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Division of Fractions

Division of fractions involves the following steps:

  • express any mixed numerals as improper fractions
  • change the divide sign to multiplication sign
  • take the reciprocal of the fraction after the division sign (i.e. flip the fraction upside down)
  • now it becomes a case of multiplication of fractions, and you have to follow steps to multiply fractions

Examples of division of fractions:

  1. 2 ÷ 1/6=  {2/1}~*~{6/1}  (we are taking the reciprocal of the fraction after the division sign, and changing the division sign to a multiplication sign)

    =  12

  2. 13/4 ÷ 1/2First change the mixed numerals into improper fractions. So

    13/4 ÷ 1/2  =  7/4 ÷ 1/2

    =  7/4 x 2/1 (take reciprocal and change to multiply sign)

    =  14/4

    =  7/2

 

When we divide a number with a fraction, the number of divided parts increase, therefore when we divide the fraction, the answer becomes larger.

  1. For example, take 2 ÷ 1/2. Here we have 2 full blocks, and divide each block into two, thus making 4 parts.2 ÷ 1/2  =  2 x 2  =  4
  2. Similarly 2 ÷ 1/3  =  2 x 3  =  6
  3. What about 1/2 ÷ 1/2?Here we need to ask ourselves the question “what should be the original block if when cut will give half”

    So 1/2 ÷ 1/21/22/1  =  1

  4.  1/3 ÷ 1/2Here we have to ask “what should be the original block to get 1/3 when cut in half”

    1/3 ÷ 1/21/3 x 2/1  =  2/3

  5.  2/3 ÷ 4/5=  2/3 x 5/4

    =  10/12

    =  5/6