Using a Rule to Add Fractions...4 Formal Addition and Subtraction of Fractions Using a Rule to Add Fractions • You can add fractions by creating equivalent fractions with the same
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Formal Addition and Subtraction of Fractions4Using a Rule to Add Fractions
• You can add fractions by creating equivalent fractions with the same denominator. The same denominator is often called a common denominator.
• When you use a grid and counters to model adding fractions with different denominators, the model shows a common denominator. For example, to model 1
3 + 38 , you can make a 3-by-8 grid, which has 24 cells.
You can model 13 by filling in 1 of the 3 rows. So, you are renaming 1
3 as 824.
You can model 38
by filling in 3 of the 8 columns. So, you are renaming 38
as 924
. When you move the counters so that each cell has only one counter, you can see that 8
24 + 9
24 = 17
24.
• To choose a common denominator without a model, you can multiply the two given denominators. For example, for 1
3 + 38 , you could multiply 3 by 8 to get a common denominator
4 Formal Addition and Subtraction of Fractions (continued)
Using a Rule to Subtract Fractions
• You can subtract fractions by creating equivalent fractions with the same denominator.
• When you use a grid and counters to model subtracting fractions with different denominators, the model shows a common denominator. For example, to model 4
5 − 13 , you can make a 5-by-3 grid, which has 15 cells.
You can model 45 by filling in 4 of the 5 rows. So, you are renaming 4
5 as 1215.
You can model 13 by filling in 1 of the 3 columns. So, you are renaming 1
3 as 515 .
Since both fractions have the same denominator now, you can subtract more easily: 1215 − 5
15 = 715 .
• To find a common denominator without a model, you can multiply the two given denominators. For example, for 4
5 − 13 , you could multiply 5 by 3 to get a common denominator
4 Formal Addition and Subtraction of Fractions (continued)
Notes
It is important to remember that it’s not that you can’t add fractions with different denominators; it’s just that it’s not easy to visualize the exact answer without using a model.
For example, you can add 35 + 4
7 by thinking of the number 35, determining 35
of it (as 21) and 47 of it (as 20), and then add the two numbers to get 41. Then you
have to remember the unit is 35ths, so it’s 4135. You have actually created equivalent
fractions, but you might not even realize it.
Definitions
common denominator: a denominator shared by two or more fractions
equivalent fractions: fractions that name the same part of the same whole or are in the same position on a number line; for example, 2