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1-4
Adding and Subtracting with
Unlike Denominators
Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes
1-4
Adding and Subtracting with
Unlike Denominators
Warm Up
Add or subtract.
1. 1 35 + – 25
115
7
2. 3 11
12 – 2 12
1
13
3. 6.5 + (–1.2)
5.3
4. 3.4 – 0.9
2.5
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Adding and Subtracting with
Unlike Denominators
Problem of the Day
The least common multiple of 6 and a
number is 24. What is the other number?
8 or 24
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Adding and Subtracting with
Unlike Denominators
Learn to add and subtract fractions
with unlike denominators.
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Adding and Subtracting with
Unlike Denominators
Two hikers on the Appalachian Trail are
5
3
1
from
the trail ahead. The hikers walk 2 miles
4
8
before taking a break. They then hike
1
another 1 2 miles before taking a second
break. How many more miles do they have to
hike before reaching the summit?
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Adding and Subtracting with
Unlike Denominators
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).
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Adding and Subtracting with
Unlike Denominators
Additional Example 1A: Adding and Subtracting
Fractions with Unlike Denominators
Add or Subtract.
Method 1:
A. 1 + 2
7
8
2 8
1 7
+
7 8
8 7
7
16
23
=
+
56
56
56
Find a common
denominator: 8(7)=56.
Multiply by fractions
equal to 1.
Rewrite with a common
denominator.
Simplify.
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Adding and Subtracting with
Unlike Denominators
Additional Example 1B: Adding and Subtracting
Fractions with Unlike Denominators
Add or Subtract.
Method 2:
1
5
B. 1 6 – 1 8
7
– 13
8
6
7 4
– 13 3
8 3
6 4
11
28
39
=
–
– 24
24
24
Write as improper fractions.
List the multiples of each
denominator and find the LCD
Multiples of 6: 6; 12; 18; 24; 30
Multiples of 8: 8; 16; 24; 32
Multiply by fractions equal to 1.
Rewrite with a common
denominator. Simplify.
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Adding and Subtracting with
Unlike Denominators
Check It Out: Example 1A
Add or Subtract.
Method 1:
5
1
A.
+
8
3
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.
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Adding and Subtracting with
Unlike Denominators
Check It Out: Example 1B
Add or Subtract.
Method 2:
1
B. 2 6
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.
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Adding and Subtracting with
Unlike Denominators
Additional Example 2: 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 t.
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Adding and Subtracting with
Unlike Denominators
Check It Out: Example 2
Evaluate
5
9
5
9
– h for h =
–7
.
12
–
–7
12
Substitute
+
7
12
5
9
5 4
9 4
20
36
5
9
+
+
7 3
12 3
21
36
41
or 1 5
36
36
–
–7
12
=
–7
12
5
9
for h.
7
+ 12
Multiply by fractions equal to 1.
Rewrite with lowest common
denominator (36).
Simplify.
Adding and Subtracting with
1-4 Unlike Denominators
Additional Example 3: Consumer Application
Two dancers are making necklaces from ribbon
for their costumes. They need pieces measuring
13 3 inches and 12 7 inches. How much ribbon
8
4
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.
288
103
–
8
8
75
,
or 9 3
8
8
–
110
8
Rewrite with a common
denominator. Simplify.
3
There will be 9 8 inches left.
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Adding and Subtracting with
Unlike Denominators
Check It Out: Example 3
Fred and Jose are building a tree house. They
need to cut a 6 3 foot piece of wood and a 4 5
4
12
foot piece of wood from a 12 foot board. How
much of the board will be left?
Subtract both amounts
3
5
12 – 6 4 – 4 12
from 12 to find the
amount of board left.
144
12
–
27
4
144
81
–
12
12
10
,
or 5
12
6
– 53
12
–
53
12
Write as improper
fractions. The LCD is 12.
Rewrite with a common
denominator. Simplify.
5
There will be 6 foot left.
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Adding and Subtracting with
Unlike Denominators
Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems
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Adding and Subtracting with
Unlike Denominators
Lesson Quiz
Add or subtract.
1.
5
1
+
14
7
2.
2
83
3.
3
5
–
1
2
1
12
7
1
6
1
+ –2 23
–2 15
9
4. Evaluate 1 38 – n for n = 16
.
1
62
13
16
inches tall. Judy is 5
5. Robert is 5 feet
feet 3 34 inches tall. How much taller is
3
Robert than Judy? 2 4 in.
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Adding and Subtracting with
Unlike Denominators
Lesson Quiz for Student Response Systems
1. Add.
7 + 1
6
12
A. 1
2
C. 1 1
3
B. 3
4
D. 1 1
2
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Adding and Subtracting with
Unlike Denominators
Lesson Quiz for Student Response Systems
2. Subtract.
83 – 61
4
4
A. 2 1
2
C. 3
B. 2 3
4
D. 3 1
4
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Adding and Subtracting with
Unlike Denominators
Lesson Quiz for Student Response Systems
3. Add or subtract.
8 + –3 1
2
9
A. –2 11
18
C. 2 1
3
B. –2 1
3
D. 2 4
9
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Adding and Subtracting with
Unlike Denominators
Lesson Quiz for Student Response Systems
4. Evaluate 1
5
1
– x for x =
.
14
7
A. 1
C. 11
14
B. 13
14
D.
9
14
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Adding and Subtracting with
Unlike Denominators
Lesson Quiz for Student Response Systems
1
5. A pine tree is 20 feet 3 inches tall.
4
3
Another pine tree is 20 feet 5 4 inches tall.
How much taller is the second pine tree
than the first?
A. 2 1 in.
C. 3 1 in.
4
4
B. 2 1 in.
2
D. 3 1 in.
2