Example 1 Comparing Fractions

a. Compare and .41

52

SOLUTION

a. The LCM of 4 and 5 is 20, so the LCD is 20.

5•4

5•1=

4

1=

20

5

4•5

4•2=

5

2=

20

8

5 < 8, so .<20

8

20

5

Example 1 Comparing Fractions

4

1

5

2ANSWER < .

Example 1 Comparing Fractions

3•8

3•3=

8

3=

24

9–

––

–

2•12

2•5=

12

5=

24

10– –

SOLUTION

b. The LCM of 8 and 12 is 24, so the LCD is 24.

b. Compare and .83

125– –

9 > 10, so > .24

10

24

9– – – –

Example 1 Comparing Fractions

ANSWER > .8

3–

12

5–

, , ,

Example 2

What is the order of 2, , , and from least to greatest? 8

359 1–

, , ,

28

3

5

91– , , ,

25

9

8

31–

28

3

5

91–, , ,

28

3

5

91–

SOLUTION

STEP 1 Find the least common denominator of the fractions. The LCM of 8 and 5 is 40, so the LCD is 40.

Multiple Choice Practice

Example 2

STEP 2 Use the least common denominator to write equivalent fractions.

40

40•2=2 =

40

80

5•8

5•3=

8

3=

40

15

8•5

8•9=

5

9=

40

721– = 1 =

40

40

STEP 3 Compare the numerators: 15 < 40, 40 < 72, and

72 < 80. It follows that , , and4015

<4040

4040

<4072

4072

< .4080

Multiple Choice Practice

So, from least to greatest, the numbers are

and 2. This can be illustrated on a number line.

, , ,

Example 2

83

591–

ANSWER The correct answer is D.

Multiple Choice Practice

Guided Practice

Copy and complete the statement with < or >.

for Examples 1 and 2

ANSWER >1. 8

5

3

2?

ANSWER >20

15

4

2?– –2.

ANSWER <4

2?

10

33.

ANSWER >18

11

16

9?– –4.

Guided Practice for Examples 1 and 2

Order the numbers from least to greatest. Then graph the numbers on a number line.

5. , , , and83

317–

9

52

, , , 83

317–

9

52ANSWER

Guided Practice for Examples 1 and 2

Order the numbers from least to greatest. Then graph the numbers on a number line.

6. 2

7, , , 5

3

13

8

38

2

7, , , 5

3

13

8

38ANSWER