1. EXAMPLE 1
Comparing Fractions Using the LCD 7 10 3 4
Julie kayaks a distance of mile, and Seth kayaks mile. Who kayaks the greater distance?
Kayaking
SOLUTION
Find the LCD of the fractions, to compare and Because the LCM of 10 and 4 is 20, the
LCD of the fractions is 20.
STEP 1 3 4 7 10
Use the LCD to write equivalent fractions.
STEP 2
Julie: 7 10 = 7 10 2 = 14 20
Seth: 3 4 = 3 4 5 = 15 20

2. EXAMPLE 1
Comparing Fractions Using the LCD
STEP 3
<
Compare the numerators: 14 20 15 3 4 7 10 , so
ANSWER
Seth kayaks the greater distance.
Graph the numbers on a number line.
Check :
Because 14 20
is to the left of
< 15 3 4 7 10 ,

3. EXAMPLE 2
Standardized Test Practice
SOLUTION
STEP 1
Find the LCD. The LCD is the LCM of 3, 4, 8, and 6, which is 24.

4. EXAMPLE 2
Standardized Test Practice
STEP 2
Use the LCD to write equivalent fractions. 2 3 = 2 3 8 = 16 24 3 8 = 3 8 = 9 24 1 6 6 = 1 4 = 4 24 3 4 = 3 4 6 = 18 24
STEP 3
Compare the numerators: 4 24 9 16 18
<
, so 1 6 3 8 2 4
<
The order of the fractions from least to greatest is
ANSWER
The correct answer is B. 1 6 3 8 2 4 ,
, and .

5. EXAMPLE 3
Comparing Fractions Using Approximations
Use approximation to tell which
portion in each package is
greater 13 24 17 36 or . ,
Notice that the numerator of
each fraction is about half the
denominator.
You know that 12 24
,so 1 2 = 13
> .
<
You know that 18 36
,so 1 2 = 17 .

6. EXAMPLE 3
Comparing Fractions Using Approximations 13 24 17 36
ANSWER
You can conclude that
so the package with
package with
has a greater portion of pencils in it.
so the
>

7. GUIDED PRACTICE
EXAMPLE 3
Comparing Decimals
for Examples 1, 2, and 3
1. Copy and complete the statement using <, >, or =: 5 8 7 12 ?
SOLUTION
STEP 1 8
Find the LCD of the fractions, to compare and Because the LCM of 8 and 12 is 24,
the LCD of the fractions is 24. 7 12 5
Use the LCD to write equivalent fractions.
STEP 2 5 8 = 5 8 3 = 15 24 7 12 = 7 12 2 = 14 24

8. EXAMPLE 3
GUIDED PRACTICE
Comparing Decimals
for Examples 1, 2, and 3 24
> , 15 14
> 12 8 so 7 5
STEP 3
Compare the numerators:

9. EXAMPLE 3
GUIDED PRACTICE
Comparing Decimals
for Examples 1, 2, and 3
2. Order the fractions from least to greatest: 9 14 3 4 5 28 7 ,
SOLUTION
STEP 1
Find the LCD. The LCD is the LCM of 15, 7, 4, and 28, which is 28.
STEP 2 Use the LCD to write equivalent fractions. 9 14 = 9 14 2 = 18 28 5 7 = 5 7 4 = 20 28 3 4 = 3 4 7 = 21 28 5 28 = 5 28 1 = 5 28

10. EXAMPLE 3
GUIDED PRACTICE
Comparing Decimals
for Examples 1, 2, and 3
STEP 3 Compare the numerators: 5 28 18 20 21
<
, so 5 28 9 14 7 3 4
<
The order of the fractions from least to greatest is
ANSWER 5 28 15 7 3 4 , . 9

11. GUIDED PRACTICE
EXAMPLE 3
Comparing Decimals
for Examples 1, 2, and 3
Use approximation to tell which fraction is greater. 8 15 11 24 ,
Notice that the numerator of
each fraction is about half the
denominator.
You know that 8 16 1 2 =
,so 8 15
> 1 2 .
You know that 12 24 1 2 =
<
,so 11 24 1 2 . 8 15
ANSWER

12. GUIDED PRACTICE
EXAMPLE 3
Comparing Decimals
for Examples 1, 2, and 3
Use approximation to tell which fraction is greater. 16 33 11 18 ,
Notice that the numerator of
each fraction is about half the
denominator.
You know that 16 32 1 2 =
,so 16 33
< 1 2 .
You know that 9 18 1 2 =
>
,so 11 18 1 2 . 11 18
ANSWER

13. GUIDED PRACTICE
EXAMPLE 3
Comparing Decimals
for Examples 1, 2, and 3
Use approximation to tell which fraction is greater. 23 48 31 56 ,
Notice that the numerator of
each fraction is about half the
denominator.
You know that 24 48 1 2 =
,so 23 48
< 1 2 .
You know that 28 56 1 2 =
>
,so 31 56 1 2 . 31 56
ANSWER

14. GUIDED PRACTICE
EXAMPLE 3
Comparing Decimals
for Examples 1, 2, and 3
Use approximation to tell which fraction is greater. 16 30 60
130 ,
Notice that the numerator of
each fraction is about half the
denominator.
You know that 15 30 1 2 =
,so 16 30
> 1 2 .
You know that 65
130 1 2 =
<
,so 60
130 1 2 . 16 30
ANSWER