1. Adding and Subtracting Fractions and Mixed Numbers

2. Agenda Finding the Least Common Multiple Adding Fractions with Unlike Denominators Adding Mixed Numbers Short Quiz on Quia

3. LCM? When we add or subtract fractions, the denominator has to be the same, so the size of the parts we are adding or taking away is the same. To get the denominators to be the same, we have to find their lowest common multiple and use that as the denominator.

4. Let’s Practice Finding the Least Common Multiple! LCM = Least Common Multiple. What are the multiples of 4? 4, 8, 12, 16, 20, 24, 28, 32… What are the multiples of 3? 3, 6, 9, 12, 15, 18, 21, 24… The LCM of 4 and 3 is 12

5. LCM? So… if I were adding or subtracting two fractions, and their denominators were 4 and 3, I would have to get both of their denominators to be 12 (the LCM) before I continued!

6. Find the LCM Let’s do a few together! What is the LCM of 9 and 7? 9, 18, 27, 36, 45, 54, 63… 7, 14, 21,28, 35, 42, 49, 56, 63… LCM of 9 and 7 is 63 What is the LCM of 6 and 8? 6, 8, LCM of 6 and 8 is

7. Let’s Go!

8. Adding and Subtracting Fractions 3 4 2 + 8 Step 1: Find the LCM of the denominators. The denominators are 4 and 8. 4, 8, 12, 16, 20, 24, 28… 8, 16, 24, 32, 40, 48… The LCM is 8. You need to make 8 your new denominator. Answer is

9. Adding and Subtracting Fractions 3 x 2 6 4 x 2 8 2 x 1 2 + 8 x 1 8 Step 2: Determine what times the old denominator gives you the new denominator. For example, What times 4 gives you 8? What times 8 gives you 8? Multiply the top and bottom by the same numbers. Answer is

10. Adding and Subtracting Fractions 3 x 2 6 4 x 2 8 2 x 1 2 + 8 x1 8 8 Step 3: Add or subtract the new fractions with the same denominators. Remember – only add or subtract the numerators (top numbers)! We are adding how many eighths we have! 6+2 = 8. We have eight eighths! Step 4 : Check to see if it needs to be simplified or reduced. Answer is

11. ONLY COPY THE PROBLEM AND STEP 3 3 x 2 6 4 x 2 8 2 x 1 2 + 8 x1 8 8 Step 1: Find the LCM of the denominators. Step 2: Multiply both the top and bottom by the same number so the denominator becomes the LCM. Step 3: Add or subtract the new fractions with the same denominators. If there are whole numbers, add or subtract those next. Step 4 : Check to see if it needs to be simplified or reduced. 8/8 = 1! Answer is

12. Remember Remember to check to see if your answer needs to be simplified or reduced. For example, if your answer was 3 9 Step 1: In order to simplify or reduce, find the GCF (Greatest Common Factor) of 3 and 9. Factors of 3 are 1 and 3 Factors of 9 are 1, 3, and 9 GCF =3 Step 2: Divide the top and bottom by GCF 3 ÷ 3= 1 9 ÷3 = 3

13. Let’s Go!

14. Let’s Practice! 2 1 - + - 7 2

15. Let’s Practice! 2 1 - + - 7 2 What do we do first? Find the…

16. Let’s Practice! 2 1 - + - 7 2 LCD of 7 and 2? 14! Let’s get both denominators to be 14! How do we do that?

17. Let’s Practice! 2 X 2 1 x 7 --- + --- 7 X 2 2 x 7 4 7 ---+---14 LCD of 7 and 2? 14! Let’s get both denominators to be 14! Now what do we add?

18. Let’s Practice! 2 X 2 1 x 7 --- + --- 7 X 2 2 x 7 4 7 ---+---14 LCD of 7 and 2? 14! Let’s get both denominators to be 14! Now what do we add? 4+7=11 Answer= 11/14!

19. ✔ For Understanding Go to your handout and complete the adding and subtracting fractions 1-4. You will have 10 minutes.

20. Did you get the right answer? Don’t forget to simplify the fraction.

21. Quia You will have 15 minutes to show us what you know. Log onto Quia and take the quiz titled Fractions_March 4_2011.