Proper and improper fractions. Mixed numbers


A concise but great lesson about improper fractions, proper fractions, and mixed numbers.




Improper fractions:

Fractions with a numerator that is bigger than the denominator.

For instance, the following fractions are improper.

9 / 2
   ,  
7 / 4
,and  
8 / 3


Proper fraction:

A fraction with a numerator that is smaller than the denominator.

For instance, the following are all proper fractions.

2 / 3
   ,  
1 / 4
,and  
6 / 8


Mixed number:

A number written as the sum of a whole number and a proper fraction.

For instance,   2 +
1 / 3
  is a mixed number.


The + sign is usually omitted so as to write   2
1 / 3


Mixed numbers can be converted to improper fractions and vice versa.

In our example above,

2
1 / 3
=   
7 / 3


To get  
7 / 3
 multiply 2 by 3 and then add 1. Keep the same denominator.


The above is a shortcut!

To get 
7 / 3
,you will normally add
 
2 / 1
  and  
1 / 3


Using the shortcut however takes less time!

Notice that the denominator for 2 is 1 since 2 =  
2 / 1




Improper fractions:

Fractions with a numerator that is bigger than the denominator.

For instance, the following fractions are improper.

9 / 2
   ,  
7 / 4
,and  
8 / 3


Proper fraction:

A fraction with a numerator that is smaller than the denominator.

For instance, the following are all proper fractions.

2 / 3
   ,  
1 / 4
,and  
6 / 8


Mixed number:

A number written as the sum of a whole number and a proper fraction.

For instance,   2 +
1 / 3
  is a mixed number.


The + sign is usually omitted so as to write   2
1 / 3


Mixed numbers can be converted to improper fractions and vice versa.

In our example above,

2
1 / 3
=   
7 / 3


To get  
7 / 3
 multiply 2 by 3 and then add 1. Keep the same denominator.


The above is a shortcut!

To get 
7 / 3
,you will normally add
 
2 / 1
  and  
1 / 3


Using the shortcut however takes less time!

Notice that the denominator for 2 is 1 since 2 =  
2 / 1


Converting to a mixed number

You can also convert an improper fraction to a mixed number

Say you want to convert  
13 / 5
 to a mixed number


Ask yourself, " How many 5 can go into 13? " The answer is 2

2 is your whole number piece of the mixed number

What is the remainder of this division? 5 × 2 = 10 and 13 - 10 = 3

3 is the numerator of the fraction piece

The denominator remains the same, so it will be 5

The mixed number is 2
3 / 5


Another example will make this crystal clear may be

Convert  
25 / 6
to a mixed number


Ask yourself, " How many 6 can go into 25? " The answer is 4

4 is your whole number piece of the mixed number

What is the remainder of this division? 6 × 4 = 24 and 25 - 24 = 1

1 is the numerator of the fraction piece

The denominator remains the same, so it will be 6

The mixed number is 4
1 / 6



Proper fractions, improper fractions, and mixed number quiz.



Still struggling with fractions? Get rid of your fears and frustrations once and for all!

Buy my ebook. It offers a thorough coverage of fractions!


Fractions ebook cover



Recent Articles

  1. Proof that There is no Rational Number Whose Square is 2

    Feb 17, 19 12:04 PM

    There is no rational number whose square is 2. An easy to follow proof by contraction.

    Read More

New math lessons

Your email is safe with us. We will only use it to inform you about new math lessons.

            Follow me on Pinterest


Math quizzes

 Recommended

Scientific Notation Quiz

Graphing Slope Quiz

Adding and Subtracting Matrices Quiz  

Factoring Trinomials Quiz 

Solving Absolute Value Equations Quiz  

Order of Operations Quiz

Types of angles quiz


Tough algebra word problems

Tough Algebra Word Problems.

If you can solve these problems with no help, you must be a genius!

Recent Articles

  1. Proof that There is no Rational Number Whose Square is 2

    Feb 17, 19 12:04 PM

    There is no rational number whose square is 2. An easy to follow proof by contraction.

    Read More

K-12 math tests


Everything you need to prepare for an important exam!

K-12 tests, GED math test, basic math tests, geometry tests, algebra tests. 

Real Life Math Skills

Learn about investing money, budgeting your money, paying taxes, mortgage loans, and even the math involved in playing baseball.