Rational numbers ppt

Rational numbers

1. Rational Numbers Created by  Mathukutty sunny

2. Definition of Rational Numbers The integers which are in the form of p/q where q ≠ 0 are known as Rational Numbers. Examples : 5/8; -3/14; 7/-15; -6/-11

3. Properties of Rational Numbers Closure Property Associative Property Distributive Law Additive Inverse Multiplicative Inverse

4. Closure Property Rational numbers are closed under addition. That is, for any two rational numbers a and b, a+b s also a rational number For Example - 8 + 3 = 11 ( a rational number. )  Rational numbers are closed under multiplication. That is, for any two rational numbers a and b, a * b is also a rational number . For Example - 4 * 2 = 8 (a rational number. ) 

5. Commutative Property Addition Rational numbers can be added in any order. Therefore, addition is commutative for rational numbers . For Example :-  -3/8 + 1/7 = 1/7 + (-3/8) (-21 + 8 )/56 = (8 – 21)/56 -13/56 = -13/56

6.   Subtraction  Subtraction is not commutative for rational numbers  For Example - Since, -7 is unequal to 7 Hence, L.H.S. Is unequal to R.H.S - 3/7 – 1/7 ≠ 3/7 – (- 1/7 )

7. Multiplication Rational numbers can be multiplied in any order. Therefore, it is said that multiplication is commutative for rational numbers.  For Example : -7/3*6/5 = 6/5 * (-7/3 ) -14/5 = -14/5

8. Associative Property Addition  Addition is associative for rational numbers. That is for any three rational numbers a, b and c, : a + (b + c) = (a + b) + c. For Example  : 2 + (5 + 3) = (2 + 5) + 3 2 + 8 = 7 + 3 10 = 10

9. Multiplication Multiplication is associative for rational numbers. That is for any rational numbers a, b and c : a* (b*c) = (a*b) * c For Example : 2 * (5*3) = (2*5) *3 2*15 = 10*3 30 = 30

10.   Distributive Law    For all rational numbers a, b and c, a ( b+c ) = ab + ac a (b-c) = ab – ac  For Example : 2(5+3) = 2*5 + 2*3 2*8 = 10 + 6 16 = 16 2(5-3) = 2*5 - 2*3 2*2 = 10 - 6 4 = 4

11. Additive Inverse  Additive inverse is also known as negative of a number. For any rational number a/b, a/b +(-a/b)= (-a/b)+a/b = 0 Therefore , ‘-a/b’ is the additive inverse of ‘a/b’ and ‘a/b’ is the Additive Inverse of (- a/b). 

12. Multiplicative Inverse   Multiplicative inverse is also known as reciprocal number. For any rational number a/b, a/b * b/a = 1

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