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

For instance, if you have $\dfrac{3}{4}$ of a pizza and your friend wants $\dfrac{2}{4}$ of a pizza, you can subtract those to see what you have left.  Both of you are dealing with pizza that is cut into 4 equal parts, so you can take your 3 pieces, give him 2 pieces, and see what you have left.


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



Students often ask why not subtract the denominators? The answer is: because the denominator names the item you have.  The numerator tells you how many you have. When you say this problem: "Three fourth minus two fourths," you can see why you can just subtract the numerators.  You have two groups of the same item, so you can subtract them by subtracting the number, not the name of the item.  

6 dogs - 3 dogs = 3 dogs

4 apple - 2 apples = 2 apples

3 fourth - 2 fourths = 1 fourth

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

$\dfrac{6}{9} - \dfrac{2}{9} = \dfrac{4}{9}$

Whenever you have fractions with the same denominator, just subtract them by subtracting the numerators!

Practice Problems:

  • Fraction Subtraction (Like Denominators)

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

    1.  $\dfrac{3}{5}$ -  $\dfrac{2}{5}$=

    2.  $\dfrac{20}{40}$ -  $\dfrac{16}{40}$=

    3.  $\dfrac{15}{18}$ -  $\dfrac{8}{18}$=

    4.  $\dfrac{9}{16}$ -  $\dfrac{5}{16}$= 

    5.  $\dfrac{21}{25}$ -  $\dfrac{18}{25}$=

    6.  $\dfrac{9}{20}$ -  $\dfrac{8}{20}$=

    7.  $\dfrac{7}{9}$ -  $\dfrac{2}{9}$=

    8.  $\dfrac{43}{50}$ -  $\dfrac{9}{50}$=

    9.  $\dfrac{13}{15}$ -  $\dfrac{6}{15}$=

    10. $\dfrac{7}{9}$ -  $\dfrac{2}{9}$=

    11.  $\dfrac{8}{10}$ -  $\dfrac{5}{10}$=

    12.  $\dfrac{15}{20}$ -  $\dfrac{11}{20}$=