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Chapter 3: Rational Numbers

Chapter 3: Rational Numbers. 3.1 What Is a Rational Number? Pg 94-105. Quick Review of What You SHOULD Know. If we are looking for the SUM of two numbers, that means two numbers added together. Ex. The sum of 2 and 3 is? Aka. 2+3=?. Quick Review of What You SHOULD Know.

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Chapter 3: Rational Numbers

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  1. Chapter 3:Rational Numbers 3.1 What Is a Rational Number? Pg 94-105

  2. Quick Review of What You SHOULD Know • If we are looking for the SUM of two numbers, that means two numbers added together. • Ex. The sum of 2 and 3 is? • Aka. 2+3=?

  3. Quick Review of What You SHOULD Know • The DIFFERENCE between two numbers is one number subtracted by another number. • Ex. What is the difference of 5 and 2? • Aka. 5-2=?

  4. Quick Review of What You SHOULD Know • The PRODUCT of two numbers is one number multiplied by the other. • Ex. The product of 12 and 5 is?. • Aka. 12 x 5 = ?

  5. Quick Review of What You SHOULD Know • 4 5 = = 0.8 • This would be called finding the quotient • What are these quotients? • ¾ • 6/2 • -11/2

  6. Quickly what are the different types of numbers we know? Natural numbers: 1, 2, 3, 4, 5, 6, ….. Whole Numbers: 0, 1, 2, 3, 4, 5, 6, …… Integers: ……, -6, -5, -4, -3, -2, -1, 0, +1, +2, +3, +4, +5, +6, ... • ????? Anything bigger? • Integers • Whole • Natural

  7. But what about……? • Where does 0.5 fit in? • Or what about ? • Are these numbers? Do they fit in the sets we have?

  8. We need a new set to fit these numbers • They are called rational numbers.

  9. Rational Numbers • Rigorous Definition: • A rational number is of the form m/n where m and n are any integer and n ≠ 0

  10. What does that actually mean? • Basically if you can write a number as a fraction, it is rational. • SO! All integers are rational because we can write them like this. • 2=2/1 , 439=439/1 , 7993857667=7993857667/1 • And obviously all fractions are rational.

  11. Do all decimals work? • 0.25? 0.5? Why? • What about something like this? • 0.123456789123456789123456789……. • 3.1415962535897……..

  12. Not all decimals will be rational. They will be rational if they are not infinite, or they have a finite repeatable pattern. • So if something is not rational it must then be…

  13. IRRATIONAL!

  14. So everything that isn’t rational is then irrational. • The example I gave was Pi • Part of your homework is to find two other irrational numbers.

  15. How to write a rational number on a number line. • First we need to review what a zero pair is. • ZERO PAIR is two numbers that have the same value but opposite sign. • Exs. -2, +2 -20.5, +20.5 -926, +926 • Take any of these pairs and add them, you will get zero every time. Thus zero pair. • Zero pairs have the same distance from zero

  16. How to write a rational number on a number line. Let’s try placing these values onto a number line: 2, 3, -1, -4, 0.5, -0.75 -5 -2 5 -4 -3 -1 0 1 2 3 4

  17. What do we do if they are fractions? • How do we put numbers like or onto a number line? -5 -2 5 -4 -3 -1 0 1 2 3 4

  18. Easy. Turn them into decimals and place (to a reasonable estimation) onto the number line. = 0. = -0.8 -5 -2 5 -4 -3 -1 0 1 2 3 4

  19. Ordering Rational #’s • List in order from least to greatest. • Same strategy; place them on a number line and list them off in order. • -3/5, 1.1, 13/12, -0.5, 12/12 -5 -2 5 -4 -3 -1 0 1 2 3 4

  20. How do you write a rational number between two given numbers? • How many can we find between -5 and 5? -5 -2 5 -4 -3 -1 0 1 2 3 4

  21. Everything is contained in the Real Numbers • Rational Irrational • Integer • Whole • Natural

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