Download Compare and Order Integers and Rational Numbers

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
2
+7
5
+4.3 -2.1
Negative fraction rationals can be written in three ways:
-6 =
2
6
-2
=
_ 6
2
These three fractions have the identical value
Rule of thumb: place the negative sign in the denominator
1
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
(-5 is less than 3)
-1 > -2
(-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
2
3) Positive Fractions with common denominators can be
compared by viewing their numerators
3
8
<
5
8
3 out of 8 pieces of pie is less than 5 out of 8
Negative Fractions with common denominators are
compared by viewing their numerators
-3
8
>
-5
8
-3 is closer to zero than -5, so it is larger
-3 is more than -5
Other examples
_________________________________________________
4) Positive Fractions with common numerators are
compared by looking at their denominators
3
5
> 3
6
3 out of 5 is more than 3 out of 6
Other examples
5) Negative Fractions with common numerators are compared
by viewing their denominators
3
-5
<
3
-6
-6 is smaller than -5 so you get more from 3
out of -6 than 3 out of -5
In these two cases, a smaller denominator means a larger fraction
3
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
8
Convert 5 = 0.625 now compare 0.625 to 0.25
8
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
2
4
Practicing the strategies using the > < signs to compare and order
Strategy #1
-52 -12
Strategy #2
-3
-1
17
-1/4
-3/4
-5.6
Strategy #3
7/9
2/9
-7/9 -2/9
10
-2.7
14/52
-14/52
10/52
-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
5
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
6
Page 196 do 4 and from page 197 do 6 (refer to the strategies you
learned)
Page 197:
- using your number line, do 5 (place the negative sign in the
denominator)
- using your number line, do 7 8ad
- do 9d use 1/2 as a reference point on your number line or
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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