Holt CA Course 1 3-6 - Jefferson School District
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
A number that can be written as a fraction with integers for its numerator and denominator.
Holt CA Course 1
3-6 Comparing and Ordering Rational Numbers
To compare fractions with the same denominator, just compare the numerators.
=
2
9
7
9 >
2
9 because 7 > 2.
Holt CA Course 1
3-6 Comparing and Ordering Rational Numbers
One way to compare fractions with unlike denominators is to use models. For example,
=
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
Example 1A: Comparing Fractions
Compare the fractions. Write < or >.
7
9
5
8
The LCM of the denominators 9 and 8 is 72.
7
9 =
5
8 =
56
72
>
7 8
9 8
5 9
8 9
45
72
=
=
56
72
45
72
Write equivalent fractions with 72 as the denominator.
Compare the numerators.
Holt CA Course 1
3-6 Comparing and Ordering Rational Numbers
Example 1B: Comparing Fractions
Compare the fractions. Write < or >.
–
2
5
–
3
7
Both fractions can be written with a denominator of 35.
–
2
5 5
7
7
–
3
7 7
5
5
–
14
35
> –
15
35
=
=
–14
35
–15
35
Write equivalent fractions with 35 as the denominator .
Put the negative signs in the numerators.
, and so –
2
5
> .
Holt CA Course 1
3-6 Comparing and Ordering Rational Numbers
Helpful Hint!
A fraction less than 0, such as written as -
2
5
, , or .
-
2
5
-
2
5
, can be
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
Example 2A: Comparing Decimals
Compare the decimals. Write < or >.
0.427
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
Example 2B: Comparing Decimals
Compare the decimals. Write < or >.
0.73
_
0.73 =
0.734
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
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
Example 3: Ordering Fractions and Decimals
Order
4
5
, 0.93, and 0.9 from least to greatest.
Write as decimals with the same number of places.
4
5 = 0.80
0.93 = 0.93
0.9 = 0.90
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
5
, 0.9, 0.93
.
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
6 =
7
8 =
40
48 <
5 8
6 8 =
7
8
42
6
6 =
40
48
42
48
5
6
<
7
8
Write equivalent fractions with 48 as the denominator.
Compare the numerators.
Holt CA Course 1
3-6 Comparing and Ordering Rational Numbers
Check It Out!
Example 2A
Compare the decimals. Write < or >.
0.535
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 3
Write as decimals with the same number of places.
3
5 = 0.60
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 , 0.7, 0.84
.
Holt CA Course 1
