SUBTRACTING FRACTIONS


In this page, we will learn subtracting fractions having

    • Same denominators
    • Different denominators
    • Mixed numbers


    Type 1: Subtracting fractions with same denominators

    For subtracting fractions having same denominators, subtract numerators and just write the common denominator in the final difference.

    Example:

    Subtract 2/5 from 3/5 Or Find 3/5 – 2/5

    Solution:

    Since denominator 5, is same in both 2/5 and 3/5, therefore:

    In the final answer, i.e the difference of the two fractions, write 5 in denominator and 3 – 2 = 1 in numerator.

    So, 3/5 – 2/5 = (3 – 2)/5

    Note:

    To subtract 3/5 from 2/5, i.e. to find 2/5 – 3/5

    Follow the same steps

    So, 2/5 – 3/5 = (2 – 3)/5 = -1/5

    Type 2: Subtracting fractions having different denominators

    For subtracting fractions having different denominators, follow the below steps

    Step 1: Find LCM of the various denominators in the fractions.

    Step 2: Write equivalent fractions of the original fractions with LCM in denominator. (to make denominators same)

    Step 3: Add the equivalent fractions.

    Example:

    Subtract 3/4 from 5/6

    Solution:

    Step 1:

    First, what is the LCM of the denominators 4 and 6?

    4 = 2 × 2, and 6 = 2 × 3

    So, LCM of 4 and 6 = 2 × 2 × 3 = 12

    Step 2:

    Now, write equivalent fractions for 3/4 and 5/6 having LCM 12 as the common denominator.

    Equivalent fraction for 3/4

    Now, 4 × ? = 12, it is

    12 ÷ 4 = 3

    So, multiply 3 to 1 and 4 in ¼ to get 12 in denominator.

    3/4 = (3 × 3)/ (3 × 4) = 9/12

    Equivalent fraction for 5/6

    6 × ? = 12, it’s

    12 ÷ 6 = 2

    So, multiply 2 to both 5 and 6 in 5/6 to get 12 in denominator

    5/6 = (5 × 2)/ (6 × 2) = 10/12

    Step 3:

    Finally,

    To find the difference: 10/12 – 9/12  

    Subtract the equivalent fraction 9/12 from 10/12

    10/12 – 9/12 = 1/12

    Therefore,

    (5/6) – (3/4) = 1/12

    Short-cut for subtracting fractions having different denominators

    To find (a/b) – (c/d)

    First, find (a × d – b × c)/(b × d)

    Next, reduce the fraction so obtained into simplest term.

    Example:

    Find (5/6) – (3/4)

    • First, (5/6) – (3/4)

    = (5 × 4 – 3 × 6)/6 × 4

    = (20 – 18)/24

    = 2/24

    2. Next, reduce 2/24, by cancelling the common factor 2, as below:

    2/24 = (2 × 1)/ (2 × 12) = 1/12

    Type 3: Subtracting fractions which are mixed numbers

    Subtract mixed numbers in two different methods. They are:

    1st method:

    • First, subtract the whole numbers and the fractions separately.
    • Next, add the differences of the whole numbers and the fractions obtained in the first step

    2nd method:

    • First, convert the mixed fractions into improper fractions
    • Next, subtract the two improper fractions.

    Example:

    Find the difference: 32/3 – 23/4


    Below, let us apply both of the above methods for subtracting fractions.

    Method 1:

    Step 1:

    Subtract the whole numbers: 3 – 2 = 1, and

    Subtract the fractions: 2/3 – 3/4

    Now, lcm of 3 and 4 is 3 × 4 = 12

    {If two numbers do not have any common factor, then their LCM is their product}

    2/3 = (2 × 4)/ (3 × 4) = 8/12, and

    3/4 = (3 × 3)/ (4 × 3) = 9/12

    So, 2/3 – 3/4 = (8/12) – (9/12) = -1/12

    Step 2:

    Next, add the fractions’ difference and the whole numbers’ difference

    1 + (-1/12) = 1 – 1/12 = (12/12) – (1/12) = 11/12

    Method 2 is

    Subtracting fractions by converting them into improper fractions.

    The mixed fraction 32/3 = (3 × 3 + 2)/3 = 11/3, and

    The mixed fraction 23/4 = (4 × 2 + 3)/4 = 11/4.

    Step 2:

    Next, subtract the above two improper fractions, for subtracting fractions

    32/3 and 23/4

    i.e. 32/3 – 23/4 = (11/3) – (11/4)

    = (11× 4)/(3 × 4) – (11 × 3)/(4 × 3)

    {converting into equivalent fractions}

    = (44/12) – (33/12) = 11/12

    32/3 – 23/4

    Or, using the above short-cut for subtracting fractions, we have

    (11/3) – (11/4)

    = (11× 4 – 11× 3)/ ( 3 × 4) =

    = (44 – 33)/12 = 11/12

     

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