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Rational numbers or fractions can be used in many different ways. One source of confusion, especially with fractions, is the difference between absolute and relative reasoning. In Part A, we used a rational number to compare a part to a whole. It's important to understand, however, that there is more than one way to make a comparison.
Here is a situation that you can think about numerically in at least two different ways: A baby and an adult both gain two pounds in one month.
• | You could think about the fact that each of them gained an equal amount of weight -- two pounds. |
• | You could think about the fact that the baby's gain was greater, because the gain was a greater percentage of the baby's original weight than of the adult's original weight. |
These are examples of two types of reasoning. The first uses absolute reasoning, which refers to a quantity by itself, without respect to its relation to other quantities (each gains two pounds, period). In contrast, the second uses relative reasoning, which compares that quantity to the originals to see how they relate to one another (the baby's gain is greater with respect to its original weight).
We can relate these two types of reasoning to operations. Absolute thinking is additive: Two boys each grew two inches last year. (Add two inches to their original heights.) In contrast, relative thinking is multiplicative -- the two inches might be 1/10 of the infant boy's prior height but only 1/24 of the first grader's prior height. Note 7
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