Overview:
Adding and subtracting fractions is similar to adding and subtracting whole numbers, with one important difference. The denominators must be the same, so that if the fractions do not have the same denominator, they must be changed into equivalent fractions with the same denominator. Then the general pattern of adding or subtracting fractions can be followed.
What Is the Putting-Together Model for Addition?
By the putting-together model for addition, similar units can be combined. Suppose there are x CD’s in one box and y CD’s in another box. The total number of CD’s in both boxes is x + y. Similarly, if there are t tulip bulbs planted in one flowerbed and 6 more tulip bulbs planted in another flowerbed, there are t + 6 total bulbs planted all together. In order for elements to be combined, they must be the same type of unit. Also, there must not be an overlap in the things to be added together. None of the elements in the x set can be also in the y set for the resulting sum to be x + y.
How Can Fractions Be Added?
Adding fractions is a type of putting- together. If the fractions have the same denominators, they are the same type of unit, so that 1/8 and 2/8 can be added together as 3/8. Similarly, 4/16 and 5/16 can be added together as 9/16. Generally, the rule using variables is that a/c + b/c, when c is not equal to 0 is the same thing as adding (a +b)/c.
What about Common Denominators?
In order for fractions to be the same type of unit, they must have common denominators. Suppose the fractions were 1/3 and 1/4. In order for them to be added, 1/3 would have to be changed to its equivalent 4/12 and ¼ would have to be changed to its equivalent 3/12. Then they could be added together as 7/12.
How Can Fractions Be Subtracted?
Subtraction is adding the inverse of the number to be subtracted, so that a – b means the same thing as a + -b. Similarly subtracting a/c- b/c means the same thing as a/c + –b/c. In order for fractions to be subtracted, they must also have a common denominator. Suppose the expression were 5/6 – ½ . The equivalent of ½ is 3/6, so that 5/6 – 3/6 is 2/6. In simplest terms, 2/6 is 1/3.
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