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Comparing & Connecting Rationals
Agenda:  Return & discuss the Quiz  Collect homework; will discuss on Tues.  Handout exam review sheet  Discuss Sec. 6.5  Comparing , Connecting Rationals Homework: Sec. 6.5 1, 4, 5, 7, 8, 9, 10, 21, 23, 27 
Sec. 6.5  Comparing & Connecting Rationals

Area model: (show 3/8 > 1/3) 
How do we compare fractions with paper & pencil
techniques? If the denominators are the same ...


The rational numbers have a denseness property
(which states that a rational number can always be found between any two rational numbers . The study of rational numbers is the first time students work with a set of numbers that is dense rather than discrete. This means we should avoid statements like : 0.6 is the number right next to 0.5, or 3/5 is the fraction between 2/5 and 4/5 
Exercise: b) Find three rational numbers between 11/15 and 0.8.

So we know the set of rational numbers is dense
("there exists a rational number between any two rational numbers"). Does this imply... a) That there are an infinitely many rationals between any two rational numbers? Yes

We have seen that every terminating or repeating
decimal is rational (i.e., it can be expressed as a ratio of two integers .) Let's see how we can find these fraction representations ... The easy case terminating decimals :

The interesting case repeating decimals :

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