1. Comparing and Ordering Fractions
Lesson 3.04

2. Comparing and Ordering Fractions
In the Real World
Kayaking Julie and Seth are kayaking down a river. Julie kayaks a distance of mile and Seth kayaks mile. Who kayaked the greater distance? — 7 10 3 4

3. Comparing and Ordering Fractions
In the Real World
Kayaking Julie and Seth are kayaking down a river. Julie kayaks a distance of mile and Seth kayaks mile. Who kayaked the greater distance? — 7 10 3 4
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.

4. Comparing Two or More Fractions
Comparing and Ordering Fractions
NOTE
BOOK
Comparing Two or More Fractions
Find the LCD of the fractions.
Use the LCD to write equivalent fractions.
Compare the numerators.

5. 1 Comparing and Ordering Fractions × 2 × 5
EXAMPLE 1
Comparing Fractions Using the LCD
To find who kayaked a greater distance, as described above, you need to compare and . — 7 10 3 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: — 7 10 =
× 2 = 14 20
Seth: — 3 4 =
× 5 = 15 20 14 20 15
< , 7 10 3 4
so < . 3
Compare the numerators:
ANSWER
Seth kayaked the greater distance.

6. 2 Comparing and Ordering Fractions × 8 × 3 × 4 × 6
EXAMPLE 2
Ordering Fractions Using the LCD
Order the fractions , , , and from least to greatest. — 2 3 8 1 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 3 =
× 8 = — 16 24 — 3 8 =
× 3 = — 9 24 — 1 6 =
× 4 = — 4 24 — 3 4 =
× 6 = — 18 24
Compare the numerators: < < < , — 16 24 9 18 4 — 2 3 8 4 1 6
so < < < . 3
From least to greatest, the fractions are , , , — 2 3 8 4 1 6
ANSWER

7. 3 Comparing and Ordering Fractions
EXAMPLE 3
Comparing Fractions Using Approximation
Use approximation to tell which fraction is greater, or — 13 24 15 34
Notice that and are both approximately equal to — 13 24 1 2 15 34
because the numerator of each fraction is about half the denominator.
Because = , — 12 24 1 2 — 13 24 1 2
you know that > . — 15 34 1 2
you know that < .
Because = , — 17 34 1 2 — 15 34 13 24
So, >
ANSWER