1i Develop a logical argument to demonstrate the ‘denseness’ of

rational numbers. (DOK 3)

By: Deia Sanders(Lesson 1)

Pre-TestName a number that is between

321 and

212

Name a number that is between87

43 and

Name a number that is between 2.7 and 2.66.

What does “denseness” mean?

Denseness is a property that reflects the number of items that exist in a given space

What is a “rational” number?

Numbers that end and do not go on forever (like ).

•Decimals (that end or repeat)•Fractions•Whole Numbers•Square roots

Any number that can be made by dividing one integer by another.

Book definition!

For us…

Quick Question…

How many rational numbers are there between 2 and 3?

How many rational numbers are there between 2.4 and 2.5?

How many rational numbers are there between 2.4 and 2.42?

Good News!

You only have to learn

2 steps today!

1.Find LCD (for mixed number we need to change to improper fractions first!)

2. List all numbers between the two new numerators, write them over LCD.

Today we will focus on fractions!Applying the Property of DensenessExamples:Name a number that is between

Find the LCD. In this example, the LCD = 6.Convert the fractions to the same LCD.

Compare numerators (top numbers). Any fraction having a denominator of 6 and a numerator that isbetween 2 and 5 is between

65

31 and

62

22

31

65

11

65

65

31 and

Why does the

numerator need

to be between 2

and 5 in this

problem???

More fraction examples…

Name a number that is between321 and

212

Convert to improper fractions.

Write both fractions with the LCD.

Any fraction having a denominator of 6 and a numerator that is between 10 and 15will meet the condition.

Try this on your own!

Name a number that is between213 and

314

Follow your steps!1. Find LCD (for mixed

number we need to change to improper fractions first!)

2. List all numbers between the two numerators, write them over LCD.

Another Example…

Name a number that is between87

43 and

Follow your

steps and solve!

Pick 2

322

432

852

2