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,

$\frac{- p}{q}$ or

$\frac{p}{- q}$ ; 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,

$\frac{- p}{q}$ or

$\frac{p}{- q}$ ; where

$q ≠ 0$ and

$|p| ≥ |q|$ .

Example: