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Rational number class 8th

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Shivani Sharma
Shivani Sharma

The document defines rational numbers as numbers that can be expressed as p/q, where p and q are integers and q is not equal to 0. It discusses properties of rational numbers such as closure under addition, subtraction, multiplication, and division. It also covers the identity properties of 0 and 1 for addition and multiplication, as well as inverse properties and representation of rational numbers on a number line.

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RATIONAL NUMBERS
DEFINITION OF RATIONAL NUMBERS COMPARISON OF RATIONAL AND IRRATIONAL NUMBERS PROPERTIES OF RATIONAL NUMBERS OPERATIONS ON RATIONAL NUMBERS ROLE OF 0 and 1 NEGATIVE OF RATIONAL NUMBERS RECIPROCAL OF RATIONAL NUMBERS REPRESENTATION OF RATIONAL NUMBERS ON NUMBER LINE RATIONAL NUMBERS BETWEEN ANY TWO RATIONAL NUMBERS
Rational number class 8th
Rational number class 8th
Def:- Rational numbers :- The numbers are of the form i)p/q form ii)p,q 贈 Z iii)q 0 Rational numbers are indicated by capital Q (QUOZIENTE---ITALIAN---QUOTIENT)
CLOSURE PROPERTY:-If a , b are any two rational numbers then they are under 1. ADDITION a+bQ--------- CLOSED 2. SUBTRACTION a-bQ ---------CLOSED 3. MULTIPLICATION axbQ---------CLOSED 4. DIVISION a歎bQ -------- CLOSED
If a , b are any two rational numbers then they are under 1. ADDITION a+b=b+a-------- TRUE 2. SUBTRACTION a-bb-a ------ FALSE 3. MULTIPLICATION axb=bxa-------TRUE 4. DIVISION a歎bb歎a ------------FALSE
If a, b, c are any three rational numbers then they are under 1. ADDITION (a+b)+c=a+(b+c)----- TRUE 2. SUBTRACTION (a-b)-ca-(b-c) --- FALSE 3. MULTIPLICATION (axb)xc=ax(bxc) --TRUE 4. DIVISION (a歎b)歎ca歎(b歎c) --------FALSE
When we multiply the given number by the other number the result is 1.,then one of the number is the reciprocal of the other number. then the multiplied number is called multiplicative inverse Here 1 is called multiplicative identity of rational numbers.
When a rational number is multiplied with the reciprocal or multiplicative inverse of its own, result will be one (1) i.e. x/y y/x = 1. Example: 2/7 7/2 = 1; etc.
When any rational number is added to zero (0), then it will result in the same rational number i.e. x/y + 0 = x/y. Zero is called the identity for the addition of rational numbers. Example: 2/3 + 0 = 2/3; -5/7 + 0 = -5/7; etc.
When any rational number is multiplied with one (1), then it will result in the same rational number i.e. x/y 1 = x/y. One is called the multiplicative identity for rational numbers. Example: 2/7 1 = 2/7; -8/3 1 = -8/3; etc.
When we add any number to the given number the result is 0. Adding number is called NEGATIVE OF A GIVEN RATIONAL NUMBER. Then the added number is called a additive inverse . Here 0 is called additive identity of rational numbers.
) When a rational number is added to the negative or additive inverse of its own, result will be zero (0) i.e. x/y + (-y/x) = 0. Example: 2/7 + (-7/2) = 0; etc.
: Closure Property Associative Property Commutative Property Distributive Property Identity Property Inverse property
Property Addition Multiplication Subtraction Division 1. Commutative Property x + y = y+ x x y = y x x y y x x 歎 y y 歎 x 2. Associative Property x + (y + z) = (x + y) +z x (y z) = (x y) z (x y) z x (y z) (x 歎 y) 歎 z x 歎 (y 歎 z) 3. Identity Property x + 0 = x =0 + x x 1 = x = 1 x x 0 = x 0 x x 歎 1 = x 1 歎 x 4. Closure Property x + y Q x y Q x y Q x 歎 y Q 5. Distributive Property x (y + z) = x y + x z x (y z) = x y x z
Rational numbers can also be represented on the Number line
Rational numbers can also be represented on the Number line example of 4/9 Step (1) In a rational number, the numeral below the bar, i.e., the denominator, tells the number of equal parts into which the first unit has been divided. The numeral above the bar i.e. the numerator, tells how many of these parts are considered So in this particular example, we need to divide the first unit into 9 parts and we need to move to the 4th part
Step (2) Draw the straight line. Divide the first unit into equal parts equal to the denominator of the rational number. And then mark each equal part to the right of the line and reach the desired number

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Rational number class 8th

  • 2. DEFINITION OF RATIONAL NUMBERS COMPARISON OF RATIONAL AND IRRATIONAL NUMBERS PROPERTIES OF RATIONAL NUMBERS OPERATIONS ON RATIONAL NUMBERS ROLE OF 0 and 1 NEGATIVE OF RATIONAL NUMBERS RECIPROCAL OF RATIONAL NUMBERS REPRESENTATION OF RATIONAL NUMBERS ON NUMBER LINE RATIONAL NUMBERS BETWEEN ANY TWO RATIONAL NUMBERS
  • 5. Def:- Rational numbers :- The numbers are of the form i)p/q form ii)p,q 贈 Z iii)q 0 Rational numbers are indicated by capital Q (QUOZIENTE---ITALIAN---QUOTIENT)
  • 6. CLOSURE PROPERTY:-If a , b are any two rational numbers then they are under 1. ADDITION a+bQ--------- CLOSED 2. SUBTRACTION a-bQ ---------CLOSED 3. MULTIPLICATION axbQ---------CLOSED 4. DIVISION a歎bQ -------- CLOSED
  • 7. If a , b are any two rational numbers then they are under 1. ADDITION a+b=b+a-------- TRUE 2. SUBTRACTION a-bb-a ------ FALSE 3. MULTIPLICATION axb=bxa-------TRUE 4. DIVISION a歎bb歎a ------------FALSE
  • 8. If a, b, c are any three rational numbers then they are under 1. ADDITION (a+b)+c=a+(b+c)----- TRUE 2. SUBTRACTION (a-b)-ca-(b-c) --- FALSE 3. MULTIPLICATION (axb)xc=ax(bxc) --TRUE 4. DIVISION (a歎b)歎ca歎(b歎c) --------FALSE
  • 9. When we multiply the given number by the other number the result is 1.,then one of the number is the reciprocal of the other number. then the multiplied number is called multiplicative inverse Here 1 is called multiplicative identity of rational numbers.
  • 10. When a rational number is multiplied with the reciprocal or multiplicative inverse of its own, result will be one (1) i.e. x/y y/x = 1. Example: 2/7 7/2 = 1; etc.
  • 11. When any rational number is added to zero (0), then it will result in the same rational number i.e. x/y + 0 = x/y. Zero is called the identity for the addition of rational numbers. Example: 2/3 + 0 = 2/3; -5/7 + 0 = -5/7; etc.
  • 12. When any rational number is multiplied with one (1), then it will result in the same rational number i.e. x/y 1 = x/y. One is called the multiplicative identity for rational numbers. Example: 2/7 1 = 2/7; -8/3 1 = -8/3; etc.
  • 13. When we add any number to the given number the result is 0. Adding number is called NEGATIVE OF A GIVEN RATIONAL NUMBER. Then the added number is called a additive inverse . Here 0 is called additive identity of rational numbers.
  • 14. ) When a rational number is added to the negative or additive inverse of its own, result will be zero (0) i.e. x/y + (-y/x) = 0. Example: 2/7 + (-7/2) = 0; etc.
  • 15. : Closure Property Associative Property Commutative Property Distributive Property Identity Property Inverse property
  • 16. Property Addition Multiplication Subtraction Division 1. Commutative Property x + y = y+ x x y = y x x y y x x 歎 y y 歎 x 2. Associative Property x + (y + z) = (x + y) +z x (y z) = (x y) z (x y) z x (y z) (x 歎 y) 歎 z x 歎 (y 歎 z) 3. Identity Property x + 0 = x =0 + x x 1 = x = 1 x x 0 = x 0 x x 歎 1 = x 1 歎 x 4. Closure Property x + y Q x y Q x y Q x 歎 y Q 5. Distributive Property x (y + z) = x y + x z x (y z) = x y x z
  • 17. Rational numbers can also be represented on the Number line
  • 18. Rational numbers can also be represented on the Number line example of 4/9 Step (1) In a rational number, the numeral below the bar, i.e., the denominator, tells the number of equal parts into which the first unit has been divided. The numeral above the bar i.e. the numerator, tells how many of these parts are considered So in this particular example, we need to divide the first unit into 9 parts and we need to move to the 4th part
  • 19. Step (2) Draw the straight line. Divide the first unit into equal parts equal to the denominator of the rational number. And then mark each equal part to the right of the line and reach the desired number