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Fractions Addition
Denominator is the bottom, or Down number in a fraction -- and both Denominator and Down start with the letter D.
Adding Fractions with COMMON Denominators
Adding fractions with COMMON denominators is simple.
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Just add the top numbers (the numerators) together,
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Place the resulting answer in the top of a fraction using the existing denominator for the bottom number.
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Then reduce the fraction, if possible.
Example 1: Simple fraction addition
No reduction is possible, so we have found the answer!
Example 2: Reducing the fraction answer
Then reduce:
Example 3: Converting the answer to a mixed number
Then convert the improper fraction to a mixed number:
Creating Common Denominators
How do we do that? Simple! Remember, if you multiply the top and bottom of a fraction by the same number, it doesn't effect the value of the fraction.
Example 1: If we have the fraction 2/3, we can multiply the top and bottom by 2, and not change its value:
(2/2) x (2/3) = 4/6
Then if we reduce 4/6, we still get the original number, 2/3
Example 2: If we have the fraction 2/3, we could multiply top and bottom
by 5, and not change its value:
(5/5) x (2/3) = 10/15.
Then if we reduce 10/15, we still get the original number, 2/3.
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Why does this work?
- Because any number divided by itself equals one.
- 2/2 = 1, 5/5 = 1, etc.
- Any number multiplied by 1 equals itself!
- The point is, you don't change the value of a fraction if you multiply its top and
bottom numbers by the same number!
Adding Fractions with DIFFERENT denominators
- You can only add together fractions which have the same denominator,
- so you must first change one or both of the fractions so that you end up with two fractions having a common denominator.
- The easiest way to do this, is to simply select the opposite
fraction's denominator to use as a top and bottom multiplier.
Example 1:
Say you have the fractions 2/3 and 1/4
Select the denominator of the second fraction (4) and multiply the top and bottom of the first fraction (2/3) by that number:
Select the denominator of the first fraction (3) and multiply the top and bottom of the second fraction (1/4) by that number:
These two fractions (8/12 and 3/12) have common denominators - the number 12 on the bottom of the fraction.
Add these two new fractions together:
Example 2:
Say you have the fractions 3/5 and 2/7
Select the denominator of the second fraction (7) and multiply the top and bottom of the first fraction (3/5) by that number
Select the denominator of the first fraction (5) and multiply the top and bottom of the second fraction (2/7) by that number
These two fractions (21/35 and 10/35) have common denominators -- the number 35 on the bottom of the fraction.
We can now add these two fractions together, because they have common denominators: