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Adding and Subtracting Fractions and Mixed Numbers

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Adding and Subtracting Fractions and Mixed Numbers Agenda Finding the Least Common Multiple Adding Fractions with Unlike Denominators Adding Mixed Numbers Short Quiz ... – PowerPoint PPT presentation

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Title: Adding and Subtracting Fractions and Mixed Numbers


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
Lets 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 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
  • Lets 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
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
10
Adding 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
11
ONLY 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
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
  • Lets Go!

14
Lets Practice!
  • 2 1
  • - -
  • 7 2

15
Lets Practice!
  • 2 1
  • - -
  • 7 2

What do we do first? Find the
16
Lets Practice!
  • 2 1
  • - -
  • 7 2

LCD of 7 and 2? 14! Lets get both denominators
to be 14! How do we do that?
17
Lets 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?

18
Lets 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.

20
Did you get the right answer? Dont 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.
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