Adding and Subtracting Fractions and Mixed Numbers Agenda

Adding and Subtracting Fractions and Mixed Numbers

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

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.

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

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!

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

Let’s Go!

Adding and Subtracting Fractions 3 4 + 2 8 Answer is 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. Step 1:

Adding and Subtracting Fractions 3 x 2 4 x 2 + 2 x 1 8 x 1 Answer is 6 8 2 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.

Adding and Subtracting Fractions + 3 x 2 4 x 2 6 8 2 x 1 8 x 1 2 8 Answer is 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 eighths! Step 4: Check to see if it needs to be simplified or reduced.

ONLY COPY THE PROBLEM AND STEP 3 + 3 x 2 4 x 2 6 8 2 x 1 8 x 1 2 8 Answer is 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!

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

Let’s Go!

Let’s Practice! 2 - + 7 1 2

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

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

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

Let’s Practice! 2 X 2 --7 X 2 4 --14 1 x 7 + --2 x 7 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!

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

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

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