Adding and Subtracting with
Unlike Denominators
3.5
Warm Up
Add or subtract.
1.
1 35
+–
2
5
7
2. 3 11
12 – 2 12
1
15
1
13
3. 6.5 + –1.2
5.3
4. 3.4 – 0.9
2.5
Learn to add and subtract fractions
with unlike denominators.
Vocabulary
least common denominator (LCD)
1
93
A pattern for a double-circle skirt requires
yards of 45-inch-wide material. To add a
2
ruffle takes another 2 5 yards. If the total
amount of material for the skirt and ruffle are
1
cut from a bolt of fabric 15 2 yards long, how
much fabric is left?
To solve this problem, add and subtract
rational numbers with unlike denominators.
First find a common denominator using one
of the following methods:
Method 1 Find a common denominator by
multiplying one denominator by the
other denominator.
Method 2 Find the least common denominator
(LCD); the least common multiple of the
denominators.
Example: Adding and Subtracting
Fractions with Unlike Denominators
Add or Subtract.
Method 1:
A.
2
1
+
7
8
2 8
1 7
+
7 8
8 7
Find a common
denominator: 8(7)=56.
Multiply by fractions
equal to 1.
7
16
23
=
+
56
56
56
Rewrite with a common
denominator.
Simplify
Example: Adding and Subtracting
Fractions with Unlike Denominators
Add or Subtract.
Method 2:
Write as an improper fraction.
1
5
B. 1 6 + 8
List the multiples of each
7
6
+
5
8
5 3
7 4
Remember!
6 4 +8 3
denominator and find the LCD
Multiples of 6: 6; 12; 24; 30
Multiples of 8: 8; 16; 24; 32
Multiply by fractions equal to 1.
The least common multiple of two numbers is the
a acommon
28 smallest
15
43
19 Rewrite
number
other
than zerowith
that is
multiple of
= 24 = 1 24 denominator. Simplify.
24 +
the24
two numbers.
Try This
Add or Subtract.
Method 1:
5
1
A. 3 + 8
1 8
5 3
+
3 8
8 3
8
23
15
=
+
24 24
24
Find a common
denominator 3(8)=24.
Multiply by fractions
equal to 1.
Rewrite with a common
denominator.
Try This
Add or Subtract.
Method 2:
B.
1
26
13
6
26
12
13
6
2
2
+
9
12
+
3
4
+
3
4
+
3
4
Write as an improper fraction.
List the multiples of each
denominator and find the LCD
Multiples of 6: 6; 12; 24; 30
Multiples of 4: 4; 8; 12; 16
3
3
Multiply by fractions equal to 1.
Rewrite with a common
35
= 12 = 2 11
12 denominator. Simplify.
Example: Evaluating Expressions with
Rational Numbers
4
Evaluate t –
5
5
for t =
.
6
4
5
–
5
6
Substitute
4 6
5 5
–
5 6
6 5
Multiply by fractions equal to 1.
1
25
24
=
–
30
30
30
Rewrite with a common
denominator: 6(5) = 30.
5
6
for n.
Try This
Evaluate
5
9
5
9
41
36
– h for h
–7
= 12
.
–
–7
12
Substitute
+
7
12
5
9
5 4
9 4
20
36
5
9
+
+
or
7 3
12 3
21
36
5
1 36
–
–7
12
=
–7
12
5
9
for h.
7
+ 12
Multiply by fractions equal to 1.
Rewrite with lowest common
denominator (36).
Simplify.
Example: Consumer Application
Two dancers are making necklaces from ribbon
for their costumes. They need pieces measuring
3
7
13 4 inches and 12 8 inches. How much ribbon
will be left over after the pieces are cut from a
36-inch length?
Subtract both amounts
3
7
36 – 12 8 – 13 4
from 36 to find the
amount of ribbon left.
Write as improper
288
103 55
– 8 –4
8
fractions. The LCD is 8.
Rewrite with a common
110
288
103
– 8 – 8
denominator. Simplify.
8
75
,
8
or 9 38
3
There will be 9 8 inches left.
Try This
Fred and Jose are building a tree house. They
5
need to cut a 6 3
foot
piece
of
wood
and
a
4
4
12
foot piece of wood from a 12 foot board. How
much of the board will be left?
12 –
144
12
–
3
64
27
4
144
81
–
12
4
10
,
12
or
5
6
–
5
412
– 53
12
–
53
12
Subtract both amounts
from 12 to find the
amount of board left.
Write as improper
fractions. The LCD is 12.
Rewrite with a common
denominator. Simplify.
5
There will be 6 inches left.
Lesson Quiz: Part 1
Add or subtract.
1.
5
1
+
14
7
2.
2
83
3.
3
5
1
12
1
76
–2 23
1
–2 15
–
+
1
2
4. Evaluate
3
18
– n for n =
9
.
16
13
16
Lesson Quiz: Part 2
1
62
inches tall. Judy is 5
5. Robert is 5 feet
3
feet 3 4 inches tall. How much taller is
Robert than Judy?
3
24
in.