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

What is Rational Numbers?

Is Every Rational Number a Natural Number?

Is Zero a Rational Number?

Is Every Rational Number an Integer?

Is Every Rational Number a Fraction?

Positive Rational Number

Negative Rational Number

Equivalent Rational Numbers

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

Addition of Rational Numbers

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

Product of Rational Numbers

Properties of Multiplication of Rational Numbers

Rational Expressions Involving Addition, Subtraction and Multiplication

Reciprocal of a Rational  Number

Division of Rational Numbers

Rational Expressions Involving Division

Properties of Division of Rational Numbers

Rational Numbers between Two Rational Numbers

To Find Rational Numbers

8th Grade Math Practice 

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