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
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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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