Adding Fractions with Different DenominatorsFind each sum, and write it in lowest terms.
(a)
To find the least common denominator, first factor both denominators.
and
Since 5 and 3 appear as factors, and 3 is a factor of 9 twice, the LCD is
15 9,or 45.
Write each fraction with 45 as denominator.
and
Add the two equivalent fractions.4
15
+
5
9
=
12
45
+
25
45
=
37
45
5
9
=
5 # 5
9 # 5=
25
45
4
15
=
4 # 3
15 # 3=
12
45
5 # 3 # 3
15 = 5 # 3 9 = 3 # 3
4
15
+
5
9
EXAMPLE 6
SECTION 1.1 Fractions 7
NOW TRY
EXERCISE 6
Find each sum, and write it in
lowest terms.
(a) (b) 3
1
4
+ 5
5
8
5
12
+
3
8
NOW TRY ANSWERS
- (a)^1924 (b)^718 , or 8 (^78)
At this stage, the
fractions are not
in lowest terms.
(b)
Method 1
Write each mixed number
as an improper fraction.= Add. Write as a mixed number.
25
4
, or 6
1
4
=
14
4
+
11
4
3
1
2
+ 2
3
4
=
7
2
+
11
4
3
1
2
+ 2
3
4
Think:^7# 2
2 # 2 =
14
4Method 2
or NOW TRY
25
4
5
5
4
= 5 + 1
1
4
= 6
1
4
,
+ 2
3
4
= 2
3
4
3
1
2
= 3
2
4 Write as Then add vertically.
Add the whole numbers and
the fractions separately.3 12 3 24.⎧
⎪
⎪
⎨
⎪
⎪
⎩
The differencebetween two numbers is found by subtracting the numbers. For
example, 9 - 5 = 4,so the difference between 9 and 5 is 4.
Subtracting FractionsIf and are fractions, then
That is, to find the difference between two fractions having the samedenomina-
tor, subtract the numerators and keep the same denominator.
a
b
c
b
ac
b
.
c
b
a
b
Find a common denominator.
The LCD is 4.