CCBC Math 081
Addition of Fractions and of Mixed Numbers
Section 3.4
Third Edition
23 pages
3.4 Addition of Fractions and Mixed Numbers
Recall that in order to add or subtract two things, they have to be the same type of thing. That is,
you can add two apples to five apples and get seven apples, but you cannot add two apples and
five pears and say that you have seven apples or seven pears. Unless you call both of them fruit,
they can’t be added. This principle applies to fractions as well. You cannot add or subtract two
fractions unless they have the same denominator since the denominator labels or defines the
name of the whole. You add the numerators and keep the “name” that is in the denominator.
1 3
 , you are adding 1 eighth and 3 eighths and the resulting
8 8
1 3 4
sum would be 4 eighths. Numerically, that would be written as
 .
8
8
Sometimes, you will need to reduce the fractional sum to lowest terms after you finish adding. In
4
2 2
2 2
1
4

 .
this example we have the answer which can be reduced. As 
8 2 2 2 2 2  2 2
8
For example, if you are adding
Let’s illustrate this same problem visually with the following situation.
After a party, you are cleaning up and find two partly eaten pizzas in their boxes. One has only 1
1
3
out of 8 pieces left   , and the other has 3 out of 8 pieces left   . You combine them
8
8
together and would like to express how much pizza you have left. You would do this by adding.
1
8


4 1

8 2
188
3
8
CCBC Math 081
Addition of Fractions and of Mixed Numbers
Section 3.4
Third Edition
23 pages
Note: When working with fractions, always simplify your final answer by dividing out common
factors in the numerator and denominator.
Adding Fractions with Like (the Same) Denominators
Example 1:
Add:
2 5
+
8 8
2 5 25
 
8 8
8

First check: Are denominators the same? Yes, they are.
Add the numerators together and keep the common
denominator. Check to see if the answer can be reduced
(it is already simplified in this example).
7
8
Watch it:
3 2

7 7
http://youtu.be/JwfjsO1EqnM
Example 2:
Add:
Practice 1:
Add:
Answer:
5
7
5 9

11 11
5 9 59
 
11 11 11

First check: Are denominators the same? Yes, they are.
Add the numerators together and keep the common
denominator. Check to see if the answer can be reduced
(it is already simplified in this example). This is the
answer as an improper fraction.
14
11
To write as a mixed number, divide the denominator into the numerator.
Whole number part
1
Denominator  11 14
11
3
 1
3
11
This is the answer as a mixed
Numerator
number.
Practice 2:
Watch it:
7 4

9 9
http://youtu.be/sPpdL1HtJBI
Add:
Answer:
189
11
2
1
9
9
CCBC Math 081
Addition of Fractions and of Mixed Numbers
Section 3.4
Third Edition
Example 3:
23 pages
Add:
4 7
+
11 11
4 7 47
 
11 11
11
11
11

1
Practice 3:
Add:
First check: Are denominators the same? Yes, they are.
Add the numerators together and keep the common
denominator.
The answer can be reduced. Rewrite this improper
fraction as a whole number.
5 1

6 6
Answer:
Watch it:
http://youtu.be/-zqWJowbjyg
Example 4:
Add:
5 7
+
8 8
5 7 57
 
8 8
8
Watch it:
First check: Are denominators the same? Yes, they are.

12
8
Add the numerators together and keep the common
denominator. Check to see if the answer can be reduced

3 4
2 4
Factor the numerator and denominator.

3 4
2 4
Divide out common factors in the numerator and
denominator.

3
2
This is the answer as an improper fraction.
1
Practice 4:
1
1
2
This is the answer as a mixed number.
5 9

6 6
http://youtu.be/I7nDCWySo90
Add:
Answer:
190
7
1
2
3
3
CCBC Math 081
Addition of Fractions and of Mixed Numbers
Section 3.4
Third Edition
23 pages
Example 5:
Add:
2 4

9
9
2 4 2  (4)


9
9
9
6

9
Practice 5:
Add:
Watch it:
First check: Are denominators the same? Yes, they
are.
Add the numerators together and keep the common
denominator. Check to see if the answer can be
reduced

2  3
3 3
Factor the numerator and denominator.

2  3
3 3
Divide out common factors in the numerator and
denominator.

2
2

3
3
Your answer can be written in either form.
1 2

6
6
Answer:

1
2
http://youtu.be/GEGjLCbYk-k
FRACTIONS AND NEGATIVE

a a
a


b
b b
a a

b b
If only the numerator is negative or only the
denominator is negative, the fraction is negative.
If both the numerator and the denominator are
negative, the fraction is positive.
Addition with Mixed Numbers
When one or both of the fractions are mixed numbers, there are two different ways that you can
perform that addition. Each method has advantages and disadvantages, but when done correctly
either method will bring you to the same answer. You should choose the method you are most
comfortable with using and use it all of the time.
Method 1: In the first method for adding mixed numbers, you keep the mixed numbers in that
form. You add the fractional parts together, add the whole numbers together, and simplify the
answer if necessary. The advantage to this method is that the numbers you are working with
remain small. Always make sure that your final mixed number answer does not have an
improper fraction in it.
191
CCBC Math 081
Addition of Fractions and of Mixed Numbers
Section 3.4
Third Edition
Example 6:
23 pages
1
2
Add: 6 + 4
5
5
6
4
6
4
1
5
2
5
1
5
2
5
3
5
1
5
2
4
5
3
10
5
Set up the problem vertically as shown.
First, add the fractional parts. They have a common
denominator, so add the numerators and keep the common
denominator.
6
Practice 6:
Watch it:
Now add the whole numbers together. Write the resulting
mixed number; reduce the fraction to lowest terms, if
necessary
2
1
Add: 5  3
7
7
Answer:
http://youtu.be/x58K5JqRvEQ
192
8
3
7
CCBC Math 081
Addition of Fractions and of Mixed Numbers
Section 3.4
Third Edition
Example 7:
23 pages
5
6
Add: 2 + 1
7
7
5
2
7
6
1
7
Set up the problem vertically as shown.
5
7
6
1
7
11
7
First, add the fractional parts. They have a common
denominator, so add the numerators and keep the common
denominator.
5
7
6
1
7
11
3
7
Now add the whole numbers together. Write the resulting
mixed number; reduce the fraction to lowest terms, if
necessary
2
2
3
11
11
 3
7
7
4
 3 1
7
4
4
7
11
as a mixed number by dividing 11 by 7, and
7
add the result to the whole number 3.
Rewrite
Note: Remember how to change an improper fraction to a mixed number.
Divide the denominator into the numerator.
Whole number part
1
Denominator  7 11
7
4

1
4
7
Numerator
Practice 7:
Watch it:
4
3
Add: 4  2
5
5
Answer:
http://youtu.be/ZBpS2ofrnHw
193
7
2
5
CCBC Math 081
Addition of Fractions and of Mixed Numbers
Section 3.4
Third Edition
23 pages
 7
 5
Add:   3    1 
 8
 8
We are adding two negative numbers. Therefore we will use the SSS (same, sum, same)
Method because the signs are the same. We will add (sum) the absolute value of the numbers
and then keep the sign the same. The answer will be negative.
7
3
8
Add the absolute value of the 2 negative numbers. Set
5
up the problem vertically as shown.
1
8
Example 8:
7
8
5
1
8
12
8
First, add the fractional parts. They have a common
denominator, so add the numerators and keep the
common denominator.
7
8
5
1
8
12
4
8
Now add the whole numbers together. Write the
resulting mixed number; reduce the fraction to lowest
terms, if necessary.
3
3
4
12
12
 4
8
8
4
 4 1
8
4
5
8
1
5
2
1
 7
 5
  3    1   5
2
 8
 8
Practice 8:
Watch it:
12
as a mixed number by dividing 12 by 8,
8
and add the result to the whole number 4.
Rewrite
Simplify the fraction part by dividing out common
factors in the numerator and denominator.
Remember the last step of the SSS Method is to keep
the sign of the original same signed numbers. So the
answer is negative.
 3
 1
Add:   2     5 
 4
 4
Answer:
http://youtu.be/woSjs6qOzk0
194
-8
CCBC Math 081
Addition of Fractions and of Mixed Numbers
Section 3.4
Third Edition
23 pages
Method 2: In the second method, change the mixed numbers to improper fractions, add the
fractions together, and rewrite the sum in mixed number form, reducing the fractional part to
lowest terms (if necessary). The problems below are the same as the ones done using Method 1
so that you can compare the two methods.
Example 9:
1
2
Add: 6 + 4 (using Method 2)
5
5

(5  6)  1 (5  4)  2

5
5
=
31 22
+
5
5
=
31+ 22 53
=
5
5
3
= 10
5
Rewrite each mixed number as an improper
fraction.
Since the denominators are the same, add the
numerators.
Rewrite the improper fraction as a mixed number
by dividing 53 by 5. Check to see if the proper
fraction can be reduced. In this example it is
already simplified.
Practice 9:
2
1
Add: 5  3 (using Method 2)
7
7
Watch it:
http://youtu.be/L7Q7RAba-1I
Answer:
59
3
8
7
7
5
6
Example 10: Add: 2 + 1 (using Method 2)
7
7

(7  2)  5 (7 1)  6

7
7
=
19 13
+
7 7
=
19 + 13 32
=
7
7
Rewrite each mixed number as an improper
fraction.
Since the denominators are the same, add the
numerators.
Rewrite the improper fraction as a mixed number
by dividing 32 by 7. Check to see if the proper
fraction can be reduced. In this example it is
already simplified
4
3
37
2
Practice 10: Add: 4  2 (using Method 2)
Answer:
7
5
5
5
5
4
=4
7
Watch it:
http://youtu.be/i67htU8wrxU
195
CCBC Math 081
Addition of Fractions and of Mixed Numbers
Section 3.4
Third Edition
23 pages
 7
 5
Example 11: Add:   3    1 
 8
 8
(using Method 2)
 (8  3)  7 
 (8 1)  5 
 
  
 Rewrite each mixed number as an improper
8
8



 fraction.
 31 
 13 
     
8
8

31 13

8
8

 31   13   44
8
Since the denominators are the same, add the
numerators together using the SSS Method.
8
Rewrite the improper fraction as a mixed
number by dividing 44 by 8. Check to see if
the proper fraction can be reduced.
 44 
 4
    5 
 8 
 8
 5
44
1
 5
84
2
Reduce the fractional part.
 3
 1
Practice 11: Add:   2     5  (using Method 2)
 4
 4
Watch it:
Answer:
-8
http://youtu.be/nsq5jqDN9n0
As you can see, comparing Example 6 with Example 9, Example 7 with Example 10, and
Example 8 with Example 11, the answer is the same—whether you use Method 1 or Method 2.
Adding Fractions and Whole Numbers
Sometimes, one of the numbers in the problem is a whole number, while the other number is a
fraction or a mixed number.
Example 12: Add:
3
+2
4
The mixed number 2
3
3
means 2 +
4
4
3
3
3
3
+ 2 is equal to 2 + , it follows that + 2 = 2 .
4
4
4
4
196
CCBC Math 081
Addition of Fractions and of Mixed Numbers
Section 3.4
Third Edition
23 pages
Practice 12: Add:
Watch it:
5
6
8
Answer:
6
5
8
http://youtu.be/pd2K76NoTd4
Sometimes, mixed numbers are added to whole numbers. When this situation occurs, add the two
whole numbers together and add the fraction to that sum.
Example 13: Add: 1+ 5
= 1+ 5 +
= 6+
=6
3
4
Add the whole numbers together.
3
4
3
4
Practice 13: Add: 3  2
Watch it:
3
4
Write the mixed number answer.
1
3
Answer:
5
1
3
http://youtu.be/dF5UVIqmhNY
Adding Fractions with Different Denominators
Recall that you can add (or subtract) fractions only if they have the same denominator. Thus, in
order to add two fractions with different denominators, you must first rewrite each fraction using
a common denominator. In order to do this, you will need to determine what that common
denominator is and find an equivalent expression for each of the fractions using that common
denominator.
Finding Common Denominators
A common denominator is a number that both of the denominators can divide into without any
remainder; such a number is also known as a common multiple of the two denominators. You can
always find a common multiple between two numbers by multiplying them together. However,
the general practice when adding or subtracting fractions is to use the Least Common
Denominator (LCD) (the Least Common Multiple (LCM) of the two denominators).
Method 1: One way to find the Least Common Denominator (LCD) for two fractions is to
multiply the two denominators together and divide by their Greatest Common Factor (GCF).
197
CCBC Math 081
Addition of Fractions and of Mixed Numbers
Section 3.4
Third Edition
23 pages
2 1
+ , you can multiply 5  4  20 to get a common
5 4
denominator; 20 also happens to be the Least Common Denominator because the only number
that will evenly divide both 5 and 4 is 1 and 20 1  20 .
Example 14: If you are adding
1 1
 .
3 2
Answer: 6
Practice 14: Determine the Least Common Denominator in order to add
Watch it:
http://youtu.be/3kNoFGiv0Fc
1 1
+ , you can multiply 2  6  12 to get a common
2 6
denominator; however, 12 is not the Least Common Denominator. Looking at the denominators
2 and 6, we see that their greatest common factor is 2. So, if we divide 12 by 2 we get 12  2  6 .
Thus, the Least Common Denominator is 6.
Example 15: If you are adding
3 1
 .
5 10
Answer: 10
Practice 15: Determine the Least Common Denominator in order to add
Watch it:
http://youtu.be/zcX-n8Pxza0
5 7
+ , you can multiply 6  8  48 to get a common
6 8
denominator; however, 48 is not the Least Common Denominator. Looking at the denominators
6 and 8, we see that their Greatest Common Factor is 2. So, if we divide 48 by 2 we get
48  2  24 . Thus, the Least Common Denominator is 24.
Example 16: If you are adding
5 11
 ,
9 12
Answer: 36
Practice 16: Determine the Least Common Denominator in order to add
Watch it:
http://youtu.be/ePD7TRgGL7Y
Method 2: Another way to find the Least Common Denominator is to take the larger
denominator and look at its multiples (multiply it by 1, by 2, by 3, and so on) until one of the
answers is divisible by the other denominator with no remainder.
198
CCBC Math 081
Addition of Fractions and of Mixed Numbers
Section 3.4
Third Edition
23 pages
2 1
+ , the larger denominator is 5. Look at multiples of 5 until
5 4
you find one that 4 will also divide into evenly.
Example 17: If you are adding
5 1  5
5 is not evenly divisible by 4; try the next multiple.
5  2  10
10 is not evenly divisible by 4; try the next multiple.
5  3  15
15 is not evenly divisible by 4; try the next multiple.
5  4  20
20 is evenly divisible by 4 since 20  4 does not have a remainder.
This means that 20 is the Least Common Denominator for 5 and 4.
1 1
 ,
3 2
Answer: 6
Practice 17: Determine the Least Common Denominator in order to add
Watch it:
http://youtu.be/X98d6zpI8vg
1 1
+ , the larger denominator is 6. Look at multiples of 6 until
2 6
you find one that 2 will also divide into evenly.
Example 18: If you are adding
6 1  6
6 is evenly divisible by 2 since 6  2 does not have a remainder.
This means that 6 is the Least Common Denominator for 2 and 6.
3 1
 .
5 10
Answer: 10
Practice 18: Determine the Least Common Denominator in order to add
Watch it:
http://youtu.be/86fzDDjvASU
5 7
+ , the larger denominator is 8. Look at multiples of 8 until
6 8
you find one that 6 will also divide into evenly.
Example 19: If you are adding
8 1  8
8 is not evenly divisible by 6; try the next multiple.
8  2  16
16 is not evenly divisible by 6; try the next multiple.
8  3  24
24 is evenly divisible by 6 since 24  6 does not have a remainder.
This means that 24 is the Least Common Denominator for 6 and 8.
5 11
 .
9 12
Answer: 36
Practice 19: Determine the Least Common Denominator in order to add
Watch it:
http://youtu.be/H9X24IBkK7s
199
CCBC Math 081
Addition of Fractions and of Mixed Numbers
Section 3.4
Third Edition
23 pages
Finding Equivalent Fractions Using the Common Denominator
2 1
+
5 4
In Examples 14 and 17, we determined that the Least Common Denominator for these two
fractions is 20. So, we now need to determine an equivalent fraction with denominator 20 for
each of these fractions.
Example 20: Add:
2 1 2  4 1 5
 

5 4 5 4 4 5
Multiply the first fraction’s numerator and denominator
by 4. Multiply the second fraction’s numerator and
denominator by 5.

8
5

20 20
Simplify.

85
20
Add the numerators and keep the same denominator.

13
20
This fraction cannot be reduced.
1 1

3 2
http://youtu.be/UNktRGStPwk
Practice 20: Add:
Watch it:
Answer:
5
6
1 1
+
2 6
In Examples 15 and 18, we determined that the Least Common Denominator for these two
fractions is 6. So, we now need to determine an equivalent fraction with denominator 6 for each
of these fractions.
Example 21: Add:
1 1 1 3 1
 

2 6 23 6
Multiply the first fraction’s numerator and denominator by
3. The second fraction already has a 6 in the denominator.

3 1

6 6
Simplify.

3 1
6
Add the numerators and keep the same denominator.

4
6
This fraction can be reduced.
2 2
23
2 2 2


2 3 3

Factor the numerator and denominator.
Divide out common factors.
200
CCBC Math 081
Addition of Fractions and of Mixed Numbers
Section 3.4
Third Edition
23 pages
Practice 21: Add:
Watch it:
3 1

5 10
Answer:
7
10
http://youtu.be/bnZaii01a14
5 7
+
6 8
In Examples 16 and 19, we determined the Least Common Denominator for these two fractions
is 24. So, we now need to determine an equivalent fraction with denominator 24 for each of
these fractions.
Example 22: Add:
5 7 5 4 7  3
 

6 8 6 4 8 3
Multiply the first fraction’s numerator and
denominator by 4. Multiply the second
fraction’s numerator and denominator by 3.

20 21

24 24
Simplify.

20  21
24
Add the numerators and keep the same
denominator.

41
24
This fraction cannot be reduced.
1
17
24
This is the answer as a mixed number.
5 11

9 12
http://youtu.be/3z1z4YyoyKM
Practice 22: Add:
Watch it:
Example 23: Add:
Answer:
53
17
1
36
36
3 1
+
4 6
3 1
+
4 6
First check: Are denominators are the same? No.
Find the least common denominator for 4 and 6.
4  6  24  2  12
Method 1: Multiply the denominators together to
get 24. The greatest common factor for 4 and 6 is
2, so divide 24 by 2 to get the least common
denominator of 12.
Method 2: Look at multiples of 6 until you find
one that is evenly divisible by 4.
6 1  6
6 is not evenly divisible by 4, try the next multiple.
6  2  12
12 is evenly divisible by 4, so it is the least
common denominator.
201
CCBC Math 081
Addition of Fractions and of Mixed Numbers
Section 3.4
Third Edition
23 pages
Now that you know the least common denominator, set up equivalent fractions that
have a denominator of 12.
3 1 3  3 1 2
 

4 6 43 6 2
Multiply the first fraction’s numerator and
denominator by 3. Multiply the second
fraction’s numerator and denominator by 2.

9 2

12 12
Simplify.

92
12
Add the numerators and keep the same
denominator.

11
12
This fraction cannot be reduced.
1 5
Practice 23: Add: 
6 9
Watch it:
http://youtu.be/Ksohsk23YWQ
Answer:
13
18
Adding Mixed Numbers with Different Denominators
The process for adding mixed numbers is the same as before, but the fractional parts of mixed
numbers will not always start with a common denominator. This means that when you go to add
the fractions together, you need to find a least common denominator first and set up equivalent
fractions.
1
1
Example 24a: Add: 2 + 3 (using Method 1)
3 4
1
2
3
Set up the problem vertically as shown. Determine the
Least Common Multiple of the denominators. The
1
3
LCM(3, 4) = 12.
4
1 4
1
2
3 4
3

1 3
1
3
3
43
4
2
4
12
3
3
12
7
5
12
2
Write equivalent fractions with denominators of 12.
Multiply the first fraction’s numerator and denominator
by 4. Multiply the second fractions numerator and
denominator by 3.
First, add the fractional parts. They now have a common
denominator, so add the numerators and keep the common
denominator. Then, add the whole numbers together.
Write the resulting mixed number; reduce the fraction to
lowest terms, if necessary.
202
CCBC Math 081
Addition of Fractions and of Mixed Numbers
Section 3.4
Third Edition
23 pages
1
1
Practice 24a: Add: 3  5 (using Method 1)
5
6
Watch it:
Answer:
8
11
30
http://youtu.be/Dx_dBzRn_H0
1
1
Example 24b: Add: 2 + 3 (using Method 2)
3 4
(3  2)  1 (4  3)  1

3
4
Rewrite each mixed number as an improper fraction.

7
3

74
13  3

3 4
4 3
The least common denominator for 3 and 4 is 12. Rewrite
each improper fraction with denominator 12.

28
12
The denominators are the same; both are 12. Add the
fractions together.
=
13
4


39
12
28 + 39 67
=
12
12
=5
7
12
Convert the improper fraction to a mixed number by
dividing 67 by 12.
Note: Remember how to change an improper fraction to a mixed number. Divide the
denominator into the numerator.
Whole number part
5
Denominator  12 67
60
7

5
7
12
Numerator
1
1
Practice 24b: Add: 3  5 (using Method 2)
5
6
Watch it:
http://youtu.be/k9gLCuvvrao
203
Answer:
251
11
8
30
30
CCBC Math 081
Addition of Fractions and of Mixed Numbers
Section 3.4
Third Edition
23 pages
PERIMETER
Definition
Calculation
The perimeter of a
Perimeter is calculated
geometric shape is the
by adding the lengths of
distance around the shape.
all the sides of the shape.
a
d
b
c
Perimeter  a  b  c  d
Example 25: Determine the perimeter of the triangle below.
in
in
in
In order to determine the perimeter of the triangle we will add all of the sides.
Set up the problem in vertical form as shown.
4
5
3
2
5
1
1
5
8
4
5
1
All of the fractional parts have the same denominator.
Therefore, add the numerators and keep the same
denominator.
Then add the whole number parts
8
8
4  4
5
5
3
 4 1
5
5
3
in
5
The fraction part is an improper fraction. Therefore, we
must change the fraction part into a mixed number.
Add the whole numbers together. Include units in the
answer.
204
CCBC Math 081
Addition of Fractions and of Mixed Numbers
Section 3.4
Third Edition
23 pages
Practice 25: Determine the perimeter of the triangle below.
Watch it:
Answer:
22
1
7
3
3
http://youtu.be/-XxZ2GTy750
Example 26: Determine the median of the following data set.
1
4
7
2
8
6
,
,
,
,
,
13 13 13 13 13 13
1
2
4
6
7
8
,
,
,
,
,
13 13 13 13 13 13
Put the data in order from least to greatest.
1
2
,
,
13 13
There are 2 middle numbers.
4
,
13
6
7
8
,
,
13 13 13
4 6 10
 
13 13 13
Add the 2 middle numbers.
10
2
13
Divide this sum by 2.
10 2

13 1
Write the whole number as a fraction.
10 1

13 2
Change division to multiplication of the
reciprocal.
5
10 1

13 2 1
Divide out common factors in the numerator
and dominator.
5 1 5
 
13 1 13
Then multiply to find the median.
205
CCBC Math 081
Addition of Fractions and of Mixed Numbers
Section 3.4
Third Edition
23 pages
Practice 26: Determine the median of the following data set.
2
5
7
4
8
6
,
,
,
,
,
11 11 11 11 11 11
Watch it:
http://youtu.be/5appfNUrBrY
Answer:
1
2
Example 27: Determine the mean of the following data.
1
,
2
3 1
,
4 4
To determine the mean, we must add all of the numbers and divide by the number of numbers.
1 3 1
 
2 4 4
1 2 3 1 2 3 1
    
2 2 4 4 4 4 4
Write fractions with a common denominator.

6
4
Add the numerators. Keep the denominator.

62 3

42 2
Simplify the fraction by dividing by 2 in the
numerator and denominator.
After we determine the sum of all the data, we then divide by the number of data. There are 3
data values. Therefore we will divide this sum by 3.
3
3 3
3  
2
2 1
Write the whole number as a fraction.
3 1
 
2 3
Write the division problem as multiplication
of the reciprocal.
1

3 1

2 31
Divide out a 3 in the numerator and
denominator.

1
2
Multiply and simplify.
206
CCBC Math 081
Addition of Fractions and of Mixed Numbers
Section 3.4
Third Edition
23 pages
Practice 27: Determine the mean of the following data.
1 5 1
,
,
3 6 6
Watch it:
http://youtu.be/dRGSaE-IBtQ
Answer:
Watch All: http://youtu.be/mkccvARYLJ8
207
4
9
CCBC Math 081
Addition of Fractions and of Mixed Numbers
Section 3.4
Third Edition
23 pages
3.4 Addition of Fractions and Mixed Numbers Exercises
1 4
2
3
1.
Add: +
4.
Add: 5 + 5
9 9
11
11
3 1
+
8 8
5.
1 5
Add: 13 +
8 8
6.
Add: 7 + 8
2.
Add:
3.
5
7
Add: 4 + 12
8
8
7.
What is the least common denominator for
2
1
and ?
5
6
8.
What is the least common denominator for
5
1
and ?
6
4
9.
What is the least common denominator for
7
3
and ?
10
8
10.
What is the least common denominator for
4
1
and ?
9
3
11.
Set up
4 2
+ with equivalent fractions that have a common denominator but do not add.
9 3
12.
Set up
5 3
+ with equivalent fractions that have a common denominator but do not add.
7 8
13.
Set up
1 6
with equivalent fractions that have a common denominator but do not add.
+
6 15
14.
Set up
7 1
+ with equivalent fractions that have a common denominator but do not add.
20 8
15.
Add:
3 5
+
10 6
19.
Add: 5
16.
Add:
4 2
+
9 3
20.
2
4
Add: 3 + 6
3
5
17.
Add:
5 3
+
7 8
21.
 1  1
Add:  4    3 
 3  2
18.
Add:
6 5
+
11 6
22.
 3  1
Add:       
 5  3
208
1
2
2
+10
13
CCBC Math 081
Addition of Fractions and of Mixed Numbers
Third Edition
23 pages
23.
7  3
Add:     
8  4
24.
Determine the perimeter of the rectangle:
in
in
25.
Section 3.4
Determine the median:
26. Determine the mean:
5 9 7 3 1 10
, , , , ,
11 11 11 11 11 11
1 1
,
,
3 6
2
3
209
CCBC Math 081
Addition of Fractions and of Mixed Numbers
Third Edition
23 pages
3.4 Addition of Fractions and Mixed Numbers Exercises Answers
1.
2.
3.
4.
5.
6.
Section 3.4
5
9
1
2
35
1
= 17
2
2
5
10
11
3
13
4
1
15
2
16.
10
1
=1
9
9
17.
61
5
=1
56
56
18.
91
25
=1
66
66
19.
15
20.
157
7
= 10
15
15
7.
30
8.
12
9.
40
22.
10.
9
23.
11.
4 6
+
9 9
24.
12
40 21
+
56 56
25.
13.
5 12
+
30 30
26.
14.
14 5
+
40 40
15.
17
2
=1
15
15
21.
210
2
13
5
6
14

15
5
1
8
5
5 in
12
6
11
7
18
7