Rational numbers can be expressed as fractions p/q where p and q are integers and q is not equal to 0. Rational numbers have several properties including: 1) Closure under addition, subtraction, multiplication, and division. For example, the sum or product of two rational numbers is also a rational number. 2) Commutativity and associativity for addition and multiplication. For example, a + b = b + a for rational numbers a and b. 3) The distributive property relating multiplication and addition/subtraction. For example, a(b + c) = ab + ac. 4) Zero is the additive identity and one is the multiplicative identity. For example

1. RATIONAL NUMBERS
DONE BY: NIRANJANA SOOREJ
GRADE: 8A

2. CONTEN
T
• Define Rational Numbers
• Properties Of Rational
Numbers
• Additive Identity
• Multiplicative Identity
• Multiplicative Inverse
• Number Line

3. Rational Numbers
A rational number is a number that can be in the
form (p/q) where (p and q) are integers.
(q) is not equal to zero.

4. PROPERTIES OF
RATIONAL NUMBERS

5. CLOSURE
PROPERTY
 Whole Numbers
 Integers
 Rational Numbers

6. Whole numbers
 Addition- whole numbers are closed under addition.
Eg: 0 + 7 = 7 (whole number)
 Subtraction- whole numbers are not closed under subtraction.
Eg: 5 - 7 = -2 (not whole number)
 Multiplication- whole numbers are closed under multiplication.
Eg: 0 x 3 = 0 (whole number)
 Division- whole numbers are not closed under division.
Eg: 5 ÷ 8 = 5/8 (not whole numbers)

7. INTEGERS
 Addition- integers are closed under addition.
Eg: -6 + 5 = -1 (integers)
 Subtraction- integers are closed under subtraction.
Eg: -7 + (–5) = 2 (integers)
 Multiplication- integers are closed under multiplication.
Eg: 5 x 8 = 40 (integers)
 Division- integers are not closed under division.
Eg: -5 ÷ 8 = 5/8 (not integers)

8. COMMUTATIVITY
 Whole Numbers
 Integers
 Rational Numbers

9. WHOLE NUMBERS
 Addition- Addition is commutative.
Eg: 0 + 7 = 0 + 7 =7
 Subtraction- subtraction is not commutative.
Eg: 5 – 8 = 8 - 5
 Multiplication- multiplication is commutative.
Eg: 13 x 2 = 2 x 13 = 26
 Division- division is not commutative.
Eg: 14 ÷ 7 = 7 ÷ 14

10. INTEGERS
 Addition- Addition is commutative.
Eg: 10 + (-7) = (-7) + 10
 Subtraction- Subtraction is not commutative.
Eg: 2 – (-7) = (-7) - 2
 Multiplication- Multiplication is commutative
Eg: 7 x (-1) = (-1) x 7
 Division- Division is not commutative
Eg: 10 ÷ 2 = 2 ÷ 10

11. Rational numbers
 Addition- addition of two rational numbers is commutative.
Eg: 2/9 + 4/9 = 4/9 + 2/9
 Subtraction- subtraction of two rational nos. is not commutative.
Eg: 5/9 – 2/9 = 2/9 – 5/9
 Multiplication- multiplication of rational nos. is commutative.
Eg: 5/9 x 2/9 = 2/9 x 5/9
 Division- division of rational nos. is not commutative.
Eg: 2/3 ÷ 1/3 = 1/3 ÷ 2/3

12. ASSOCIATIVITY
PROPERTY
 Whole number
 Integers
 Rational numbers

13. Whole property
 Addition- addition of rational numbers is associative.
Eg: 2 + (3 + 5) = (2 + 3) + 5
 Subtraction- subtraction of rational numbers is not associative.
Eg: 3 - (7 - 6) = (3 – 7) - 6
 Multiplication- multiplication of rational numbers is associative.
Eg: 7 x (2 x 5) = ( 7x 2) x 5
 Division- division of rational numbers is not associative.
Eg: 100 ÷ (25 ÷ 5) = (100 ÷ 25) ÷ 5

14. INTEGERS
 Addition- addition of integers is associative.
Eg: (-2 + 4 ) + 3 = -2 + (4 + 3 )
 Subtraction- subtraction of integers is not associative.
Eg: 9 – (2 -5) = (9 - 2) - 5
 Multiplication- multiplication of integers is associative.
Eg: (-2 x 4) x 3 = -2 x (4 x 3)
 Division- division of integers of integers is not associative.
Eg: (9 ÷ 2) ÷ 5 = 9 ÷ (2 ÷ 5)

15. Rational numbers
 Addition- addition of rational nos. is associative.
Eg: 2/9 + (5/9 + 1/9) = (2/9 + 5/9) + 1/9
 Subtraction- subtraction of rational nos. is not associative.
Eg: 2/9 – (4/9 – 1/7) = (2/9 – 4/9) – 1/7
 Multiplication- multiplication of rational nos. is associative.
Eg: 2/7 x (7/5 x 9/2) =( 2/7 x 7/5) x 9/2
 Division- division of rational nos. is not associative.
Eg: 9/4 ÷ (7/10 ÷ 5/6) = (9/4 ÷ 7/10) ÷ 5/6

16. DISTRIBUTIV
E PROPERTY
 Multiplication Over
Addition
 Multiplication Over
Subtraction

17. MULTIPLICATION OVER
ADDITION.
Distributive property of Multiplication over
addition.
Eg: 1/3 x (2/5 + 1/5) = 1/3 x 3/5 = 3/5
OR
1/3 x (2/5 + 1/5) = 1/3 x 2/5 + 1/3 x 1/5 = 3/15

18. Multiplication over subtraction
Distributive property of Multiplication over
Subtraction.
Eg: 1/3 x (2/5 – 1/5) = 1/3 x 1/5 =1/15
OR
1/3 x (2/5 – 1/5) = 1/3 x 2/5 – 1/3 x 1/5

19. ADDITITIVE
IDENTITY
 The sum of any rational number and
zero is the rational number itself
 Zero is the additive identity for rational
numbers.
Eg: 2/7 + 0 = 0 + 2/7 = 2/7

20. MULTIPLICATIVE
IDENTITY
 The product of any rational number
and 1 is the rational number itself.
 ‘One’ is the multiplicative identity for
rational numbers.
Eg: 5/7 x 1 = 1x 5/7 = 5/7

21. RATIONAL NUMBERS ON A
NUMBER LINE