INTRODUCTION
    The numbers of the form p/q, where p and q are integers and q 0 are called rational numbers.

Note :
    •    All natural numbers, whole numbers, integers and fractions are rational numbers.
    •    A fraction is a rational number, but a rational number may or may not be a fraction.
    •    Zero is also a rational number.
    •    Every natural number is a rational number but a rational number need not be a natural number.

Chaper-9

Rational numbers

Rational numbers on number line

Rational numbers and integers

Natural Numbers

All positive integers like 1, 2, 3, 4……..are natural numbers.

Whole Numbers

All natural numbers including 0 are whole numbers.

Integers

All negative and positive numbers including 0 are called Integers.

Rational Numbers

Rational Numbers are the numbers that can be expressed in the form p/q where p and q are integers (q ≠ 0). It includes all natural, whole numbers, fractions and integers.

Number line or coordinate axis

rational Numbers can also be represented on a number line like integers i.e. positive rational numbers are on the right to 0 and negative rational numbers are on the left of 0.

Opposite numbers

Like integers, the additive inverse of rational numbers is also the same.

This shows that the additive inverse of 3/7 is - (3/7)
This shows that

Plotting a rational number

Basic rules of representing rational no. on number line

  • If the rational no fraction is proper then, it lies between 0 and 1.
  • If the rational no .fraction  is improper then, we first convert it to mixed fraction and then the given rational no. lies between the whole number and next whole number.

We use following steps to represent a rational number or fraction for example, 5757 on the number line.

Step 1 − We draw a number line.

Step 2 − As the number 5757 is a positive number, it lies on the right side of zero.

Step 3 − So, after zero mark, we have 17,27,37,47,57,67,17,27,37,47,57,67, and (7777 = 1).

Step 4 − The rational number 5757 on the number line is shown as follows.

Numerator less than denominator

Let us consider 3/4 and −3/4. First, let us plot  3/4.                     

  • Here, the numerator 3 is less than the denominator 4.
  • Then the positive rational number will be between 0 and 1. 
  • Now, let us draw a number line and plot 1 and −1. 
  • Then the number 34 has to lie somewhere between 0 and 1.
  • Now we divide the length between 0 and 1 into equal parts.
  • The Denominator gives us the number of equal parts(4).
  • It is 4, so we divide it into 4 equal parts
  • The numerator tells us the number of parts starting from zero.
  • Here, it is 3. So we mark the point 3 parts away from the zero as shown in the below figure

Similarly, −3/4 can be marked using the same procedure because −3/4 is the corresponding value of 34.
We know that it lies between 0 and −1. So, we divide it into four equal parts and mark 3 parts away from the zero, as shown in the below figure.

Numerator greater than denominator

Let us consider 64 and −64. First, let us plot  64.                     

  • Here, the numerator 6 is greater than the denominator 4.
  • Then, we have to convert it into a mixed fraction.
  • A mixed fraction of 64 is 124.
  • Now, let us draw a number line and plot 1,−1 and 2,−2.
  • Then the number 124 has to lie somewhere between 1 and 2.
  • Now we divide the length between 1 and 2 into equal parts.
  • The Denominator gives us the number of equal parts.
  • It is 4, so we divide it into 4 equal parts.
  • The numerator tells us the number of parts starting from 1.
  • Here, it is 2. So we mark the point 2 parts away from the 1.

 Similarly,  −6/4 can be marked using the same procedure because −6/4 is the corresponding value of 6/4.
We know that it lies between −1 and −2. So, we divide it into four equal parts and mark 2 parts away from the −1.
 

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clas 7 math
Medha Sharma

Course : CBSE Class 7

Start Date : 05.02.2023

End Date : 18.07.2023

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