Transcript 4.4 – Adding and Subtracting Like Fractions Adding and Subtracting 1. The denominators can not equal zero ( fraction would be undefined). 2.

4.4 – Adding and Subtracting Like Fractions
Adding and Subtracting
1. The denominators can not equal zero ( fraction would be
undefined).
2. Denominators must be the same.
3. Numerators may be added or subtracted if the values of the
denominators are the same (common denominator).
4. The denominators are not added or subtracted to each other.
8
3
5 35



11
11
11 11
13 2 13  2 11



15
15
15 15
4.4 – Adding and Subtracting Like Fractions
Adding and Subtracting
26
20 6 20  6



 2
13
13
13 13
5 1
6
3
5
1




8x
8x
4x
8x 8x
5
11 6 11  6



12
12
12 12
8
4
8 4
4




17 17
17
17
4.4 – Adding and Subtracting Like Fractions
Adding and Subtracting
2 7y
2 7y


5
5
5
463 23
5
4
6
3

 
 

11
11
11
11 11 11
10
5
Evaluate x  y, if x  
and y 
.
12
12
5
10 5  10  5




12
12 12
12
4.4 – Adding and Subtracting Like Fractions
Adding and Subtracting
Find the perimeter of a square if the
3
length of the sides is
of a mile.
20
3  3  3  3 12
3
3
3
3
3
mile






20
20
5
20 20 20 20
4.4 – Adding and Subtracting Like Fractions
Adding and Subtracting
13
As part of a training routine, an athlete ran
miles
4
11
on Monday and
miles on Wednesday. How much
4
further did he run on Monday than on Wednesday ?
2
1
13 11
13  11
mile




4
2
4
4
4
4.4 – Adding and Subtracting Like Fractions
Least Common Denominator - LCD
The Least Common Denominator of a list of fractions is the
smallest positive number that is divisible by all denominators
from the list.
The Least Common Denominator is also the Least Common
Multiple.
To find the LCD, review the multiples of the largest denominator
and select the first one that is divisible by all denominators.
Find the LCD of the following fractions.
1 3
,
4 7
LCD 28
13 19
,
25 30
LCD 150
4.4 – Adding and Subtracting Like Fractions
Least Common Denominator - LCD
Find the LCD of the following fractions.
3 5 3
, , LCD 24
4 6 8
2
8
6
4
2
22
2
2,3
3
2
4
2
2
23
LCD:
23  3  8  3  24
4.4 – Adding and Subtracting Like Fractions
Least Common Denominator - LCD
Find the LCD of the following fractions.
7 13 11
,
,
20 24 45
2
10
2
2
45
24
20
5
3
12
3
6
2
5
32 ,5
2
2 ,5
15
2
3
3
2 ,3
3
2
LCD: 2  3  5  8  9  5  360
4.4 – Adding and Subtracting Like Fractions
Least Common Denominator - LCD
Find the LCD of the following fractions.
1 3 5
, ,
2 y 7
LCD: 14 y
4.4 – Adding and Subtracting Like Fractions
Equivalent Fractions
Given a fraction, find the equivalent fraction with the stated
denominator.
7

8 56
3x

7
42
7 7

8 7
3x 6

7 6
49
56
18x
42
1

4 20
9

4 x 36 x
1 5

4 5
5
20
9 9

4x 9
81
36 x
4.5 – Adding and Subtracting Unlike Fractions
Adding and Subtracting
1. Find the LCD of the fractions.
2. Write each fraction as an equivalent fraction with the LCD
as the denominator.
3. Add or subtract the like fractions.
4. Simplify the answer.
2 8
LCD : 21

7 21
2 3 8
6
8
2
14
 




7 3 21 21 21 21
3
4.5 – Adding and Subtracting Unlike Fractions
Adding and Subtracting
Add or subtract the following fractions.
5 9

7 10
LCD : 70
5 10 9 7


 
7 10 10 7
50 63


70 70
13

70
4.5 – Adding and Subtracting Unlike Fractions
Adding and Subtracting
Add or subtract the following fractions.
5 1 1
 
8 3 12
LCD : 24
5 3 1 8 1 2
15
8
2 15  8  2
   
 




8 3 3 8 12 2
24 24 24
24
72

24
5
24
4.5 – Adding and Subtracting Unlike Fractions
Adding and Subtracting
Add or subtract the following fractions.
y
5
4
LCD : 4
5 4 y
20 y
20  y
  
 
1 4 4
4
4
4
4.5 – Adding and Subtracting Unlike Fractions
Comparing Fractions
Insert < or > to create a true statement.
5
8
11
20
LCD : 40
5 5

8 5
25
40
11 2

20 2
22
40
25 22

40 40
4.5 – Adding and Subtracting Unlike Fractions
Comparing Fractions
Insert < or > to create a true statement.
17

20
4

5
LCD : 20
17

20
4 4
 
5 4
17

20
16

20
17
16


20
20