Fractions
Let's review some basic functions as well as some basic operations with fractions.
Understanding Fractions
Type of Fraction | Definition | Example |
Proper | The numerator is less than the denominator | 5/8 or 11/22 |
Improper | The numerator is greater than (or equal to) the denominator | 12/7 or 8/8 |
Mixed | A whole number and proper fraction together | 1 1/3 or 2 1/4 |
Converting Fractions
- Divide the numerator by the denominator.
- Write down the whole number answer.
- Then write down any remainder above the denominator
Example: Convert the improper fraction 7/4 to a mixed fraction.
Solution:
Divide the numerator by the denominator 7÷4 = 1 with a remainder of 3.
So we write down the 1 as a whole number and then write down the remainder (3) above the denominator (4), like this: 1 3/4
To convert from a mixed fraction to an improper fraction, follow these steps:
- Multiply the whole number part by the fraction denominator,
- Add that to the numerator,
- Then write the result on top of the denominator.
Example: Convert the mixed fraction 5 6/7 to an improper fraction.
Solution:
Multiply the whole number by the denominator: 5 x 7= 35
Add the numerator to that: 35 + 6 = 41
Then write that down above the deonominator (7), like this: 41/7
Equivalent Fractions
Before doing operations with fractions one must understand equivalent fractions. For example, these fractions are really all the same:
1/3 = 2/6 = 3/9
They are all the same because any time you multiply or divide both the numerator and denominator by the same number, the fraction keeps its value. For example, 1/7 x 2/2 = 2/14 means that 1/7 = 2/14. For equivalent fractions, always remember that what you do to the numerator, you must do to the denominator. This process will help you in understanding how to obtain a common denominator for two fractions.