Comparing and Ordering Fractions

Section 4.5

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?

—710

—34

Comparing and Ordering Fractions

In the Real World

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.

Kayaking Julie and Seth are kayaking

down a river. Julie kayaks a distance

of mile and Seth kayaks mile.

Who kayaked the greater distance?

—710

—34

Comparing and Ordering Fractions

NOTE BOOK

Find the LCD of the fractions.

Use the LCD to write equivalent fractions.

Compare the numerators.

Comparing Two or More Fractions

Comparing and Ordering Fractions

Comparing Fractions Using the LCDEXAMPLE 1

To find who kayaked a greater distance, as described above, you need

to compare and .—710

—34

Find the LCD of the fractions.

Use the LCD, 20, to write equivalent fractions.

Julie: —710

= —710 Seth: —3

4= —3

4

Compare the numerators:

Because the LCM of 10 and 4 is 20, the LCD is 20.

Comparing and Ordering Fractions

ANSWER Seth kayaked the greater distance.

=1420

=1520

710

3 4

so < .1420

1520< ,

1

2

3

× 2× 2

× 5× 5

Ordering Fractions Using the LCDEXAMPLE 2

Order the fractions , , , and from least to greatest.—23

—38

—16

—34

Find the LCD of the fractions.

Because the LCM of 3, 8, 6 and 4 is 24, the LCD is 24.

Use the LCD to write equivalent fractions.

—23

= —23

= —1624

—38

= —38

= —924

—16

= —16

= —424

—34

= —34

= —1824

Compare the numerators: < < < , —1624

—924

—1824

—424

Comparing and Ordering Fractions

ANSWER From least to greatest, the fractions are , , , . —23

—38

—34

—16

—23

—38

—34

—16 so < < < .

1

2

3

× 8× 8

× 4× 4

× 3× 3

× 6× 6

EXAMPLE 3

Use approximation to tell which fraction is greater, or .—1324

—1534

Because = , —1224

—12

Because = , —1734

—12

—1534

—1324

So, > .ANSWER

Comparing Fractions Using Approximation

Comparing and Ordering Fractions

—1324

—12

you know that > .

Notice that and are both approximately equal to—1324

—12

—1534

because the numerator of each fraction is about half the denominator.

—1534

—12you know that < .