Proper Fractions

Given a fraction p/q, a proper fraction has p<q, and therefore p/q < 1 always. Also, p/q can never be zero.
Positive proper fractions, therefore, will always lie between 0 and 1 on the number line. Negative will lie on the left side of the origin, between 0 and -1.

Examples for Proper Fractions on Number Line

Example 1: Representation of 5/9 on the number line.

Solution:

• First, we mark the origin and integer value 1 on the number line, since proper rational numbers lie between 0 and 1.
• Next, we divide this region into equal parts, such that these parts are equal to the denominator value.
• Then, we mark the part with the value equal to the numerator.
   

Example 2: Representation of -3/4 on the number line.

Solution:

• First, we mark the origin and integer value -1 on the number line, since proper rational numbers lie between 0 and -1.
• Next, we divide this region into 4 equal parts.
• To mark -3, move three parts on the left-side of zero.
                 4

Example 3: Representation of 1/11 on the number line

Solution:

• First, we mark the origin and integer value 1 on the number line, since proper rational numbers lie between 0 and 1.
• Next, we divide this region into 11 equal parts.
• To mark 1/11, move one part on the right-side of zero.

Rational numbers are the integers p and q expressed in the form of p/q where q>0. Rational numbers can be positive, negative or even zero. Rational numbers can be depicted on the number line. The centre of the number line is called Origin (O). Positive rational numbers are illustrated on the right side of zero (called origin), and negative on left side of origin. The representation of rational numbers on the number line depends on the type of fraction.