Transcript Compare Rational Numbers-eng

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Math 8
Comparing and Ordering
Rational Numbers
Comping Numbers
Decimals and Fractions
There are 4 simple principles you can use to
compare and order fractions and decimal
numbers:
1.
2.
3.
4.
Use points of reference
Use common denominators
Use common numerators
Convert to fractions or decimal numbers.
Reference Points
When we speak of reference points (benchmarks)
be familiar with common fractions and their decimal
equivalents as good reference points:
1/
8
= 0.125
1/
3
= 0.3333…
1/
5
= 0.20
3/
4
= 0.75
1/
4
= 0.25
1/ =
2
0.5
2/
3
1/
10
=0.6666…
= 0.1
A special pattern with denominator of
«9»
_
1/ = 0.1
9
_
2/ = 0.2
9
_
3/ = 0.3
9
_
4/ = 0.4
9
__
1/ = 0.01
99
__
2/ = 0.02
99
__
3/ = 0.03
99
__
11/ = 0.11
99
__
12/ = 0.12
99
___
1/
999 = 0.001
___
31/
999 = 0.031
etc……
What is the decimal value of this
fraction?
1
1 ?
4
1.25
What is the decimal value of this
fraction?
1
2 ?
3
-2,333…
What is the decimal value of this
fraction?
3
8 ?
4
8.75
What is the decimal value of this
fraction?
2
3  ?
3
-3.666…
What fraction is greater?
2
3
or
?
3
4
3
4
If the 2 fractions
are converted to
decimals, it’s
easy…
2/
3
= 0.666…
3/
4
= 0.75
Then 3/4 is
greater.
What fraction is greater?
9
3
or
?
10
4
Reference Points!
3/
4
9/
= 0.75
10
9
10
is closer to 1
So 9/10 is
greater.
What fraction is greater?
3
5
or ?
7
8
We can use ½ as a
reference point.
3/
7
<
1/
2
5/
>
1/
8
5
8
2
So 5/8 is greater.
Comparing negative numbers
If the numbers are negative, the numbers further left
are smaller than numbers to the right on a number
line.
Example:
What number is
greater?
-0.56 ou -0.5?
-0.5 is closer
to zero so it
is greater
What number is greater?
9
3

ou  ?
10
4
-1
0
3

4
- 3/4 is closer to zero
so it is greater
+1
Comparing with common
denominators.
-1
0
If you compare - 4/7 and - 3/7 you see
- 3/7 is closer to zero so it is greater.
+1
Comparing with common
denominators.
You can also change the fraction to have
common denominators to compare:
Example: What fraction is greater?
9
3
or
?
10
4
18
15
or
?
20
20
18
20
What fraction is greater?

3
1
or  ?
7
3
9
7

or 
21
21
When you find
equivalent fractions
- 7/21 is closer to zero
so it is greater.
1
0
+
1
Use common numerators to compare
fractions.
• If the numerators are
the same, the
fraction with the
smaller denominator
is the greater
absolute value.
4
6
4

5
What fraction is greater?
3
3
or ?
7
9
3
7
What fraction is greater?
6
6

or  ?
7
8
-1
-6/8 is greater because
it is closer to zero
0
+1
6

8
Compare fractions by
converting to decimal numbers
Example: What fraction is greater?
1
2
or
?
8
18
So 1/8 is greater.
1
 1  8  0.125
8
2
 2  18  0.1
18
What fraction is greater?
1
2
or
?
13
27
So, 1/13 is the greater fraction.
1
 1  13  0.077...
13
2
 2  27  0.074...
27
Place the row of numbers in order
from least to greatest:
11
0.7
10
2
5
2
3 1
0.69
1
3
4 5
2
5
2
3 11 1
0.69 0.7
1
3
4 10 5
Place the row of numbers in order
from least to greatest:
 0.3
2

3
1

3
2

5
2

3
1

3
 0.15
 0.3
1

10
1

5
1

5
 0.15
2

5
1

10