Fractions: Operations on Mixed Numbers
Vocabulary
Mixed Number
The sum of a whole number and a proper fraction
Example: 2
3
4
An improper fraction can always be written as a mixed number or a whole number (if the denominator
is a factor of the numerator).
To convert from an improper fraction to a mixed number:
Divide the numerator by the denominator.
11
4
2, r = 3
4 11
2
If there is a remainder, write the remainder over the original denominator.
11 divided by 4 is 2 with a remainder of 3.
The mixed number is composed of the integer quotient as the whole number
part and the remainder, if any, as the numerator of the proper fraction part.
3
4
TRY:
Convert each of the following improper fractions to mixed numbers.
17
3
−19
4
−20
5
23
5
To convert from a mixed number to a improper fraction:
2
Multiply the whole number by the denominator.
3
4
(2 • 4) + 3
11
4
Add the numerator of the fraction to that product.
Write that sum over the original denominator.
TRY:
Convert each of the following mixed numbers to improper fractions.
4
3
5
−3
1
7
−6
5
3
4
developed by Dr. Susan Harrison, Math Department, University of Wisconsin-Eau Claire
To MULTIPLY two mixed numbers:
3
5
2 •1
4 33
Change each mixed number to improper fractions.
11 38
•
4 33
Simplify if possible.
1 19
•
2 3
11 2 ⋅19
•
2 ⋅ 2 3 ⋅11
Multiply the resulting fractions.
19
6
CAUTION:
3 1
3 1
2 • 1 ≠ (2 • 1) + ( • )
4 7
4 7
Be sure to convert each mixed number to improper fractions first!
3 1 11 8 11 2 22
2 •1 = • = • =
4 7 4 7 1 7 7
TRY:
Multiply.
1 4
4 •
5 7
1
8
−3 • 2
7 11
To DIVIDE two mixed numbers:
Change each mixed number to improper fractions and follow the rules for dividing fractions.
3
1
5 ÷2
5
10
28 21
28 10
4⋅7 5⋅2
4 2
8
2
÷
•
•
• 2
5 10
5 21
5 ⋅1 3 ⋅ 7
1 3
3
3
TRY:
Divide.
1
2
−3 ÷ 2
7
21
1
−4 ÷ 3
5
To multiply or divide a mixed number and whole number, write the whole number as an improper fraction first.
developed by Dr. Susan Harrison, Math Department, University of Wisconsin-Eau Claire
To ADD two mixed numbers:
Change each mixed number to improper fractions and follow the rules for adding fractions.
3
1
−5 + 2
5
10
−28 21
−56 21
−35
5
1
+
+
−3
−3
5 10
10 10
10
10
2
TRY:
Add.
1
3
3
−3 + 2 + 1
7
4 14
To SUBTRACT two mixed numbers:
Change each mixed number to improper fractions and follow the rules for subtracting fractions.
3
1
5 −2
5
10
5−2
1
10
28 21
56 21
56 −21
35
5
1
−
−
+
3
3
5 10
10 10
10 10
10
10
2
25 21
50 21
50 −21
29
9
−
−
+
2
5 10
10 10
10 10
10
10
TRY:
Subtract.
1
2
3 −2
7
21
−4 − 3
2
7
developed by Dr. Susan Harrison, Math Department, University of Wisconsin-Eau Claire