Adding Fractions with Unlike Denominators

 
 
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[
OBJECTIVE
]
 
The student will add fractions with unlike
denominators.
[
MY
 
SKILLS
]
 
Equivalent fractions
Adding fractions with like denominators
[
ESSENTIAL
 
QUESTIONS
]
 
1. 
How does it help our understanding of adding
fractions to build with concrete materials?
2. 
How does it help our understanding of adding
fractions to build with pictorial models?
3. 
How can we add fractions with unlike
denominators?
[
LESSON
]
 
Dino and Mark are doing a project for art
class. It is due on Tuesday. Dino begins by
drawing a      -inch line, and Mark draws a
-    - inch line. What is the total length of
the lines?
 
S
 
Study the Problem
Underline the question.
This problem is asking me to find
the sum of the lengths of the lines.
[Cooperative Pairs]
 
 
P
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A
 
 
P
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B
Add Fractions – Unlike Denominators
 
First Addend:
RED
 
Second Addend:
YELLOW
 
The
denominators
are different.
 
The strips are
different
colors.
Add Fractions – Unlike Denominators
 
Before the fractions can be added, they
must be all in one color.
 
Let’s legally trade the fractions for
fraction strips of all one color.
Add Fractions – Unlike Denominators
 
Legally trade
so that all the
strips are the
same color.
Add Fractions – Unlike Denominators
 
We push the
strips
together and
get the
answer:
Add Fractions – Unlike Denominators
 
What happened to the 
denominators
 when the
fractions were added?
 
The denominators were not alike, so one had to be
changed to make a fraction that was equivalent with a
common denominator.
Add Fractions – Unlike Denominators
What happened to the
 numerators 
when the
fractions were added?
 
The numerator of one fraction changed when the
denominator was changed. Once the two fractions
had a common denominator, the numerators were
added together to find the sum.
Add Fractions – Unlike Denominators
 
Can we legally trade the sum for fewer fraction
strips in another color?
 
No, the sum is in simplest form.
Add Fractions – Unlike Denominators
 
First Addend:
GREEN
 
Second Addend:
BROWN
 
The
denominators
are different.
 
The strips are
different
colors.
Add Fractions – Unlike Denominators
 
Before the fractions can be added, they
must be all in one color.
 
Let’s legally trade the fractions for
fraction strips of all one color.
Add Fractions – Unlike Denominators
 
Legally trade
Add Fractions – Unlike Denominators
 
Legally trade
 
 
 
Now all the
strips are the
same color.
Add Fractions – Unlike Denominators
 
We push the
strips
together and
get the
answer:
Add Fractions – Unlike Denominators
 
What happened to the 
denominators
 when the
fractions were added?
 
The denominators were not alike, and they both had
to be changed to make fractions that have a common
denominator.
Add Fractions – Unlike Denominators
What happened to the 
numerators
 when the
fractions were added?
 
The numerators both changed when the
denominators were changed. Once the two fractions
had a common denominator, the numerators were
added together to find the sum.
Add Fractions – Unlike Denominators
Can we legally trade the sum for fewer fraction
strips in another color?
 
No, the sum is in simplest form.
Add Fractions – Unlike Denominators
Add Fractions – Unlike Denominators
 
Addend
 
Addend
 
Sum
Add Fractions – Unlike Denominators
Add Fractions – Unlike Denominators
Can we legally trade the sum for fewer fraction
strips in another color?
 
No, the sum is in simplest form.
Add Fractions – Unlike Denominators
 
Take a look back at what happened when we did
our legal trade.
 
What happened mathematically?
The 3 in the denominator was multiplied by 3 and
the 1 in the numerator was also multiplied by 3.
Add Fractions – Unlike Denominators
 
Addend
 
Addend
 
Sum
Add Fractions – Unlike Denominators
 
List the multiples of both denominators
until you find a common one!
 
5: 5, 10, 15
2: 2, 4, 6, 8, 10, 12
Add Fractions – Unlike Denominators
 
What happened mathematically?
The 5 in the denominator was multiplied by 2 and
the 1 in the numerator was also multiplied by 2.
Add Fractions – Unlike Denominators
 
What happened mathematically?
The 2 in the denominator was multiplied by 5 and
the 1 in the numerator was also multiplied by 5.
Add Fractions – Unlike Denominators
Add Fractions – Unlike Denominators
Can we legally trade the sum for fewer fraction
strips in another color?
 
No, the sum is in simplest form.
Add Fractions – Unlike Denominators
Add Fractions – Unlike Denominators
List the multiples of both denominators
until you find a common one.
 
2: 2, 4, 6
6: 6, 12
Add Fractions – Unlike Denominators
Add Fractions – Unlike Denominators
 
What happened mathematically?
The 2 in the denominator was multiplied by 3 and
the 1 in the numerator was also multiplied by 3.
Add Fractions – Unlike Denominators
Add Fractions – Unlike Denominators
Can we legally trade the sum for fewer fraction
strips in another color?
 
No, the sum is in simplest form.
Add Fractions – Unlike Denominators
Add Fractions – Unlike Denominators
List the multiples of both denominators
until you find a common one.
 
4: 4, 8, 12, 16
6: 6, 12, 18
Add Fractions – Unlike Denominators
Add Fractions – Unlike Denominators
 
What happened mathematically?
The 4 in the denominator was multiplied by 3 and
the 2 in the numerator was also multiplied by 3.
Add Fractions – Unlike Denominators
Add Fractions – Unlike Denominators
 
What happened mathematically?
The 6 in the denominator was multiplied by 2 and
the 2 in the numerator was also multiplied by 2.
Add Fractions – Unlike Denominators
Add Fractions – Unlike Denominators
 
Can we legally trade the sum for fewer fraction
strips in another color?
 
Yes, let’s simplify.
Add Fractions – Unlike Denominators
Add Fractions – Unlike Denominators
 
List the multiples of both denominators
until you find a common one.
 
6: 6, 12, 18
3: 3, 6, 9, 12, 15, 18
Add Fractions – Unlike Denominators
 
•2
 
•2
Add Fractions – Unlike Denominators
 
Can we legally trade the sum for fewer fraction
strips in another color?
 
No, the answer is in the simplest form.
Add Fractions – Unlike Denominators
 
List the multiples of both denominators
until you find a common one.
 
5: 5, 10, 15, 20
2: 2, 4, 6, 8, 10, 12, 14, 16, 18
Add Fractions – Unlike Denominators
 
•2
 
•2
Add Fractions – Unlike Denominators
 
•5
 
•5
Add Fractions – Unlike Denominators
 
Can we legally trade the sum for fewer fraction
strips in another color?
 
No, the answer is in the simplest form.
Fractions Foldable
Fractions
Foldable
Fractions Foldable
 
Addition
Unlike
Denominators
Page 2
Dino and Mark are doing a project for art
class. It is due on Tuesday. Dino begins by
drawing a      -inch line, and Mark draws a
-    - inch line. What is the total length of
the lines?
S
 
Study the Problem
Underline the question.
This problem is asking me to find
t
he sum of the lengths of the lines.
SOLVE
 
Dino and Mark are doing a project for art
class. It is due on Tuesday. Dino begins by
drawing a      -inch line, and Mark draws a
-    - inch line. What is the total length of
the lines?
 
O 
Organize the Facts
Identify the facts.
Eliminate the unnecessary facts.
List the necessary facts.
Dino -       -inch line
Mark-        -inch line
 
L
 
Line Up a Plan
 
Choose an operation or operations.
 
Addition
 
Write in words what your plan of action will be.
 
Add the length of the line Mark draws to the
length of the line Dino draws. Change the
fractions to fractions with common
denominators by finding equivalent fractions for
each. Find the common multiple to determine
the common denominator, and then change
each fraction to an equivalent fraction using the
common denominator. Then add, and simplify if
needed.
 
V
 
Verify Your Plan with Action
Estimate your answer.
About 1 inch
Carry out your plan.
 
 
 
E
 
Examine Your Results
Does your answer make sense?
(compare your answer to question.)
Yes, because we are looking for the total
length of the lines.
Is your answer reasonable?
(compare your answer to the estimate.)
Yes, because it is close to our estimate of
about one inch.
 
Is your answer accurate?
(check your work.)
Yes.
Write your answer in a complete sentence.
The sum of the lengths of the lines drawn by
Dino and Mark is        inch.
[
ESSENTIAL
 
QUESTIONS
]
 
1.
How does it help our understanding of
adding fractions to build with concrete
materials?
 
(Using concrete materials helps us see
and touch the fractions we are adding.)
[
ESSENTIAL
 
QUESTIONS
]
 
 
2.
How does it help our understanding of
adding fractions to build with pictorial
models?
 
(Using pictorial models helps us see the
relationship between the fractions we are
adding.)
[
ESSENTIAL
 
QUESTIONS
]
 
3.
How can we add fractions with unlike
denominators?
 
(Represent both fractions, legally trade for
one color if necessary, push together and
simplify; fewest pieces of one color.)
 
Addends
Sum
Denominators
Numerators
Equivalent
Legal Trade
Simplest Form
 
 
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Explore a lesson on adding fractions with unlike denominators using visual models and concrete materials. Enhance your skills in equivalent fractions and learn to add fractions with different denominators through engaging activities. Work on practical problems and cooperative learning tasks to deepen your understanding of fractions.


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  1. Lesson 17 Add Fractions Unlike Denominators

  2. [OBJECTIVE] The student will add fractions with unlike denominators.

  3. [MYSKILLS] Equivalent fractions Adding fractions with like denominators

  4. [ESSENTIALQUESTIONS] 1. How does it help our understanding of adding fractions to build with concrete materials? 2. How does it help our understanding of adding fractions to build with pictorial models? 3. How can we add fractions with unlike denominators?

  5. [LESSON] Dino and Mark are doing a project for art class. It is due on Tuesday. Dino begins by drawing a -inch line, and Mark draws a - - inch line. What is the total length of the lines? 1 __ 2 1 __ 3 S Study the Problem Underline the question. This problem is asking me to find the sum of the lengths of the lines.

  6. [Cooperative Pairs] Partner A Partner B

  7. Add Fractions Unlike Denominators 3 8 + 1 4 The denominators are different. 1 1 ___ 1 ___ 1 ___ 8 1 ___ 4 The strips are different colors. 8 8 First Addend: RED Second Addend: YELLOW

  8. Add Fractions Unlike Denominators Before the fractions can be added, they must be all in one color. Let s legally trade the fractions for fraction strips of all one color.

  9. Add Fractions Unlike Denominators 3 8 + 1 4 Legally trade 1 4 for 2 8 1 so that all the strips are the same color. 1 ___ 1 ___ 1 ___ 8 1 ___ 4 8 8 1 ___ 1 ___ 8 8

  10. Add Fractions Unlike Denominators 3 8 + 5 8 1 4 = We push the strips together and get the answer: 5 8 1 1 ___ 1 ___ 1 1 ___ 1 ___ 8 ___ 8 8 8 8

  11. Add Fractions Unlike Denominators 3 8 + 3 8 + 1 4 2 8 5 8 = What happened to the denominators when the fractions were added? The denominators were not alike, so one had to be changed to make a fraction that was equivalent with a common denominator.

  12. Add Fractions Unlike Denominators 3 8 + 3 8 + 1 4 2 8 5 8 = What happened to the numerators when the fractions were added? The numerator of one fraction changed when the denominator was changed. Once the two fractions had a common denominator, the numerators were added together to find the sum.

  13. Add Fractions Unlike Denominators 3 8 + 5 8 1 4 = 1 1 ___ 1 ___ 1 1 ___ 1 ___ 8 ___ 8 8 8 8 Can we legally trade the sum for fewer fraction strips in another color? No, the sum is in simplest form.

  14. Add Fractions Unlike Denominators 1 3 + 1 2 The denominators are different. 1 1 ___ 3 1 ___ 2 The strips are different colors. First Addend: GREEN Second Addend: BROWN

  15. Add Fractions Unlike Denominators Before the fractions can be added, they must be all in one color. Let s legally trade the fractions for fraction strips of all one color.

  16. Add Fractions Unlike Denominators 1 3 + 1 2 Legally trade 1 3 for 2 6 1 1 ___ 3 1 ___ 2 1 1 ___ 6 ___ 6

  17. Add Fractions Unlike Denominators 1 3 + 1 2 Legally trade 1 2 for 3 6 1 1 ___ 3 1 ___ 2 Now all the strips are the same color. 1 1 1 1 1 ___ 6 ___ 6 ___ 6 ___ 6 ___ 6

  18. Add Fractions Unlike Denominators 1 3 + 5 6 1 2 = We push the strips together and get the answer: 5 6 1 1 1 1 1 1 ___ 6 ___ 6 ___ 6 ___ 6 ___ 6

  19. Add Fractions Unlike Denominators 1 3 + 2 6 + 1 2 3 6 5 6 = What happened to the denominators when the fractions were added? The denominators were not alike, and they both had to be changed to make fractions that have a common denominator.

  20. Add Fractions Unlike Denominators 1 3 + 2 6 + 1 2 3 6 5 6 = What happened to the numerators when the fractions were added? The numerators both changed when the denominators were changed. Once the two fractions had a common denominator, the numerators were added together to find the sum.

  21. Add Fractions Unlike Denominators 1 3 + 5 6 1 2 = 1 1 1 1 1 1 ___ 6 ___ 6 ___ 6 ___ 6 ___ 6 Can we legally trade the sum for fewer fraction strips in another color? No, the sum is in simplest form.

  22. Add Fractions Unlike Denominators 1 3 + 4 9 1 1 1 1 1 ___ 9 ___ 9 ___ 9 ___ 9 1 ___ 3

  23. Add Fractions Unlike Denominators 1 3 + Addend 4 9 Addend Sum

  24. Add Fractions Unlike Denominators 1 3 + 1 3 3 9 9 + 4 9 4 9 3 7 9 = =

  25. Add Fractions Unlike Denominators 1 3 + 4 9 7 9 = Can we legally trade the sum for fewer fraction strips in another color? No, the sum is in simplest form.

  26. Add Fractions Unlike Denominators Take a look back at what happened when we did our legal trade. 1 3 = 3 9 What happened mathematically? The 3 in the denominator was multiplied by 3 and the 1 in the numerator was also multiplied by 3. 1 3 3 3 3 9 =

  27. Add Fractions Unlike Denominators 1 5 + Addend 1 2 Addend Sum

  28. Add Fractions Unlike Denominators 1 5 + 1 2 List the multiples of both denominators until you find a common one! 5: 5, 10, 15 2: 2, 4, 6, 8, 10, 12

  29. Add Fractions Unlike Denominators 1 5 2 = 10 What happened mathematically? The 5 in the denominator was multiplied by 2 and the 1 in the numerator was also multiplied by 2. 1 2 5 2 2 = 10

  30. Add Fractions Unlike Denominators 1 2 5 = 10 What happened mathematically? The 2 in the denominator was multiplied by 5 and the 1 in the numerator was also multiplied by 5. 1 5 2 5 5 = 10

  31. Add Fractions Unlike Denominators 1 5 + 2 10 10 1 2 5 7 + = 10

  32. Add Fractions Unlike Denominators 1 5 + 2 10 10 1 2 5 7 + = 10 Can we legally trade the sum for fewer fraction strips in another color? No, the sum is in simplest form.

  33. Add Fractions Unlike Denominators 1 2 + 2 6

  34. Add Fractions Unlike Denominators 1 2 + 2 6 List the multiples of both denominators until you find a common one. 2: 2, 4, 6 6: 6, 12

  35. Add Fractions Unlike Denominators 1 2 3 6 =

  36. Add Fractions Unlike Denominators 1 2 3 6 = What happened mathematically? The 2 in the denominator was multiplied by 3 and the 1 in the numerator was also multiplied by 3. 1 3 2 3 3 6 =

  37. Add Fractions Unlike Denominators 1 2 + 3 6 + 2 6 2 6 5 6 =

  38. Add Fractions Unlike Denominators 1 2 + 3 6 + 2 6 2 6 5 6 = Can we legally trade the sum for fewer fraction strips in another color? No, the sum is in simplest form.

  39. Add Fractions Unlike Denominators 2 4 + 2 6

  40. Add Fractions Unlike Denominators 2 4 + 2 6 List the multiples of both denominators until you find a common one. 4: 4, 8, 12, 16 6: 6, 12, 18

  41. Add Fractions Unlike Denominators 2 4 6 = 12

  42. Add Fractions Unlike Denominators 2 4 6 = 12 What happened mathematically? The 4 in the denominator was multiplied by 3 and the 2 in the numerator was also multiplied by 3. 2 3 4 3 6 = 12

  43. Add Fractions Unlike Denominators 2 6 4 = 12

  44. Add Fractions Unlike Denominators 2 6 4 = 12 What happened mathematically? The 6 in the denominator was multiplied by 2 and the 2 in the numerator was also multiplied by 2. 2 2 6 2 4 = 12

  45. Add Fractions Unlike Denominators 2 4 + 6 12 12 2 6 4 10 12 + =

  46. Add Fractions Unlike Denominators 2 4 + 6 12 12 2 6 4 10 12 + = Can we legally trade the sum for fewer fraction strips in another color? Yes, let s simplify.

  47. Add Fractions Unlike Denominators 2 4 + 6 12 12 2 6 4 10 12 5 6 + = =

  48. Add Fractions Unlike Denominators 1 6 + 2 3 List the multiples of both denominators until you find a common one. 6: 6, 12, 18 3: 3, 6, 9, 12, 15, 18

  49. Add Fractions Unlike Denominators 4 6 2 3 2 = 2

  50. Add Fractions Unlike Denominators 1 6 + 1 4 6 6 + Can we legally trade the sum for fewer fraction strips in another color? No, the answer is in the simplest form. 2 3 5 6 =

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