1. 3
Chapter
Chapter 2
Fractions and Mixed Numbers

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

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

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

5. 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

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

7. Examples
Subtract and simplify. a. b.
Objective B

8. Examples
Add:
Objective B

9. Example
Subtract:

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

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

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

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

14. 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

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

16. 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

17. 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

18. 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

19. 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.

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

21. Example
Find the LCD of

22. Write Equivalent Fractions.
Objective E
Write Equivalent Fractions.

23. 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

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

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

26. Example
Write an equivalent fraction with the given denominator.