Rational Numbers on the Number Line
We will learn how to represent rational numbers on the number line with the help of the following examples.
1. Represent \(\frac{5}{3}\) and \(\frac{-5}{3}\) on the number line.
Solution:
In order to represent \(\frac{5}{3}\) and \(\frac{-5}{3}\) on the number line, we first draw a number line and mark a point O on it to represent zero.
Now we find the points X and X' on the number line representing the positive integers 5 and -5 respectively as shown in the below figure.
Now divide the segment OX into three equal parts. Let A and B be the points of division so that OA = AB = BX. By construction, OA is one-third of OX.
Therefore, A represents the rational number \(\frac{5}{3}\).
Point X' represents -5 on the number line. Now, divide OX' into three equal parts OA', CB' and B'X'. The point A' is such that OA' is one third of OX'. Since X' represents the number -5.
Therefore, A' represents the rational number \(\frac{-5}{3}\).
2. Represent \(\frac{8}{5}\) and \(\frac{-8}{5}\) on the number line.
Solution:
To
represent \(\frac{8}{5}\) and \(\frac{-8}{5}\) on the number line, on the number line, draw a
number line and mark a point O on it to represent zero. Now, mark two
points M and M' representing integers 8 and -8 respectively on the number
line. Divide the segment OM into five equal parts. Let A, B, C, D be
the points of division so that OA = AB = BC = CD = DM. By construction,
OA is one-fifth of OM. So, A represents the rational number \(\frac{8}{5}\).
Now, M' represents -8 on the number line. Divide OM' into five equal parts OA', A'B', B'C', C'D', and D'M'. Since M' represents -8 . Therefore, A' represents the rational number -8/5.
● Rational Numbers
Introduction of Rational Numbers
Is Every Rational Number a Natural Number?
Is Every Rational Number an Integer?
Is Every Rational Number a Fraction?
Equivalent form of Rational Numbers
Rational Number in Different Forms
Properties of Rational Numbers
Lowest form of a Rational Number
Standard form of a Rational Number
Equality of Rational Numbers using Standard Form
Equality of Rational Numbers with Common Denominator
Equality of Rational Numbers using Cross Multiplication
Comparison of Rational Numbers
Rational Numbers in Ascending Order
Rational Numbers in Descending Order
Representation of Rational Numbers on the Number Line
Rational Numbers on the Number Line
Addition of Rational Number with Same Denominator
Addition of Rational Number with Different Denominator
Properties of Addition of Rational Numbers
Subtraction of Rational Number with Same Denominator
Subtraction of Rational Number with Different Denominator
Subtraction of Rational Numbers
Properties of Subtraction of Rational Numbers
Rational Expressions Involving Addition and Subtraction
Simplify Rational Expressions Involving the Sum or Difference
Multiplication of Rational Numbers
Properties of Multiplication of Rational Numbers
Rational Expressions Involving Addition, Subtraction and Multiplication
Reciprocal of a Rational Number
Rational Expressions Involving Division
Properties of Division of Rational Numbers
Rational Numbers between Two Rational Numbers
8th Grade Math Practice
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● Rational Numbers - Worksheets
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