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3-6
Comparing and Ordering Rational Numbers
Preview
Warm Up
California Standards
Lesson Presentation
Holt CA Course 1
3-6
Comparing and Ordering Rational Numbers
Warm Up
Write each mixed number as an
improper fraction.
1. 1 3
7
4
2. 2 7
8
23
8
3. 1 5
6
11
6
1
4. 812
97
12
4
Holt CA Course 1
3-6
Comparing and Ordering Rational Numbers
California
Standards
NS1.1 Compare and order positive
and negative fractions, decimals, and mixed
numbers and place them on a number line.
Also covered:
NS2.4
Holt CA Course 1
3-6
Comparing and Ordering Rational Numbers
Vocabulary
rational number
Holt CA Course 1
3-6
Comparing and Ordering Rational Numbers
Which is greater, 7 or 2 ?
9
9
To compare fractions with the same
denominator, just compare the numerators.
7
= 9
2
= 9
Holt CA Course 1
7 > 2 because 7 > 2.
9
9
3-6
Comparing and Ordering Rational Numbers
One way to compare fractions with unlike
denominators is to use models. For example,
the models show that 3 < 1 .
2
8
=3
8
=1
2
Another way to compare fractions with unlike
denominators is to first write equivalent
fractions with common denominators. Then
compare the fractions.
Holt CA Course 1
3-6
Comparing and Ordering Rational Numbers
Additional Example 1A: Comparing Fractions
Compare the fractions. Write < or >.
7
9
5
8
The LCM of the denominators 9 and 8 is 72.
7 =7  8
56
9  8 = 72
9
5 =5  9
45
8  9 = 72
8
56
45 , and so 7
5.
>
>
72
72
9
8
Holt CA Course 1
Write equivalent
fractions with 72 as
the denominator.
Compare the
numerators.
3-6
Comparing and Ordering Rational Numbers
Additional Example 1B: Comparing Fractions
Compare the fractions. Write < or >.
– 2
5
– 3
7
Both fractions can be written with a denominator of 35.
Write equivalent fractions
with 35 as the
denominator.
Put the negative signs
in the numerators.
3
– 14 > – 15 , and so – 2 > –
.
5
7
35
35
–14
–2  7
– 2 =
=
5
35
57
–15
–3  5
3
– 7 =
=
35
75
Holt CA Course 1
3-6
Comparing and Ordering Rational Numbers
Helpful Hint!
A fraction less than 0, such as - 2 , can be
5
-2
2
2
written as - , , or .
5 5
-5
Holt CA Course 1
3-6
Comparing and Ordering Rational Numbers
Check It Out! Example 1A
Compare the fractions. Write < or >.
5
6
7
8
The LCM of the denominators 6 and 8 is 48.
5 =5  8
40
6
6  8 = 48
7 =76
42
8  6 = 48
8
40
42 , and so 5
7.
<
<
48
48
6
8
Holt CA Course 1
Write equivalent
fractions with 48 as
the denominator.
Compare the
numerators.
3-6
Comparing and Ordering Rational Numbers
Check It Out! Example 1B
Compare the fractions. Write < or >.
5
– 6
–
8
7
Both fractions can be written with a denominator of 56.
–42
–6  7
– 6 =
=
8
56
87
–40
–5  8
5
– 7 =
=
56
78
Write equivalent fractions
with 56 as the denominator.
Put the negative signs
in the numerators.
5
– 42 < – 40 , and so – 6 < –
.
8
7
56
56
Holt CA Course 1
3-6
Comparing and Ordering Rational Numbers
To compare decimals, line up the
decimal points and compare digits
from left to right until you find the
place where the digits are different.
Holt CA Course 1
3-6
Comparing and Ordering Rational Numbers
Additional Example 2A: Comparing Decimals
Compare the decimals. Write < or >.
0.427
0.427
7
0.425
5
0.425
Line up the decimal points.
The tenths and hundredths are
the same.
Compare the thousandths:
7 > 5.
Since 0.007 > 0.005, 0.427 > 0.425.
Holt CA Course 1
3-6
Comparing and Ordering Rational Numbers
Additional Example 2B: Comparing Decimals
Compare the decimals. Write < or >.
0.73
_
0.734
3
0.73 = 0.733…
0.734
4
0.73 is a repeating decimal.
Line up the decimal points.
The tenths and hundredths are
the same.
Compare the thousandths:
3 < 4.
Since 0.003 is < 0.004, 0.73 < 0.734.
Holt CA Course 1
3-6
Comparing and Ordering Rational Numbers
Check It Out! Example 2A
Compare the decimals. Write < or >.
0.535
0.535
5
0.538
8
0.538
Line up the decimal points.
The tenths and hundredths are
the same.
Compare the thousandths:
5 < 8.
Since 0.005 < 0.008, 0.535 < 0.538.
Holt CA Course 1
3-6
Comparing and Ordering Rational Numbers
Check It Out! Example 2B
Compare the decimals. Write < or >.
0.3
0.334
3
0.3 = 0.3333…
0.3 is a repeating decimal.
0.334
4
Line up the decimal points.
The tenths and hundredths are
the same.
Compare the thousandths:
3 < 4.
Since 0.003 is < 0.004, 0.3 < 0.334.
Holt CA Course 1
3-6
Comparing and Ordering Rational Numbers
A rational number is a number that
can be written as a fraction or quotient
of integers with a nonzero denominator.
When rational numbers are written in a
variety of forms, you can compare the
numbers by writing them all in the same
form.
Holt CA Course 1
3-6
Comparing and Ordering Rational Numbers
Remember!
The values on a number line increase as you
move from left to right.
Holt CA Course 1
3-6
Comparing and Ordering Rational Numbers
Additional Example 3: Ordering Fractions and
Decimals
Order 4 , 0.93, and 0.9 from least to greatest.
5
Write as decimals with the same number of places.
4 = 0.80
0.93 = 0.93
0.9 = 0.90
5
Graph the numbers on a number line.
0.93
0
0.2
0.4
0.6
0.8
1
0.80 < 0.90 < 0.93 Compare the decimals.
From least to greatest, the numbers are 4 , 0.9, 0.93.
5
Holt CA Course 1
3-6
Comparing and Ordering Rational Numbers
Check It Out! Example 3
Order 3 , 0.84, and 0.7 from least to greatest.
5
Write as decimals with the same number of places.
3 = 0.60
5
0.84 = 0.84
0.7 = 0.70
Graph the numbers on a number line.
0.84
0
0.2
0.4
0.6
0.8
1
0.60 < 0.70 < 0.84 Compare the decimals.
From least to greatest, the numbers are 3 , 0.7, 0.84.
5
Holt CA Course 1
3-6
Comparing and Ordering Rational Numbers
Lesson Quiz
Compare the fractions. Write > or <.
3 and 4 >
2 <
1.
2. 5
8 and 3
10
7
Compare the decimals. Write < or >.
3. 0.32 and 0.312
>
4. Order 5 , 0.8, 0.826 from least to greatest.
6
Graph the numbers on a number line. 0.8, 0.826, 5
6
5
0.8
0.80
Holt CA Course 1
0.826
0.81
0.82
6
0.83
0.84
0.85