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

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

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

Adding and Subtracting Fractions

3 x 2 6 4 x 2 8

2 x 1 2+ 8 x1 8

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

ONLY COPY THE PROBLEM AND STEP 3

3 x 2 6 4 x 2 8

2 x 1 2+ 8 x1 8

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

RememberRemember to check to see if your answer needs to be

simplified or reduced. For example, if your answer was 3 9Step 1: In order to simplify or reduce, find the GCF

(Greatest Common Factor) of 3 and 9. Factors of 3 are 1 and 3Factors of 9 are 1, 3, and 9 GCF =3Step 2: Divide the top and bottom by GCF 3 ÷ 3= 1 9 ÷3 = 3

Let’s Go!

Let’s Practice!2 1- + -7 2

Let’s Practice!2 1- + -7 2

What do we do first?Find the…

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?

Let’s Practice!2 X 2 1 x

7--- + ---7 X 2 2 x 7

4 7--- + ---14 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 1 x

7--- + ---7 X 2 2 x 7

4 7--- + ---14 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.