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Add Fractions (like denominators)

Fractions show the number of pieces a whole is cut into (the denominator) and the number of those pieces that you have (numerator).  So, if you have $\dfrac{1}{4}$ of a pizza, you know that the pizza is cut into 4 equal pieces and you have one of them. 

Because fractions are numbers, you can add, subtract, multiply, and divide them. 

In order to add fractions, you need to make sure that you are adding pieces of the same size.  So, you can add fractions with the same denominator because that means the wholes are cut into the same number of pieces (to learn how to add fractions with different denominators, see lesson Add Fractions (unlike denominators)).

For instance, if you have $\dfrac{1}{4}$ of a pizza and your friend has $\dfrac{2}{4}$ of a pizza, you can add those together.  Both of you are dealing with pizza that is cut into 4 equal parts, so you can push them together to see how much of a whole pizza you have.


Bottom line: if you are working with fractions of the same denominator, you have items that are the same, so just add the numerators and keep the denomiator the same.



Students often ask why not add the denominators together? The anwer is: because the denominator names the item you have.  The numerator tells you how many you have. When you say this problem: "One fourth plus two fourths," you can see why you can just add the numerators together.  You have two groups of the same item, so you can add them together.  

1 dog + 2 dogs = 3 dogs

1 apple + 2 apples = 2 apples

1 fourth + 2 fourths = 3 fourths

$\dfrac{1}{4} + \dfrac{2}{4} = \dfrac{3}{4}$

$\dfrac{2}{9} + \dfrac{5}{9} = \dfrac{7}{9}$

Whenever you have fractions with the same denominator, just add them by adding the numerator!

Practice Problems:

  • Fraction Addition (Like Denominators)

    Find the sum. Simplify all answers completely. Change improper fractions to mixed numbers. 


    1. $\dfrac{1}{2}$ + $\dfrac{1}{2}$= 

    2. $\dfrac{10}{15}$ + $\dfrac{3}{15}$= 

    3. $\dfrac{9}{10}$ + $\dfrac{2}{10}$= 

    4. $\dfrac{1}{12}$ + $\dfrac{10}{12}$=

    5. $\dfrac{4}{11}$ + $\dfrac{6}{11}$=

    6. $\dfrac{2}{8}$ + $\dfrac{7}{8}$= 

    7. $\dfrac{2}{12}$ + $\dfrac{9}{12}$= 

    8. $\dfrac{2}{3}$ + $\dfrac{2}{3}$= 

    9. $\dfrac{3}{12}$ + $\dfrac{10}{12}$= 

    10. $\dfrac{1}{5}$ + $\dfrac{3}{5}$= 

    11. $\dfrac{4}{8}$ + $\dfrac{5}{8}$= 

    12. $\dfrac{1}{11}$ + $\dfrac{5}{11}$=