Adding Fractions With Common Denominators
Learning Outcomes
- Use a model to find the sum of two fractions with the same denominator
- Add fractions with a common denominator without a model
- Add fractions with a common denominator that contain a variable
Model Fraction Addition
How many quarters are pictured? One quarter plus quarters equals quarters.
Start with one piece. | ![]() |
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Add two more pieces. | ![]() |
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The result is . | ![]() |
example
Use a model to find the sum . Solution:Start with three pieces. | ![]() |
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Add two pieces. | ![]() |
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How many pieces are there? | ![]() |
try it
Use a model to find each sum. Show a diagram to illustrate your model.Answer:
Answer:
Add Fractions with a Common Denominator
The example above shows that to add the same-size pieces—meaning that the fractions have the same denominator—we just add the number of pieces.Fraction Addition
If are numbers where , then To add fractions with a common denominators, add the numerators and place the sum over the common denominator.Example
Find the sum:Answer: Solution:
Add the numerators and place the sum over the common denominator. | |
Simplify. |
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#146182 [ohm_question height="270"]146182[/ohm_question]Example
Find the sum:Answer: Solution:
Add the numerators and place the sum over the common denominator. |
Try It
#146183 [ohm_question height="270"]146183[/ohm_question]Example
Find the sum:Answer: Solution: We will begin by rewriting the first fraction with the negative sign in the numerator.
Rewrite the first fraction with the negative in the numerator. | |
Add the numerators and place the sum over the common denominator. | |
Simplify the numerator. | |
Rewrite with negative sign in front of the fraction. |
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#146185 [ohm_question height="270"]146185[/ohm_question]Example
Find the sum:Answer: Solution:
Add the numerators and place the sum over the common denominator. | |
Combine like terms. |
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#146186 [ohm_question height="270"]146186[/ohm_question]Example
Find the sum:Answer: Solution:
Add the numerators and place the sum over the common denominator. | |
Add. | |
Simplify the fraction. |