Compare and Order Integers and Rational Numbers

Integers are positive whole numbers and their opposites (negatives). Integers do not have a fractional or decimal form.

Ex: -3 -2 -1 0 +1 +2 +3

Rationals are positive and negative numbers in fractional or decimal form:

ie -6 +7 +4.3 -2.1

2  5

Negative fraction rationals can be written in three ways:

-6 = 6 = _ 6

2 -2 2

These three fractions have the identical value

Rule of thumb: place the negative sign in the denominator

Strategies for Comparing and Ordering Rationals:

1)  Positives are always greater in value than Negatives

Let’s get an understanding of the following symbols:

-5 < 3 -1 > -2

(-5 is less than 3) (-1 is greater than -2)

2)  Negatives closer to zero have a greater value than negatives farther from zero

Let’s create three number lines:

a)  Integer number line

b)  Fraction number line

c)  Decimal number line

3)  Positive Fractions with common denominators can be compared by viewing their numerators

3 5 3 out of 8 pieces of pie is less than 5 out of 8

8 8

Negative Fractions with common denominators are compared by viewing their numerators

-3 -5 -3 is closer to zero than -5, so it is larger

8 8 -3 is more than -5

Other examples

______

4)  Positive Fractions with common numerators are compared by looking at their denominators

3 > 3 3 out of 5 is more than 3 out of 6

5 6

Other examples

5)  Negative Fractions with common numerators are compared by viewing their denominators

3 < 3 -6 is smaller than -5 so you get more from 3

-5 -6 out of -6 than 3 out of -5

In these two cases, a smaller denominator means a larger fraction

6)  When some numbers are in fraction form and others are in decimal form, convert to a common form: usually the decimal form.

Example: compare 5 to 0.25

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Convert 5 = 0.625 now compare 0.625 to 0.25

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Other examples

7)  Fractions can be compared by using reference points such as

-1 - 1 0 1 1

2 2

<______>

-1 -1 0 1 1

2 2

-1 > -5

3 8

because -1 is to the right of -1 while -5 is to the

3 2 8

left of -1

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Practicing the strategies using the > < signs to compare and order

Strategy #1

-52 -12 17 10

Strategy #2

-3 -1 -1/4 -3/4 -5.6 -2.7

Strategy #3

7/9 2/9 14/52 10/52

-7/9 -2/9 -14/52 -10/52

Strategy #4

8/10 8/12 13/25 13/40

Strategy #5

8/-10 8/-12 13/-25 13/-40

Strategy #6

4/6 0.81 10/12 0.93

Strategy#7

Using a n. line/reference point, compare -9/10 -2/8

Let’s Compare and Order Decimal Rationals:

A strategy to use when ordering and comparing decimal rationals is to order the numbers vertically along the decimal point. Below is an example of ordering vertically from Greatest to Least:

3.25

1.33

0.145

-0.238

-0.765

1. Order vertically, from Greatest to Least:

-0.182 3.573 -0.243 1.07 -0.012 7.65

2. Order vertically from Least to Greatest:

-0.231 1.25 -0.179 -0.0012 0.76

Homework/Seatwork:

Page 196 from CD do 2abcd 3

Page 196 from UA do 1ab 2ab (without fraction strips) 3

Page 196 do 4 and from page 197 do 6 (refer to the strategies you learned)

Page 197:

-  do 5 (place the negative sign in the denominator)

-  8ad

-  do 9d use 1/2 as a reference point (convert to decimal form or find a common denominator)

-  do 12 13 14acd e(hint: reduce) 16a

-  do “In Your Journal

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