Proper and Improper fraction — lesson. Mathematics CBSE, Class 6.

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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 \(1\).

1. Negative proper fraction:

A negative proper fraction will have a negative sign either in numerator or denominator.

It can be represented as,

\frac{- p}{q}

\frac{p}{- q}

; where \(q ≠ 0\) and \(|p| < |q|\).

Example:

\frac{- 9}{16}

; 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,

\frac{p}{q}

; where \(q ≠ 0\) and \(|p| < |q|\).

Example:

\frac{4}{5}

; \(p = 4\), \(q = 5 ≠ 0\) 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,

\frac{p}{q}

; \(q ≠ 0\) and \(|p| ≥ |q|\); where \(p\) is the numerator, \(q\) is the denominator.

3. Improper fractions will be always \(1\) or greater than \(1\).

Example:

\frac{3}{1}, \frac{4}{2}, \frac{13}{2}

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,

\frac{p}{q}

; where \(q ≠ 0\) and \(|p| ≥ |q|\)

Example:

\begin{array}{l} 1 / 1 = 1 \\ 5 / 3 = 1.6 > 1 \\ 9 / 8 = 1.125 > 1 \end{array}

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,