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).
Three Types of Fractions
There are three types of fraction:
Fractions
A Fraction (such as 3/4) has two numbers:
The top number is the Numerator, it is the number of parts you have.
The bottom number is the Denominator, it is the number of parts the whole is divided into.
Example: 3/4 means:
- We have 3 parts
- Each part is a quarter (1/4) of a whole
So we can define the three types of fractions like this:
| Proper Fractions: |
The numerator is less than the denominator |
| Examples: 1/3, 3/4, 2/7 |
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|
| Improper Fractions: |
The numerator is greater than (or equal to) the denominator |
| Examples: 4/3, 11/4, 7/7 |
| |
|
| Mixed Fractions: |
A whole number and proper fraction together |
| Examples: 1 1/3, 2 1/4, 16 2/5 |
Mixed Fractions
So, a mixed fraction is just a whole number and a fraction combined into one "mixed" number.
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, shown here:
Converting Improper Fractions to Mixed Fractions
To convert an improper fraction to a mixed fraction, follow these steps:
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- Divide the numerator by the denominator.
- Write down the whole number answer
- Then write down any remainder above the denominator.
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| |
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:
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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
- Then write the result on top of the denominator.
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| |
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:
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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 |
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= 1 1/2 ? |
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|
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| Improper Fraction: |
What is: |
1 + 9/4 |
|
? |
| |
It is: |
4/4 + 9/4 = 13/4 |
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