Proper and Improper Fractions

Contributed by:

Diego Tue, Jan 25, 2022 02:08 PM UTC

This pdf explains improper fractions and mixed numbers. A proper fraction is a fraction whose numerator is smaller than its denominator. An improper fraction is a fraction whose numerator is equal to or greater than its denominator. 3/4, 2/11, and 7/19 are proper fractions, while 5/2, 8/5, and 12/11 are improper fractions.

1. Understanding improper fractions and
mixed numbers

2. Proper Fractions
The numerator
This shows us the number
3
of pieces we have.
The denominator
This shows us the number
4
of parts we are dividing by.
A proper fraction is where the numerator is less than the denominator.

3. Improper Fractions
The numerator
This shows us the number
7
of pieces we have.
The denominator
This shows us the number
4
of parts we are dividing by.
An improper fraction is where the numerator is greater than or equal to
the denominator.
This happens because you have a whole or more than a whole.

4. Improper Fractions to Mixed Numbers
You can convert an improper fraction into a mixed number.
Divide the numerator (7) by the
denominator (4).
7 ÷ 4 = 1 r3
4 1 r3 written as a mixed number is 1 3
4

5. Improper Fractions to Mixed Numbers
11 14
8 10 9
5 6
4

6. Improper Fractions to Mixed Numbers
Answers
14 5
11
10
= 1 1
10 9
= 1 9
8 3
5
= 1 5
6 2 or 1
4 1
=
4 1 2

7. Mixed Numbers to Improper Fractions
You can also convert a mixed number into an improper fraction.
First you need to multiply the whole number by the denominator.
2 1
3
2×3=6
Then add the total to the numerator. 6 + 1 = 7
7
Then write the answer over the denominator. 3

8. Mixed Numbers to Improper Fractions
Convert these mixed numbers into improper fractions:
1 3
4 3 2
5
5 4
7

9. Mixed Numbers to Improper Fractions
Answers
1 3
4
=
7
4 3 2
5
=
17
5
5 4
7
=
39
7

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