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Subtracting Fractions
To subtract fractions, each fraction must have the same denominator. In some cases, this means
calculating the least common denominator.
To fi nd the least common denominator, list multiples of each denominator and then identify the
smallest common value. Once you have the least common denominator, for each fraction determine
what number is multiplied by the denominator to achieve the least common denominator and multiply
the numerator by the same number.
Once all fractions have the same denominator, subtract the numerators. Finally, simplify the
fraction.
Skills Workshop 12
See It
Find the diff erence between these fractions:
5
18
,
2
9
, and
1
3
. Calculate a
least common denominator if needed, then subtract the numerators.
Step 1: Determine the least common denominator. In this case, 18 is the least
common denominator because it is divisible by both 9 and 3.
Step 2: Multiply
2
9
by
2
2
(
2
9
×
2
2
=
4
18
).
Step 3: Multiply
1
3
by
6
6
(
1
3
×
6
6
=
6
18
).
Step 4: Subtract the numerators (5 – 4 – 6 = –5).
Step 5: Simplify the fraction –
5
18
. In this case, the fraction cannot be simplifi ed.
Check It
1.
2
5
–
1
20
–
1
5
=
2.
5
8
–
3
16
–
1
2
=
3.
7
9
–
1
18
–
1
3
=
4.
20
21
–
1
7
–
2
3
=