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Proper fraction:
1. A fraction in which the absolute value of numerator (top number) is smaller than the absolute value of denominator (bottom number).
2. It is represented as, \(p / q\); \(q ≠ 0\) and \(|p|< |q|\), where \(p\) is the numerator, \(q\) is the denominator.
3. Proper fractions are greater than \(0\) but lesser than \(1\).
A negative proper fraction will have a negative sign either in numerator or denominator.
It can be represented as, or ; where \(q ≠ 0\) and \(|p| < |q|\).
Example:
; where \(p = -9\), \(q = 16 ≠ 0\) and \(|-9| < |16|\)
2. Positive proper fraction:
A positive proper fraction will have a positive sign in both numerator and denominator.
It can be represented as, ; where \(q ≠ 0\) and \(|p| < |q|\).
Example:
; \(p = 4\), \(q = 5 ≠ 0\) and \(|4| < |5|\)
Improper fractions:
1. Fractions where the numerator (the top number) is greater than or equal to the denominator (the bottom number).
2. It is represented as, ; \(q ≠ 0\) and \(|p| ≥ |q|\); where \(p\) is the numerator, \(q\) is the denominator.
3. Improper fractions will be always \(1\) or greater than \(1\).
Example:
1. Positive improper fraction:
A positive improper fraction will have a positive sign in both numerator and denominator and the value of a positive improper fraction will always be equal or greater than \(1\).
It can be represented as, ; where \(q ≠ 0\) and \(|p| ≥ |q|\)
Example:
2. Negative improper fraction:
A negative improper fraction will have a negative sign in either numerator or denominator and the value of a negative improper fraction will always be equal or greater than \(-1\).
It can be represented as, or ; where \(q ≠ 0\) and \(|p| ≥ |q|\).
Example:
Important!
All the mixed fractions () and integers (\(-1\), \(3\), \(7\)) are improper fractions.