Download Division of Mixed Numbers

Version 7/2/2016
Hanh X. Vo
Division of Mixed Numbers
I. Introduction:
We will explain how to divide mixed numbers by a fraction, a whole number, or another mixed
number in this section.
II. How to Divide Mixed Numbers:
1) Dividing a Mixed Number by a Fraction:
Follow these simple steps:
 Convert the mixed number to improper fraction
 Find the reciprocal of the fraction
 Multiply the numerators
 Multiply the denominators
 Convert the result to mixed number as needed
 Simplify the fraction part as needed
Example 1:
1
3
Find 8 
1
2
Let’s convert the mixed number to improper fraction (See To_Improp):
1 8  3  1 25
8 

3
3
3
The reciprocal of
1
2
is 2 or
(See Reciprocal)
2
1
Multiply the two fractions:
25 2 25  2 50
 

3 1 3 1
3
Since
50
is an improper fraction, let’s convert it to mixed number (See To_Mixed):
3
1
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Hanh X. Vo
50
2
 16
3
3
Thus,
1 1
2
8   16
3 2
3
Example 2:
Find 3
1 2

2 5
Let’s convert the mixed number to improper fraction (See To_Improp):
1 3 2 1 7
3 

2
2
2
The reciprocal of
2 5
is
(See Reciprocal)
5
2
Multiply the two fractions:
7 5 7  5 35
 

2 2 2 2 4
Since
35
is an improper fraction, let’s convert it to mixed number (See To_Mixed):
4
35
3
8
4
4
Thus,
1 2
3
3  8
2 5
4
2
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Hanh X. Vo
2) Dividing a Mixed Number by a Whole Number:
Note that a whole number can be written as a fraction with the denominator as 1:
For example: 6 
6
15
3
; 15 
; 3
1
1
1
Thus, we can apply the same steps shown above for this situation.
Example 1:
1
3
Find 8  2
Let’s convert the mixed number to improper fraction (See To_Improp):
1 8  3  1 25
8 

3
3
3
And, the whole number 2 can be written as
So, the reciprocal of
2
1
2
1
is
(See Reciprocal)
1
2
Multiply the two fractions:
25 1 25  1 25
 

3 2 3 2
6
25
is an improper fraction, let’s convert it to mixed number (See To_Mixed):
6
25
1
4
6
6
Since
Thus,
1
1
8 24
3
6
Example 2:
3
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Hanh X. Vo
Find 5
1
3
4
Let’s convert the mixed number to improper fraction (See To_Improp):
1 5  4  1 21
5 

4
4
4
And, the whole number 3 can be written as
So, the reciprocal of
3
1
3
1
is
(See Reciprocal)
1
3
Multiply the two fractions:
21 1 21 1 21
 

4 3 4  3 12
The GCF of 21 and 12 is 3 (See Greatest Common Factor GCF)
The above result can be further simplified as:
21 21  3 7


12 12  3 4
7
is an improper fraction, let’s convert it to mixed number (See To_Mixed):
4
7
3
1
4
4
Since
Thus,
1
3
5 3 1
4
4
3) Dividing a Mixed Number by Another Mixed Number:
Follow these simple steps:
 Convert the first mixed number to improper fraction
 Convert the second mixed number to improper fraction
4
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Hanh X. Vo





Find the reciprocal of the second improper fraction
Multiply the numerators
Multiply the denominators
Convert the result to mixed number as needed
Simplify the fraction part as needed
Example 1:
5
8
Find 5  2
1
2
Convert the first mixed number to improper fraction (See To_Improp):
5 5  8  5 45
5 

8
8
8
Convert the second mixed number to improper fraction (See To_Improp):
1 2 2 1 5
2 

2
2
2
The reciprocal of
5
2
is
(See Reciprocal)
2
5
Multiply the two fractions:
45 2 45  2 90 9
 


8 5 8  5 40 4
Since
9
is an improper fraction, let’s convert it to a mixed number (See To_Mixed):
4
9
1
2
4
4
Thus,
5
1
1
5 2 2
8
2
4
5
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Hanh X. Vo
Example 2:
1
3
Find 3  2
3
5
Convert the first mixed number to improper fraction (See To_Improp):
1 3  3  1 10
3 

3
3
3
Convert the second mixed number to improper fraction (See To_Improp):
3 2  5  3 13
2 

5
5
5
The reciprocal of
13
5
is
(See Reciprocal)
5
13
Multiply the two fractions:
10 5 10  5 50
 

3 13 3  13 39
Since
50
is an improper fraction, let’s convert it to a mixed number (See To_Mixed):
39
50
11
1
39
39
Thus,
1
3
11
3  2 1
3
5
39
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