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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 < .