27
Adding Fractions
To add 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, add the numerators. Finally, simplify the fraction.
Skills Workshop 11
See It
Find the sum of these fractions:
3
8
,
5
16
, and
11
32
. Calculate the least
common denominator if needed, then add the numerators.
Step 1: Determine the least common denominator. In this case, 32 is the least
common denominator because it is divisible by both 8 and 16.
Step 2: Multiply
3
8
by
4
4
(
3
8
×
4
4
=
12
32
).
Step 3: Multiply
5
16
by
2
2
(
5
16
×
2
2
=
10
16
).
Step 4: Add the fractions
12
32
,
10
16
, and
11
32
(
12
32
+
10
16
+
11
32
=
11
32
) and
simplify the result (
33
32
= 1
1
32
).
Check It
1.
4
5
+
3
20
+
1
5
=
2.
3
16
+
1
2
+
5
8
=
3.
1
18
+
2
9
+
1
2
=
4.
2
3
+
20
21
+
1
7
=