Example 1 Comparing Fractions a. Compare and. 4 1 5 2 SOLUTION a. The LCM of 4 and 5 is 20, so the...
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Transcript of Example 1 Comparing Fractions a. Compare and. 4 1 5 2 SOLUTION a. The LCM of 4 and 5 is 20, so the...
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