P
O
D
Find the GCF and LCM
basic
12 and 20
GCF= 4
LCM= 60
advanced
32, 68
GCF= 4
LCM= 544
Compare and Order Rational Numbers
A rational number is a number that can be expressed as a ratio
of two integers written as a fraction, in which the denominator is
not zero.
Common fractions, terminating and repeating decimals, percents,
and integers are all rational numbers.
Not all numbers are rational. The Greek letter π (pi) represents a
non-repeating, non-terminating number whose first few digits
are 3.14…
This number is an irrational number
Comparing rational numbers
To compare fractions you can find the least common denominator
(LCD). The LCD is the LCM of the denominators. You can also use a
number line.
Ex: 1
Use <, >, or = to compare
7
12
8
18
The LCD of the denominators 12 and 18 is 36.
7×3
12 × 3
=
8×2
18 × 2
=
21
36
16
36
Since
21
36
>
16
36 ,
7
12
>
8
18
Ex. 2
Use <, >, or = to compare
-156
-116
Graph each rational number on a number line.
1
6
Mark off equal size increments of
between -2 and -1
-2
The number line shows that
-1 56
1
-1
-1 <
6
5
6
-1 46
-1 36
-1
2
6
1
-1 6
-1
Ex. 3
In Mr. Huang’s class, 20% of students own i-phones. In Mrs.
Trevino’s class, 5 out of 29 students own i-phones. In which
class does a greater fraction of students own i-phones?
Express each number as a decimal and then compare.
20% =
5
29
0.2
= 5 ÷ 29 ≈ 0.1724
5
Since 0.2 > 0.1724, 20% > 29
Remember
1. Don’t compare apples to oranges (fractions to decimals, or
decimals to percents…), convert.
2. When comparing fractions, find an LCD.
3. When using a number line, the number to the
right is greater.
4. When comparing decimals, use place value to see
which is greater.
Whiteboard time
Use <, >, or = to compare
-1
4
- 5
-
4
5
-
<
- 4
5
3
5
and
-2
5
1
- 5
- 1
use a number line
5
-
1
5
0
Elliot and Shanna are both soccer goalies. Elliot saves 3
goals out of 4. Shanna saves 7 goals out of 11. Who has
the better average? Explain.
Elliot; 3 out of four has an average of 0.75. Shanna’s 7
out of 11 has an average of 0.64
The lengths of four insects are 0.02 inch, 1/8 inch, 0.1
inch, and 2/3 inch. List the lengths from least to
greatest.
0.02, 0.1, 1/8, 2/3