Mixed Fractions

Topics: Division, Elementary arithmetic, Fraction Pages: 10 (1749 words) Published: August 26, 2013
Mixed Fractions
(Also called "Mixed Numbers")
|  | A Mixed Fraction
is a
whole number
and a proper fraction
combined. 

such as 1 3/4.|
1 3/4| | |
(one and three-quarters)| | |
Examples
2 3/8| 7 1/4| 1 14/15| 21 4/5|
See how each example is made up of a whole number and a proper fraction together? That is why it is called a "mixed" fraction (or mixed number). Names
We can give names to every part of a mixed fraction:

Three Types of Fractions
There are three types of fraction:

 
Mixed Fractions or Improper Fractions
You can use either an improper fraction or a mixed fraction to show the same amount. For example 1 3/4 = 7/4, as shown here:
1 3/4|  | 7/4|
| =| |
Converting Mixed Fractions to Improper Fractions
To convert a mixed fraction to an improper fraction, follow these steps: 

| * Multiply the whole number part by the fraction's denominator. * Add that to the numerator * Write that result on top of the denominator.|  
Example: Convert 3 2/5 to an improper fraction.
Multiply the whole number by the denominator:
3 × 5 = 15
Add the numerator to that:
15 + 2 = 17
Then write that down above the denominator, like this:
17|
|
5|
Converting Improper Fractions to Mixed Fractions
To convert an improper fraction to a mixed fraction, follow these steps: 

| * Divide the numerator by the denominator. * Write down the whole number answer * Then write down any remainder above the denominator.|  
Example: Convert 11/4 to a mixed fraction.
Divide:
11 ÷ 4 = 2 with a remainder of 3
Write down the 2 and then write down the remainder (3) above the denominator (4), like this: 2| 3|
| |
| 4|
 
When to Use Improper Fractions or Mixed Fractions
For everyday use, people understand mixed fractions better: Example: It is easier to say "I ate 2 1/4 sausages", than "I ate 9/4 sausages" But for mathematics improper fractions are actually better than mixed fractions. Because mixed fractions can be confusing when you write them down in a formula (are the two parts supposed to be added or multipled?): Mixed Fraction:| What is:| 1 + 2 1/4|  | ?|

 | Is it:| 1 + 2 + 1/4|  | = 3 1/4 ?|
 | Or is it:| 1 + 2 × 1/4|  | = 1 1/2 ?|
 |  |  |  |  |
Improper Fraction:| What is:| 1 + 9/4|  | ?|
 | It is:| 4/4 + 9/4 = 13/4|  | |
Adding and Subtracting Mixed Fractions
| Quick Definition: A Mixed Fraction is a
whole number and a fraction combined, 
such as 1 3/4.|
1 3/4| |
(one and three-quarters)| |
To make it easy to add and subtract them, just convert to Improper Fractions first: | Quick Definition: An Improper fraction has a
top number larger than or equal to
the bottom number,

such as 7/4 or 4/3

(It is "top-heavy")|
7/4| |
(seven-fourths or seven-quarters)| |
 
Adding Mixed Fractions
I find this is the best way to add mixed fractions:
* convert them to Improper Fractions
* then add them (using Addition of Fractions)
* then convert back to Mixed Fractions:
Example: What is 2 3/4 + 3 1/2 ?
Convert to Improper Fractions:
2 3/4 = 11/4
3 1/2 = 7/2
Common denominator of 4:
11/4 stays as 11/4
7/2 becomes 14/4
(by multiplying top and bottom by 2)
Now Add:
11/4 + 14/4 = 25/4
Convert back to Mixed Fractions:
25/4 = 6 1/4
When you get more experience you can do it faster like this: Example: What is 3 5/8 + 1 3/4
Convert them to improper fractions:
3 5/8 = 29/8
1 3/4 = 7/4
Make same denominator: 7/4 becomes 14/8 (by multiplying top and bottom by 2) And add:
29/8 + 14/8 = 43/8 = 5 3/8
 
Subtracting Mixed Fractions
Just follow the same method, but subtract instead of add:
Example: What is 15 3/4 - 8 5/6 ?
Convert to Improper Fractions:
15 3/4 = 63/4
8 5/6 = 53/6
Common denominator of 12:
63/4 becomes 189/12
53/6 becomes 106/12
Now Subtract:
189/12 - 106/12 = 83/12
Convert back to Mixed Fractions:
83/12 = 6 11/12
Multiplying Mixed Fractions
("Mixed...
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