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Transcript
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 • The DIFFERENCE between two numbers is one number subtracted by another number. • Ex. What is the difference of 5 and 2? – Aka. 5-2=? 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 = ? Quick Review of What You SHOULD Know • 4 4 5= = 0.8 5 • This would be called finding the quotient • What are these quotients? a. ¾ b. 6/2 c. -11/2 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 But what about……? • Where does 0.5 fit in? 3 • Or what about ? 4 • Are these numbers? Do they fit in the sets we have? • We need a new set to fit these numbers • They are called rational numbers. Rational Numbers • Rigorous Definition: – A rational number is of the form m/n where m and n are any integer and n ≠ 0 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. Do all decimals work? • 0.25? 0.5? Why? • What about something like this? – 0.123456789123456789123456789……. – 3.1415962535897…….. • 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… IRRATIONAL! • 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. 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 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 -4 -3 -2 -1 0 1 2 3 4 5 What do we do if they are fractions? 4 • How do we put numbers like or 5 onto a number line? -5 -4 -3 -2 -1 0 1 2 3 2 3 4 5 • Easy. Turn them into decimals and place (to a reasonable estimation) onto the number line. 4 2 = 0. 6 = -0.8 5 3 -5 -4 -3 -2 -1 0 1 2 3 4 5 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 -4 -3 -2 -1 0 1 2 3 4 5 • How do you write a rational number between two given numbers? • How many can we find between -5 and 5? -5 -4 -3 -2 -1 0 1 2 3 4 5 Rational Irrational Integer Whole Natural