A fraction is a number that can represent part of a whole. An example is 3/4, in which the numerator, 3, tells us that the fraction represents 3 equal parts, and the denominator, 4, tells us that 4 parts make up a whole.
How to Add Fractions with Unlike Denominators:
To add fractions containing unlike quantities (e.g. quarters and thirds), it is necessary to convert all amounts to like quantities. It is easy to work out the chosen type of fraction to convert to; simply multiply together the two denominators (bottom number) of each fraction.
Consider adding the following two quantities:
3/4 + 2/3
First, convert 3/4 into twelfths by multiplying both the numerator and denominator by three3/4 x 3/3 =9/12
Note that 3/3 is equivalent to 1. which shows that ¾ is equivalent to the resulting 9/12.
Secondly, 2/3convert into twelfths by multiplying both the numerator and denominator by four:2/3 x 4/4 = 8/12. Note that 4/4 is equivalent to 1, which shows that 2/3 is equivalent to the resulting 8/12 .
9/12 + 8/12 = 17/12.
Simplify the Fraction
Example: Find the Sum of 2/9 and 3/12
Determine the Greatest Common Factor of 9 and 12 which is 3
Either multiply the denominators and divide by the GCF (9x12=108, 108/3=36)
OR - Divide one of the denominators by the GCF and multiply the answer by the other denominator (9/3=3, 3x12=36)
Rename the fractions to use the Least Common Denominator(2/9=8/36, 3/12=9/36)
The result is 8/36 + 9/36
Add the numerators and put the sum over the LCD = 17/36
Simplify the fraction if possible. In this case it is not possible.
Example:
Find. 3/4 - 2/3
Solution:
Since the fractions have different denominators, they cannot be subtracted until they have the same denominators.
We can express both fractions as twelfths.
3/4 = 4/12 and 2/3 = 8/12
9/12 - 8/12 = 1/12.
Example:
Find
5/6 + 2/3
Solution:
Since the fractions have different denominators, they cannot be added until they have the same denominators.
We can express both fractions as sixths.
2/3 = 4/6
5/6 + 3/6 = 8/6
How to Add Fractions with Unlike Denominators:
To add fractions containing unlike quantities (e.g. quarters and thirds), it is necessary to convert all amounts to like quantities. It is easy to work out the chosen type of fraction to convert to; simply multiply together the two denominators (bottom number) of each fraction.
Consider adding the following two quantities:
3/4 + 2/3
First, convert 3/4 into twelfths by multiplying both the numerator and denominator by three3/4 x 3/3 =9/12
Note that 3/3 is equivalent to 1. which shows that ¾ is equivalent to the resulting 9/12.
Secondly, 2/3convert into twelfths by multiplying both the numerator and denominator by four:2/3 x 4/4 = 8/12. Note that 4/4 is equivalent to 1, which shows that 2/3 is equivalent to the resulting 8/12 .
9/12 + 8/12 = 17/12.
Simplify the Fraction
Example: Find the Sum of 2/9 and 3/12
Determine the Greatest Common Factor of 9 and 12 which is 3
Either multiply the denominators and divide by the GCF (9x12=108, 108/3=36)
OR - Divide one of the denominators by the GCF and multiply the answer by the other denominator (9/3=3, 3x12=36)
Rename the fractions to use the Least Common Denominator(2/9=8/36, 3/12=9/36)
The result is 8/36 + 9/36
Add the numerators and put the sum over the LCD = 17/36
Simplify the fraction if possible. In this case it is not possible.
Example:
Find. 3/4 - 2/3
Solution:
Since the fractions have different denominators, they cannot be subtracted until they have the same denominators.
We can express both fractions as twelfths.
3/4 = 4/12 and 2/3 = 8/12
9/12 - 8/12 = 1/12.
Example:
Find
5/6 + 2/3
Solution:
Since the fractions have different denominators, they cannot be added until they have the same denominators.
We can express both fractions as sixths.
2/3 = 4/6
5/6 + 3/6 = 8/6
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