Rational Numbers and Irrational. The examples of Rational Numbers and Irrational Numberspptx

Mathematics

1. Rational Numbers and Irrational Numbers • Basic properties of Rational Numbers • Use GCD to find fraction in the simplest form 6. Rational Numbers and Irrational Numbers • Complex fractions and continued fractions • Basic properties of Irrational Numbers

2. Basic Properties of Rational Numbers

3. Symbol “Q”

4. Definition Real numbers Can be written in p/q form where p and q are an integer and q (the denominator) is not equal to zero Originated from the concept of ratio.

5. Examples of Rational Numbers 1/2 or 0.5 -6/7 -0.25 or -1/4 -13/15 or -0.8666666666666667 12/17, 9/11 and 3/5

6. Commutative Property Rational numbers are commutative under the operations – addition and multiplication ] But for subtraction or division of 2 rational numbers.  a + b = b + a And, a × b = b × a ⇒ a – b ≠ b – a And, a ÷ b ≠ b ÷ a

7. Associative Property Rational numbers have the associative property for only addition and multiplication. For example: ⇒ a + (b + c) = (a + b) + c, here a and b are 2 rational numbers

8. Distributive Property T he multiplication of a whole number is distributed over the sum of the whole numbers. ⇒ a × (b + c) = (a × b) + (a × c), here a and b are 2 rational numbers For example: 1/3 x (1/6 + 1/7) = (1/3 x 1/6) + (1/3 x 1/7) =  13/126

9. Identity Property 0 is an additive identity 1 is a multiplicative identity for rational numbers. ⇒ a/b + 0 = a/b (Additive Identity) a/b x 1 = a/b (Multiplicative Identity For example: 3/4 + 0 = 3/4 (Additive Identity) 3/4 x 1 = 3/4 (Multiplicative Identity)

10. Use GCD To Find Fraction In The Simplest Form

11. Use GCD To Find Fraction In The Simplest Form

12. Use GCD in Euclid’s Algorithm

13. Complex Fractions and Continued Fractions A complex fraction is a rational expression with a fraction either in its numerator, denominator, or both. In other words, it is a fraction within a fraction.

14. Example

15. asnwers

16. Continued Fractions

17. Examples of Continued Fractions

18. Irrational Numbers

19. Irrational Numbers An irrational number cannot be written as a simple fraction Can be represented with a decimal Has endless non-repeating digits after the decimal point

20. Irrational Numbers - Examples Pi ( π) = 3.142857… Euler’s Number (e) = 2.7182818284590452……. √2 = 1.414213…

21. Some Surds Are Irrational Numbers, but not all.

22. Which of these are rational numbers? 1/3 2/3 5/3 2/7 4/9 145/123

23. Practices

24. Practices – Convert rational numbers into fractions

25. Practices on Irrational Numbers – Involving Surds Numbers