Download Comparing Fractions

Section 2-7, “Comparing and Ordering
Rational Numbers”
A RATIONAL NUMBER is a number that can be
written as a fraction with an integer for its
numerator and a nonzero integer for its
denominator.
1
2
3
5
12
1
3
1
4
2
5
“Rational Numbers”
Rational Numbers
Integers
Integers
-3,-2,-1, 0,1,2,3…
Whole Numbers
Whole Numbers
0,1,2,3,4,5…
Rational Numbers
numbers that can
represented as a
ratio or fraction
a
,b  0
b
What Do You See?
“EQUIVALENT FRACTIONS”
1
5
2
10
3
15
4
20
6
30
10
50
“Comparing Fractions”
Compare the fractions
3
4
and
4
5
.
When two fractions have different denominators, write
equivalent fractions with common denominators. Then
compare the numerators.
3 5
4 5
4 4
5 4
=
15
20
=
16
20
Same denominator,
now compare
numerators
Therefore, 4/5 is
greater 3/4.
Comparing and Ordering
Different Forms of Numbers
To make ordering easy, first convert all the
numbers to the same form.
Usually, the simplest to convert the
numbers to is decimals.
Comparing and ordering
numbers
To convert a fraction to a decimal, type the
fraction in your calculator, hit enter. Then
hit the 2nd button, followed by the PRB
button.
To change a percent to a decimal, move
the decimal point 2 places to the LEFT.
25% would become 0.25
Compare the Following Fractions
1
4
2
7
1 7

4 28
2 8

7 28
1
4
5
12
1
3
5
5 1 4


12 12 3 12
5
12
2
6
3
4
2 4

6 12
3 9

4 12
2
6
<
2
7
>
1
3
<
3
4
“Comparing Decimals”
To compare decimals, line up the decimal points and
compare the digits from left to right until you find the place
where the digits are different.
Compare the fractions. Write < or >.
0.81
<
0.84
0.81
0.84
Compare the fractions. Write < or >.
0.34
>
0.342
0.343
4 is greater than 1,
so 0.84 is greater
than 0.81
0.342
3 is greater than 2,
so 0.34 is greater
than 0.342
Order the Numbers from Least to Greatest
0.7011, 0.7, 0.71, 0.70, 0.7
Line up numbers by
the decimal point
Write all decimals in
the same place value
0.7011
0.7
0.71
0.70
0.7
0.7011
0.7000
0.7
0.7100
0.71
0.7070
0.70
0.7777
0.7
Place numbers in
order from least to
greatest
Using a Number Line
Plot the numbers on a number line. Then order them from least to greatest.
2
5 3
, 0.2, 0.67,
,
5
8 2
0.4, 0.2, 0.67, 0.625, 1.5
0
0.2
0.4
0.5 0.625 0.67
1
In order them from least to greatest.
2 5
3
0.2, , , 0.67,
5 8
2
1.5
F
D
Using a Number Line
Plot the numbers on a number line. Then order them from least to greatest.
1
3
2
, 0.21,
, 0.85,
3
5
3
0.3, 0.21, 0.6, 0.85, 0.6,
0
0.21
0.3
0.5 0.6 0.6
0.85
1
In order them from least to greatest.
0.21,
1 3 2
, , , 0.85
3 5 3
1.5