Mixed Numbers as Improper
Fractions
Jen Kershaw
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Printed: November 10, 2014
AUTHOR
Jen Kershaw
www.ck12.org
C HAPTER
Chapter 1. Mixed Numbers as Improper Fractions
1
Mixed Numbers as Improper
Fractions
Here you’ll learn how to rewrite mixed numbers as improper fractions.
Have you ever ordered multiple pizzas and then had to keep track of how many slices were eaten and how many
weren’t? Well, the sixth graders are having the same sort of dilemma.
Casey ordered eight pizzas for the drama club to enjoy. Each pizza was cut into ten slices. At the end of the pizza
party, there were two whole pizzas and two slices left.
How many slices weren’t eaten?
Can you express this as an improper fraction of pizza slices? Do you know what an improper fraction is?
This Concept is all about mixed numbers and improper fractions. At the end of it, you will know how to figure
all of this out.
Guidance
In the last Concept on measuring to a fraction of an inch, sometimes we ended up with measurements that included
whole inches and parts of a whole inch or a fraction of an inch. When we have wholes and parts together, we have a
new type of number. It is called a mixed number.
A mixed number is a number that has both wholes and parts in it.
5
1
4
Here we have a mixed number. We have five whole items and one-fourth of a whole.
Now you know how to identify a mixed number. The opposite of a mixed number is an improper fraction.
What is an improper fraction?
An improper fraction is a fraction that has a larger numerator and a smaller denominator.
Huh? What does this mean?
12
5
1
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Let’s think about what this means. If the denominator tells us how many parts the whole has been divided into,
then this whole has been divided into 5 parts. The numerator tells us how many parts of the whole we have
in this case, we have twelve parts. What? If we have twelve out of five parts, then we have MORE than one
whole. One whole would be five out of five parts, but we have 12 out of 5 parts. This is where mixed numbers
come in.
How do we write a mixed number as an improper fraction?
To write a mixed number as an improper fraction, we want to write a fraction in terms of parts instead of in terms of
wholes and parts.
Change 2 13 to an improper fraction.
To do this, we multiply the whole number times the denominator and add the numerator. Then we put this
over the original denominator.
2×3+1=7
Our original denominator is 3.
Our answer is 2 13 = 73 .
Notice that the mixed number and the improper fraction are also equivalent.
Change the following mixed numbers to improper fractions.
Example A
3 31
Solution:
10
3
Example B
5 23
Solution: 17
3
Example C
6 18
Solution:
49
8
Now back to the pizza dilemma. Have you figured out the answer? Here is the original problem once again.
Casey ordered eight pizzas for the drama club to enjoy. Each pizza was cut into ten slices. At the end of the pizza
party, there were two whole pizzas and two slices left.
2
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Chapter 1. Mixed Numbers as Improper Fractions
How many slices weren’t eaten?
Can you express this as an improper fraction of pizza slices? Do you know what an improper fraction is?
First, let’s think about how many slices weren’t eaten.
2
Two whole pizzas and two slices = 2 10
We can convert that to an improper fraction.
Our answer is
22
10
slices of pizza weren’t eaten.
Vocabulary
Mixed Number
a number made up of a whole number and a fraction
Improper Fractions
a fraction where the numerator is greater than the denominator
Equivalent
means equal
Guided Practice
Here is one for you to try on your own.
Express 4 78 as an improper fraction.
Answer
To do this, we multiply the denominator of the fraction with the whole number and add the numerator. This will give
us our new numerator which is put over the original denominator.
39
8
Interactive Practice
MEDIA
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URL: http://www.ck12.org/flx/render/embeddedobject/54812
Video Review
MEDIA
Click image to the left for use the URL below.
URL: http://www.ck12.org/flx/render/embeddedobject/5359
3
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Khan Academy Mixed Numbers and Improper Fractions
MEDIA
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URL: http://www.ck12.org/flx/render/embeddedobject/5360
James Sousa Mixed Numbers and Improper Fractions
MEDIA
Click image to the left for use the URL below.
URL: http://www.ck12.org/flx/render/embeddedobject/5361
James Sousa Example Converting a Mixed Number to an Improper Fraction
Explore More
Directions: Write each mixed number as an improper fraction.
1. 2 12
2. 3 14
3. 5 13
4. 4 23
5. 6 14
6. 6 25
7. 7 13
8. 8 25
9. 7 45
10. 8 72
11. 8 34
12. 9 56
13. 6 58
14. 9 23
15. 5 12
16. 16 14
4