Title: Adding and Subtracting Fractions and Mixed Numbers
1Adding and Subtracting Fractions and Mixed Numbers
2Agenda
- Finding the Least Common Multiple
- Adding Fractions with Unlike Denominators
- Adding Mixed Numbers
- Short Quiz on Quia
3LCM?
- 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.
4Lets 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
5LCM?
- 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!
6Find the LCM Lets 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 8Adding and Subtracting Fractions
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
9Adding and Subtracting Fractions
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.
- 3 x 2 6
- 4 x 2 8
- 2 x 1 2
- 8 x 1 8
-
-
Answer is
10Adding and Subtracting Fractions
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! 62 8. We have
eight eighths! Step 4 Check to see if it needs
to be simplified or reduced.
- 3 x 2 6
- 4 x 2 8
- 2 x 1 2
- 8 x1 8
- 8
- 8
Answer is
11ONLY COPY THE PROBLEM AND STEP 3
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!
- 3 x 2 6
- 4 x 2 8
- 2 x 1 2
- 8 x1 8
- 8
- 8
Answer is
12Remember
- 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 14Lets Practice!
15Lets Practice!
What do we do first? Find the
16Lets Practice!
LCD of 7 and 2? 14! Lets get both denominators
to be 14! How do we do that?
17Lets Practice!
- 2 X 2 1 x 7
- --- ---
- 7 X 2 2 x 7
- 4 7
- --- ---
- 14 14
- LCD of 7 and 2? 14!
- Lets get both denominators to be 14!
- Now what do we add?
18Lets Practice!
- 2 X 2 1 x 7
- --- ---
- 7 X 2 2 x 7
- 4 7
- --- ---
- 14 14
- LCD of 7 and 2? 14!
- Lets get both denominators to be 14!
- Now what do we add?
- 4711
- Answer 11/14!
19?For Understanding
- Go to your handout and complete the adding and
subtracting fractions 1-4. You will have 10
minutes.
20Did you get the right answer? Dont forget to
simplify the fraction.
21Quia
- You will have 15 minutes to show us what you
know. Log onto Quia and take the quiz titled
Fractions_March 4_2011.