Not even signed numbers cause as many problems as those two-headed monsters called fractions. But why so much trouble? Maybe because fractions have a dual nature, that is, they consist of the numerator and denominator, and most of us are poor at multitasking. But did you know that once you master fractions, you learn to handle multiple tasks as well? This is one of the benefits of mastering these pesky little creatures.
In my humble opinion, I would venture to say that any kid who is good at fractions is definitely going to be good at math. Why can I say this without reservation? Well, working with fractions is a task that requires an individual to deal with a complex object. You see, unlike other numbers, fractions consist of two parts: the top part, or numerator, and the bottom part, or denominator. Because of this duality of nature, fractions cannot be treated as ordinary numbers like the integers such as -2, 3, or 6; or the irrational numbers such as pi or e. When dealing with a fraction like 2/3, you must deal with a quotient of two integers. You can no more separate the 2 from the 3 than you can the ring finger from the hand.
Because the character of fractions is determined by both the numerator and denominator, and not by each one separately, ordinary arithmetic operations become a real headache. For example, when performing multiplication, you are not simply multiplying two numbers together, but two pairs of numbers together; moreover, you might be confronted with large numbers to multiply, which further complicates the operation. When adding or subtracting fractions, you cannot simply add numerator to numerator and denominator to denominator. Oh no! Not in fraction land.
In order to add or subtract, you must first be sure you are comparing apples to apples, so to speak. That is, you must first get a common denominator, as this is what rules in fraction land. Once you do this conversion, these creatures actually become quite tame. But getting to this common denominator can sometimes require a little work.
Although fraction mastery requires more work than mastery over ordinary numbers, the payoff is quite good. For once your children are competent with these interesting numerical creatures, they can conquer new horizons in mathematics. On this fact, I stake my reputation. And if you are somewhat skeptical, then try this out: work with your kids until they have a mastery of fractions. Then watch how their overall math grades improve. Fractions always lead the way. Once the objective of fraction mastery is accomplished, school headaches should be a thing of the past. Just think of the money you’ll save on aspirin, or should I say alleve.
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