Concept of fraction

Fraction is a number in the form of a/b.
Here ‘a’ is called numerator, ‘b’ is called denominator.

For example: ½, ¾. 

Types of fraction:

1. Proper fraction: In proper fraction numerator is less than denominator i.e.
   numerator < denominator
   For Example: 2/5, 5/8…
2. Improper fraction:In improper fraction numerator is greater than denominator i.e.
   For Example: 5/2, 8/5…
3. Mixed fraction:It is a combination of whole number and proper fraction.
   For example: 2½, 3½….

Comparison of fractions

1. Find the largest from the following:11/13, 9/11
   Trick: do cross multiplication11×11 > 13×9
   Clearly 11/13 is greater than 9/11.
2. When difference between numerator and denominator is same
1. If fraction is proper:In this case, the fraction having bigger numerator is greater.
   For example: 15/18, 7/10, 11/14, 8/11
   15/18 > 11/14 > 8/11 > 7/10
2. If fraction is improper:In this case, the fraction having smaller numerator is smaller.
   For example: 11/8, 8/5, 31/28, 17/14
   8/5 > 11/8 > 17/14 > 31/28

Addition of mixed fraction

Example: 6 ²/₃ + 3 ¹/₃ + 5 ¹/₆
                = (6 + 3 +5) + (2/3 + 1/3 + 1/6) = 15 ¹/₆

Exercise:

1. Find the value of 6 ²/₃ - 5 ¹/₆ - 4 ²/₃
2. Find the value of 999 ¹/₇ + 999 ²/₇ + 999 ³/₇ + 999 ⁴/₇ + 999 ⁵/₇ + 999 ⁶/₇.

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