Comparing and Ordering
Fractions
Section 4.5
Comparing and Ordering Fractions
In the Real World
Kayaking Julie and Seth are kayaking
down a river. Julie kayaks a distance
3
7 mile and Seth kayaks —
of —
mile.
4
10
Who kayaked the greater distance?
Comparing and Ordering Fractions
In the Real World
Kayaking Julie and Seth are kayaking
down a river. Julie kayaks a distance
3
7 mile and Seth kayaks —
of —
mile.
4
10
Who kayaked the greater distance?
You can compare fractions by using the least common denominator.
The least common denominator (LCD) of two or more fractions is
the least common multiple of the denominators.
Comparing and Ordering Fractions
Comparing Two or More Fractions
Find the LCD of the fractions.
Use the LCD to write equivalent fractions.
Compare the numerators.
Comparing and Ordering Fractions
EXAMPLE
1
Comparing Fractions Using the LCD
To find who kayaked a greater distance, as described above, you need
7 and —
3.
to compare —
10
4
1
Find the LCD of the fractions.
Because the LCM of 10 and 4 is 20, the LCD is 20.
2
Use the LCD, 20, to write equivalent fractions.
Julie:
3
14
7
7×2
—
=
= —
10
10 × 2
20
Compare the numerators:
ANSWER
15
3
3×5
=
Seth: — = —
20
4
4×5
7
3
15
14
<
, so 10 < 4 .
20
20
Seth kayaked the greater distance.
Comparing and Ordering Fractions
EXAMPLE
2
Ordering Fractions Using the LCD
2,—
3,—
1 , and —
3 from least to greatest.
Order the fractions —
3 8 6
4
1 Find the LCD of the fractions.
Because the LCM of 3, 8, 6 and 4 is 24, the LCD is 24.
2 Use the LCD to write equivalent fractions.
2
2×8
16
—
= —
= —
3
3×3
—
= —
1
1×4
—
= —
3
3×6
—
= —
3
6
3×8
24
4
= —
6×4
24
8
4
9
= —
8×3
24
18
= —
4×6
24
4
9 16 18
1
3
2
3
—
< — < — < — , so — < — < — < —.
3 Compare the numerators: 24
24 24 24
6
8
3
4
1
3
2
3
ANSWER From least to greatest, the fractions are — , — , — , — .
6
8
3
4
Comparing and Ordering Fractions
EXAMPLE
3
Comparing Fractions Using Approximation
13
15
—
—
Use approximation to tell which fraction is greater, 24 or 34 .
1
— and 15
— are both approximately equal to —
Notice that 13
24
34
2
because the numerator of each fraction is about half the denominator.
1
12
13
1
Because — = — , you know that — > — .
2
24
24
2
15
1
1 17
— <—
—
—
you
know
that
Because =
,
34
2 .
2 34
13 15
ANSWER So, — > — .
24 34