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Addition and Subtraction of Fractions Worksheets
Finding the LEAST COMMON DENOMINATOR (LCD)
When adding and subtracting fractions, there must be a common
denominator so that the fractions can be added or subtracted. Common
denominators are the same number on the bottom of fractions.
There are several methods for finding the common denominator. The
following is one in which we will find the least common denominator or
LCD. Each set of fractions has many common denominators; we will find
the smallest number that one or both fractions will change to.
Ex. Suppose we are going to add these fractions: 1  2
2 3
Step 1: Start with the largest of the denominators
Ex: 3 is the largest
Step 2: See if the other denominator can divide into the largest
without getting a remainder. If there is no remainder, then you have
found the LCD!
Ex. 3 divided by 2 has a remainder of 1
Step 3: If there is a remainder, multiply the largest denominator by
the number 2 and repeat step 2 above. If there is no remainder, then
you have found the LCD! If there is a remainder, keep multiplying the
denominator by successive numbers (3, 4, 5, etc.) until there is no
remainder. This process may take several steps but it will eventually
get to the LCD.
Ex. 3 x 2 = 6; 2 divides evenly into 6; therefore, 6 is the
LCD.
11
2 4
Step 1: 4 is the largest denominator
Step 2: 4 divided by 2 has no remainder, therefore 4 is the LCD!
Ex. 1:
11
5 6
Step 1: 6 is the largest denominator
Ex. 2:
Step 2: 6 divided by 5 has a remainder.
Multiply 6 x 2 = 12.
12 divided by 5 has a remainder
6 x 3 = 18.
18 divided by 5 has a remainder
6 x 4 = 24
24 divided by 5 has a remainder
6 x 5 = 30
30 divided by 5 has NO remainder, therefore 30 is the LCD!
Note: You may have noticed that multiplying the denominators
together also gets the LCD. This method will always get a common
denominator but it may not get a lowest common denominator.
Exercise 1
Using the previously shown method, write just the LCD for the
following sets of fractions (Do Not Solve)
1 1
2 2
5 1
1)
2)
3)
,
,
,
2 3
5 3
8 2
4)
1 1
,
4 3
5)
1 2
,
7 5
6)
4 1
,
9 3
7)
3 1
,
4 2
8)
7 3
,
8 5
9)
3 2
,
10 3
10)
13 4
,
15 5
11)
1 2 5
, ,
2 3 6
12)
3 5 7
, ,
4 8 16
13)
3 1 1
, ,
8 6 3
14)
1 1 1
, ,
7 2 3
15)
3 1 1
, ,
8 5 3
Getting equivalent Fractions and Reducing Fractions
Once we have found the LCD for a set of fractions, the next step is to
change each fraction to one of its equivalents so that we may add or
subtract it.
An equivalent fraction has the same value as the original fraction…it
looks a little different!
Here are some examples of equivalent fractions:
1 2
1 3
1 4
1 5
…etc.




2 4
2 6
2 8
2 10
2 4
2 6
2 8
2 10
…etc.




3 6
3 9
3 12
3 15
An equivalent fraction is obtained by multiplying both the numerator
and denominator of the fraction by the same number. This is called
BUILDING.
Here are some examples:
5x3 15
5 and 8 were both multiplied by 3

8x3 24
7x2 14

12x2 24
7 and 12 were both multiplied by 2
1x17 17

3x17 51
1 and 3 were both multiplied by 17
Note: the numbers used to multiply look like fraction versions of 1.
An equivalent fraction can also obtained by dividing both the
numerator and denominator of the fraction by the same number. This
is called REDUCING.
Here are some more examples:
10  2 5
10 and 12 were both divided by 2

12  2 6
84 2

12  4 3
8 and 12 were both divided by 4
200  25 8

225  25 9
200 and 225 were both divided by 25
Exercise 2
Find the number that belongs in the space by building or reducing
equivalent fractions.
2
5
1
2)
3)



1)
3 15
6 12
2 10
4)
3

4 12
5)
2

5 20
6)
5

7 21
7)
3

6 2
8)
6

8 4
9)
8

10 5
10)
12

24 2
11)
5

30 6
12)
7

14 2
13)
2

7 35
14)
7

42 6
15)
10

15 3
16)
1

8 24
17)
1

3 24
18)
20

22 11
19)
21

42 2
20)
17

51 3
21)
10

30 3
Simplifying Improper Fractions
An improper fraction is one in which the numerator is larger than the
denominator. If the answer to an addition, subtraction, multiplication,
or division fraction is improper, simplify it and reduce if possible.
Ex. 1: 4 is an improper fraction. Divide the denominator into
3
numerator.
1
3 4  11
3
3
1
10
Ex. 2:
is an improper fraction. Divide to simplify. Reduce.
8
1
10  8 10  1 2  1 1
8
8 8 4
2
Ex. 3:
136
is an improper fraction. Divide to simplify. Reduce.
20
6
136  20 136  6 16  6 4
20
20
5
 120
16
Exercise 3
Simplify the following fractions. Reduce if possible.
6
5
7
1)
=
2)
=
3)
=
5
4
3
4)
10
=
6
5)
4
=
2
6)
6
=
4
7)
15
=
3
8)
20
=
12
9)
19
=
4
10)
23
=
5
11)
18
=
3
12)
17
=
5
13)
37
=
9
14)
28
=
8
15)
47
=
9
16)
106
=
4
17)
17
=
2
18)
140
=
20
19)
162
=
10
20)
38
=
5
21)
52
=
3
Adding and Subtracting of Fractions
When adding or subtracting, there must be a common denominator. If
the denominators are different:
(a) Write the problem vertically (top to bottom)
(b) Find the LCD
(c) Change to equivalent fractions (by building)
(d) Add or subtract the numerators (leave the denominators the same)
(e) Simplify and reduce, if possible
Ex. 1:
3
1
4
The denominators are the same. Add the numerators, keep
5 5 5
the denominator. This fraction cannot be simplified or reduced.
1 2

2 4
1 1
1 1
Ex. 2:   ?  
4 4
2 4


3
5
Ex. 3:
5
8

1
3
?

8
1
3


4
The denominators are different
numbers. Therefore, change to
15
See page 3
equivalent fractions.
24
8
24
7
24
2
Ex. 4:
2
3

3
4
?

3
3
4


8
12
9
12
17
Ex. 5:
11
15

1
3
?
1
12
11 11

15 15
1
5


3
15
6
15

5
12
2
5
Simplifying and reducing
completes addition and
subtraction problems.
See page 5
Exercise 4
Add or subtract the following fractions. Simplify and reduce when
possible.
2 3
9
1
1 3
1)  
2)
3)  


14 14
6 6
7 7
4)
3 1
 
5 4
5)
2 1
 
3 2
6)
4 1
 
5 2
7)
2 3
 
4 6
8)
5 3
 
6 8
9)
7 2
 
9 3
10)
3 1
 
4 2
11)
3 1
 
5 3
12)
7 2
 
8 3
13)
5 1
 
12 4
14)
9 1
 
11 2
15)
11 5
 
12 6
16)
1 1
 
2 3
17)
5 1
 
6 4
18)
9 1
 
10 3
19)
8 1
 
20 5
20)
14 1
 
15 6
21)
4 3
 
7 8
22)
6 1
 
12 2
23)
8 2
 
9 3
24)
12 5
 
16 8
25)
3 1
 
7 6
26)
4 6


5 10
27)
2 2
 
13 3
Adding and subtracting mixed numbers
A mixed number has a whole number followed by a fraction:
1
5
1
6
1 , 2 , 176 , and 8 are examples of mixed numbers
3
8
2
7
When adding or subtracting mixed numbers, use the procedure from
page 7. Note: Don’t forget to add or subtract the whole numbers.
1
1
1
Ex. 1: 1  2  ?
Ex. 2: 6  5  ?
2
3
8
1
1
3
6
1 1
8
2
6
 5
1
2
 2 2
3
6
1
11
5
8
3
6
1 3
Ex. 3: 5   ?
3 5
1
5
5 5
3
15
3
9


5
15
14
5
15
6
1
Ex. 4: 3  1  ?
9
2
6
12
3 3
9
18
1
9
1
1
2
18
3
1
2 2
18
6
When mixed numbers cannot be subtracted because the bottom
fraction is larger than the top fraction, BORROW so that the
fractions can be subtracted from each other.
The 2 cannot be
6
3
1
1
Ex. 5: 8 - 2  ?
Ex. 6: 5  2  ?
subtracted from the 1 .
4
6
3
6
4
4
3
3
 2 2
4
4
1
5
4
8
7
The 3
cannot be
4
subtracted from nothing.
One was borrowed from the
8 and changed to 4 . 8
4
was changed to a 7.Now the
mixed numbers can be
subtracted from each other.
1
1
7
 5  4
6
6
6
1
2
2
 2 2  2
3
6
6
5
2
6
5
One was borrowed from
the 5, changed to 6
6
and then added to the
1 to make 7 . The
6
6
whole number 5 was
changed to a 4. Now the
mixed numbers can be
subtracted.
Exercise 5
Add or subtract the following mixed numbers. Simplify and reduce
when possible.
2 3
4
1
5 11
1) 8  8 =
3) 16  =
2) 1  =
3 7
5
10
8 12
11 2
 =
12 3
1
6) 4  1 =
8
4 2
11
4) 3  6  5 =
5 3 15
5) 1
1
1
7) 5  2 =
6 3
1
1
8) 14  2 =
2 8
2 1
9) 7  1 =
5 5
2 1
10) 2  =
3 4
1
2
11) 12  8 =
7
3
4
6
12) 4  3 =
7
7
5
1
13) 16  2 =
6 3
1
14) 14  2 =
9
1
15) 146 8 =
5
5 10
16) 5  =
6 12
7
17) 6 4 =
8
3
18) 11  5 =
5
4 2
20) 2  1 =
8 3
3
21) 100 4 =
8
19)
2
7=
3
Fraction Word Problems (Addition/Subtraction)
When solving word problems, make sure to UNDERSTAND THE
QUESTION. Look for bits of information that will help get to the
answer. Keep in mind that some sentences may not have key words or
key words might even be misleading. USE COMMON SENSE when
thinking about how to solve word problems. The first thing you think of
might be the best way to solve the problem.
Here are some KEY WORDS to look for in word problems:
Sum, total, more than: mean to add
Difference, less than, how much more than: mean to subtract
Ex. 1: If brand X can of beans weighs 15 1 ounces and brand Y weighs
2
3
12 ounces, how much larger is the brand X can?
4
1
2
6
15  15  14
2
4
4
3
3
3
 12  12  12
4
4
4
3
2
4
means to subtract
Borrow from the
whole number and
add to the fraction
Ex. 2: Find the total snowfall for this year if it snowed
November, 2
1
inch in
10
1
3
inches in December and 1 inches in January.
3
4
means to add
1
6

10
60
1
20
2 2
3
60
3
45
 1 1
4
60
71
11
3
4
60
60
Simplify.
Exercise 6
Solve the following add/subtract fraction word problems
7
3
1. Find the total width of 3 boards that 1 inches wide,
inch
4
8
1
wide, and 1 inches wide.
2
5
3
inches wide and a 7.15C tire is 4 inches
8
4
wide. What is the difference in their widths?
2. A 7.15H tire is 6
3. A patient is given 1
1
teaspoons of medicine in the morning and
2
1
teaspoons at night. How many teaspoons total does the
4
patient receive daily?
2
1
1
feet are cut off a board that is 12 feet long. How long is
4
3
the remaining part of the board?
4. 3
5.
3
1
of the corn in the U.S. is grown in Iowa.
of it is grown in
8
4
Nebraska. How much of the corn supply is grown in the two
states?
1
1
2
miles east, 5 miles south, and 8 miles west.
3
5
4
How far has she jogged?
6. A runner jogs 7
1
1
ounce of cough syrup is used from a 9 ounce bottle, how
4
2
much is left?
7. If 3
8. I set a goal to drink 64 ounces of water a day. If I drink 10
1
3
5
1
ounces at noon, and 20 ounces at
6
2
dinner, how many more ounces of water do I have to drink to
reach my goal for the day?
ounces in the morning, 15
9. Three sides of parking lot are measured to the following lengths:
1
3
1
108 feet, 162 feet, and 143 feet. If the distance around the
4
8
2
15
lot is 518 feet, find the fourth side.
16
10. Gabriel wants to make five banners for the parade. He has 75
1
feet of material. The size of four of the banners are: 12 ft.,
3
1
1
3
16 ft., 11 ft., and 14 ft. How much material is left for the
6
4
2
fifth banner?
Exercise 1
Exercise 2
1) 6
1) 5
2) 15
2) 10
3) 8
3) 10
4) 12
4) 9
5) 35
5) 8
6) 9
6) 15
7) 4
7) 1
8) 40
8) 3
9) 30
9) 4
10) 15
10) 1
11) 6
11) 1
11) 6
12) 16
12) 1
12)
13) 24
13) 10
13)
14) 42
14) 1
14)
15) 120
15) 2
15)
16) 3
16)
17) 8
17)
18) 10
18) 7
19) 1
19)
16 1
20) 1
20)
73
21) 1
Exercise 3
1
1) 1
5
1
2) 1
4
1
3) 2
3
2
4) 1
3
5) 2
6)
1
7) 5
1
2
2
3
3
9) 4
4
10) 4 3
8)
Exercise 4
5
1)
7
5
2)
7
2
3)
3
17
4)
20
1
5) 1
6
3
6) 1
10
7)
1
8)
9)
5
10)
11)
32
5
1
4
9
1
3
2
52
9
26 1
2
81
2
12)
13)
14)
15)
16)
17)
18)
5
19)
5
21) 17 1
3
20)
21)
1
5
24
4
1
9
1
4
4
15
5
24
1
6
7
22
1
12
1
6
7
12
17
30
3
5
23
30
11
56
1
22) 1
23) 2
9
3
24) 1
8
25) 11
42
26) 1
5
27) 32
39
Exercise 5
9
1) 16
10
2
2) 2
21
13
3) 17
24
1
4) 16
5
1
5) 1
4
1
6) 3
8
5
7) 2
6
3
8) 12
8
3
9) 8
5
10) 2 5
12
11) 310
21
5
12)
7
13) 14 1
2
8
14) 11
9
15) 154 1
5
16) 62
3
17) 1 1
8
18) 63
5
19) 7 2
3
20) 4 1
6
21) 955
8
Exercise 6
1
1) 4 inches
8
7
2) 1 inches
8
3
3) 3 teaspoons
4
11
4) 8
feet
12
5
5)
8
7
6) 21
miles
60
3
7) 5 ounces
4
1
8) 17 ounces
3
13
9) 104
feet
16
10) 20 1 ft.
4