EXAMPLE 1 Comparing Fractions Using the LCD

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 134

710

Julie: 710 = 7

1022 =

1420 Seth: 3

4 = 34

55 =

1520

710

34Julie kayaks a distance of mile, and Seth kayaks

mile. Who kayaks the greater distance?

Kayaking

Use the LCD to write equivalent fractions.STEP 2

EXAMPLE 1 Comparing Fractions Using the LCD

STEP 3 <Compare the numerators: 1420

1520

34

710< ,so

ANSWER Seth kayaks the greater distance.

Because 1420 is to the left of <15

2034

710,

Graph the numbers on a number line.Check :

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.

EXAMPLE 2 Standardized Test Practice

23 = 16

24

6= 1 44 = 4

24

38 = 3

833 =

924

34 = 3

466 = 18

24

424

924

1624

1824< < < , so 1

638

23

34< < <

The order of the fractions from least to greatest is

ANSWER

The correct answer is B.

16

38

23

34

, , , and .

STEP 2 Use the LCD to write equivalent fractions.

STEP 3 Compare the numerators:

16

= 23

88

EXAMPLE 3 Comparing Fractions Using Approximations

Notice that the numerator ofeach fraction is about half thedenominator.

You know that 1224 ,so1

2 =1324> 1

2.

Use approximation to tell whichportion in each package isgreater 13

241736

or .,

<You know that 1836

,so12 =

1736

12

.

EXAMPLE 3 Comparing Fractions Using Approximations

1324

1736

ANSWER

You can conclude that so the package with

package with has a greater portion of pencils in it.

so the>1324

EXAMPLE 3 Comparing Decimals 2.94for Examples 1, 2, and 3GUIDED PRACTICE

1. Copy and complete the statement using <, >, or =:58

712

?

SOLUTION

STEP 1 8Find the LCD of the fractions, to compare and . Because the LCM of 8 and 12 is 24,

the LCD of the fractions is 24.

712

5

58 = 5

833 =

1524

712 = 7

1222 =

1424

Use the LCD to write equivalent fractions.STEP 2

EXAMPLE 3 Comparing Decimals2.94

for Examples 1, 2, and 3GUIDED PRACTICE

STEP 3 Compare the numerators: 24 24> ,15 14 >128so 75

EXAMPLE 3 Comparing Decimals 2.94for Examples 1, 2, and 3GUIDED PRACTICE

2. Order the fractions from least to greatest:

914

34

528

57

, , ,

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.

914 = 9

1422 = 18

28

34 = 3

477 = 21

28

57 = 5

744 = 20

28

528 = 5

2811 = 5

28

EXAMPLE 3 Comparing Decimals 2.94for Examples 1, 2, and 3GUIDED PRACTICE

STEP 3 Compare the numerators:

5 28

18 28

20 28

21 28< < < , so 5

289

1457

34< < <

The order of the fractions from least to greatest is

ANSWER528 15

57

34

, , .9 ,

EXAMPLE 3 Comparing Decimals 2.94for Examples 1, 2, and 3GUIDED PRACTICE

Use approximation to tell which fraction is greater.

Notice that the numerator ofeach fraction is about half thedenominator.

815

1124

,3.

You know that 816

12 = ,so 8

15> 12

.

You know that 1224

12 = <,so 11

2412

.

815

ANSWER

EXAMPLE 3 Comparing Decimals 2.94for Examples 1, 2, and 3GUIDED PRACTICE

Use approximation to tell which fraction is greater.

Notice that the numerator ofeach fraction is about half thedenominator.

1633

1118

,4.

1118

ANSWER

You know that 1632

12 = ,so 16

33< 12

.

You know that 918

12 = >,so 11

1812

.

EXAMPLE 3 Comparing Decimals 2.94for Examples 1, 2, and 3GUIDED PRACTICE

Notice that the numerator ofeach fraction is about half thedenominator.

You know that 2448

12 = ,so 23

48< 12

.

You know that 2856

12 = >,so 31

5612

.

Use approximation to tell which fraction is greater.2348

3156

,5.

3156

ANSWER

EXAMPLE 3 Comparing Decimals 2.94for Examples 1, 2, and 3GUIDED PRACTICE

Use approximation to tell which fraction is greater.

Notice that the numerator ofeach fraction is about half thedenominator.

You know that 1530

12 = ,so 16

30 > 12

.

You know that 65130

12 = <,so 60

13012

.

1630

60130

,6.

1630

ANSWER