adding and subtracting fractions with unlike denominators

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adding and subtracting fractions with unlike denominators

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    0
    2021-09-09T01:54:31+00:00

    You must first find a common denominator.
    Change the fractions to the common denominator.
    Then you add or subtract the fractions.
    Finally, you may need to reduce the fraction.

    Example 1:

    Add

    1/5 + 1/3

    The least common denominator is 15.

    Both denominators must become 15.

    1/5 + 1/3 = 3/3 * 1/5 + 5/5 * 1/3 = 3/15 + 5/15 = 8/15

    Example 2:

    Subtract
    3/8 – 1/3

    The least common denominator is 24.

    3/3 * 3/8 – 8/8 * 1/3 = 9/24 – 8/24 = 1/24

    Both in addition and subtraction, you only add or subtract the numerators. The denominator of the answer is the common denominator.

    0
    2021-09-09T01:55:00+00:00

    To add or subtract different fractions you need to make both fractions have an L.C.D = lowest common denominator. You can find the LCD by multiplying the denominators of the fractions together. Once you have the LCD you can multiply each fraction by a ratio of one (example = 3/3 ratio = 1 ) to make the denominators equivalent. 

    Example problem: 
    2/3 + 4/5 = ?
    The L.C.D is equal to 15 (from multiplying the denominators 3 and 5 together).
    Now you can make the first fraction (2/3) have a denominator of 15 by multiplying it by a ratio of 1 (5/5).  For the second denominator (4/5) multiply it by a ratio of 1 as well (3/3). Now the fractions will be (2/3)(5/5) + (4/5)(3/3) =  10/15 + 12/15 

    Because the fractions have the same denominator now you can now add them together and then simplify the fraction to its simplest form. 
    10/15 + 12/15 = 22/15 (This fraction cannot be reduced further, it is the final answer)

     

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