objective B

Example Write an equivalent fraction with the given denominator.