Adding and Subtracting Fractions with like Denominators

1
Adding and Subtracting Fractions with like
Denominators

• You know that the bottom number of a fraction
  tells how may parts each whole is divided into.
• In this picture each circle is divided into 4
  parts so the bottom number for this fractions is
  4.
• 4
• We use or shade 5 parts so the top number of this
  fraction is 5. The picture shows the fraction
  5 .
• 4
• In a fraction the bottom number has a special
  name. The bottom number in a fraction is called
  the denominator. The denominator or the bottom
  number in a fraction tells how many parts each
  whole is divided into.

2
What are the denominators in these fractions?

• Two
• Six
• Eight
• Five
• Three
• Remember the bottom number in a fraction is
  called the denominator.

3
You have learned to add fractions using pictures.

• 1 4 5
• 3 3 3
• Fractions can be added and subtracted without
  using pictures.
• Heres a problem.
• 5 3
• 4 4
• When you add and subtract fractions you do not
  work on the top and the bottom the same way.

4

• When you add and subtract fractions you COPY the
  denominator, then you work on the top. Remember,
  you copy the denominator and then you work on the
  top.
• 5 3
• 4 4
• Look at this problem. What is the denominator?
• Yes, its 4.
• What do you do with the denominator?
• Right, you copy it in the answer so the
  denominator in the answer is 4.
• Now we can add the numbers on the top. What do we
  get when we add 5 3?
• Correct, 5 3 8.
• We put the 8 on top in the answer so 5 3
  8 .
• 4 4 4

4
5

• 7 2
• 5
• Heres a different problem. First look at the
  sign. We are subtracting in this problem.
• Next look at the denominators. What do we do with
  the denominator?
• Yes, we copy it in the answer.
• On the top the sign tells us to subtract. 7 2,
  whats the answer?
• Right, 7 2 5. We put the 5 on top.
• 5
• 5
• 7 2 5
• 5 5 5

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5
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6
Lets try another problem.

• 4 3
• 2
• First you copy the denominator then you work the
  top.
• What is the denominator?
• Yes, its 2.
• Now work on the top. What is 4 3?
• Right, its 1.
• So 4 3 1
• 2 2 2

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2
-

7
Heres a new problem.

• 2 3
• 4
• What do we do with the denominator?
• Yes, we copy the 4.
• 4
• What do we get on top?
• Good Job! 2 3 5.
• 2 3 5
• 4 4 4

8
Your Turn

• Copy these problems on your paper and write the
  answer.
• 1. 8 2
• 5 5
• 2. 5 2
• 3 3
• 3. 8 4
• 6 6
• 4. 10 3
• 4 4
• 5. 3 2
• 4 4

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Check your work
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9

• If the fraction you are working does not have the
  same denominator you cannot work the problem the
  way it is written.
• You cant work this problem the way it is written
  because the denominators are not the same.
• 6 1
• 4 3

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10
Some of these problems can be worked the way they
are written but some cannot. Look at the
denominators to decide, then write the numbers of
the problems that can be worked the way they are
written.

• 1. 7 2 4. 4 4
• 3 4 5 6
• 2. 8 2 5. 8 2
• 3 5 5 5
• 3. 6 1 6. 2 5
• 2 2 3 4

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11
Check your work. You can work problems 3 and 5
the way they are written. Remember, if you cant
copy the denominator of the fraction you are
adding or subtracting you cannot work the problem
the way it is written.

• 1. 7 2 4. 4 4
• 3 4 5 6
• 2. 8 2 5.
• 3 5
• 3. 6. 2 5
• 3 4

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8 5
2 5
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6 2
1 2




12
Look at these new problems. Write the numbers of
the problems that can be worked the way they are
written.

• 1. 6 5 4. 2 1
• 8 8 3 3
• 2. 7 2 5. 6 3
• 6 4 4 2
• 3. 1 4 6. 4 3
• 2 3 6 6

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13
Check your work. You can work problems 1, 4, and
6. Now on your paper work the problems that can
be worked the way they are written.

• 6 5
• 8 8
• 2 1
• 3 3
• 4 3
• 6 6

1. 6 5 1 8 8
8 4. 2 1 1 3 3
3 6. 4 3 7 6 6
6
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14
Lets try one more.

• 1
• 3
• What do you do in the denominator?
• Yes, you copy the denominator.
• 3
• What do you get on top?
• Thats right, 2. 112.
• 1 1 2
• 3 3

15

• New problem.
• 1 1
• 3 3
• Do we work in the denominator?
• No. What do we do in the denominator?
• Correct, we copy the denominator.
• 3
• Do we work on top?
• Yes.
• What do we get on top?
• Yes, 0.

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16
Think about the picture of this problem when you
work it.
1 1 3 3
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• You have 1 and you take away 1 . How many
  thirds do you have left?
• 3 3
• Thats Correct. You have 0 thirds left. You have
  no thirds or 0 .
• 3
• 1 1 0
• 3 3 3
• When you see a problem that is addition or
  subtraction first look at the denominators. If
  they are the same you can work the problem the
  way it is written. If the denominators are not
  the same you cannot work the problem the way it
  is written.

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17
You have learned to work problems this way.

• 3 1 4 or 7 5 2
• 4 4 4 8 8 8
• You can also work fraction addition and
  subtraction problems when they are written this
  way.
• 5 8
• 8 3
• 2 2
• 8 3
• 7 6
• 8 3
• Just like before check to see if you can work the
  problem the way it is written, copy the
  denominator, then add or subtract.

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18
Your Turn

• Copy each problem you can work the way it is
  written, then work the problem.
• 1. 2. 3. 4.
  5.
• 6 8 4 5 2
• 8 4 5 3 6
• 1 - 3 2 - 6
  - 1
• 8 4 6 3 2

19
Check your work. Problems 3 and 5 cannot be
worked the way they are written.Work problems 1,
2, and 4.

• 1. 2. 3. 4.
  5.
• 6 8 4 5 2
• 8 4 5 3 6
• 1 - 3 2 - 2
  - 1
• 8 4 6 3 2
• Remember which ever way the problem is written to
  check the denominators. If the denominators are
  the same copy the denominator in the answer and
  add or subtract the top.