Fraction Satisfaction…

Fractions are a common stumbling block on the journey to learn mathematics. But they are important to learn and become comfortable with because they are useful in so many situations like cooking and probability. The way to gain this comfort level is to embrace them, use them, and work with them.

Coach Barb decided to stamp out fraction fear and turn it into fraction satisfaction by approaching a fraction directly. She found \frac{3}{7}s to be a willing, albeit wacky, interviewee:

Coach Barb: What are you?

\frac{3}{7}: I’m a number. My name is \frac{3}{7}.

Coach Barb: Why do you look so funny?

\frac{3}{7}: I am a number that cannot be described by one whole number; two are needed. By the way, missy, I don’t look funny, I look elegant.

Coach Barb: Why can’t one number describe you?

\frac{3}{7}: One number does, and that number is \frac{3}{7}! It’s a perfectly fine number.

Coach Barb: Why can’t one whole number describe you?

\frac{3}{7}: Because my value is between two whole numbers: 0 is too small and 1 is too big.

Coach Barb: Do all fractions have values between two whole numbers?

\frac{3}{7}: No. Whole numbers can also be written as fractions. My best girlfriend, 3, sometimes goes by \frac{3}{1}, sometimes by\frac{21}{7}, and sometimes by other names. We’ll talk more about this later, but I’ll let you in on a little secret … she doesn’t do this just so we can have matching tops, though it often is about having matching bottoms.

Coach Barb: Please, please tell me now! Why would anyone want to use two whole numbers to describe a number that can be described with one whole number?

\frac{3}{7}: Don’t beg, dearie; it’s unbecoming. When whole numbers are written as fractions, it is because it’s useful to think of them that way. You may want to compare the whole number with a number that can only be written as a fraction, for instance. Or you might want to combine a whole number with one or more fractions…

The interview continues in Volume 5, Numbers 1, 2, and 3 of the Girls’ Angle Bulletin.

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2 Responses to Fraction Satisfaction…

  1. Hi, I’m sorry that this comment is not related to the post at all, but I didn’t find an email address anywhere so I decided to leave a comment if you don’t mind.
    I have a question about geometry specifically. In geometry, we learned things like “segment addition postulate” and “area addition postulate,” which were pretty intuitive statements. But then I looked at Euclid’s five postulates, and although he included several intuitive statements, he never bothered to list the “postulates” listed above. Would those statements be considered too intuitive to bother to list? Or is there actually a way to prove them (not demonstrate them)? Because I used to think they were too obvious to bother to attempt to prove, and then I found about the whole Banach-Tarski sphere dissection (which, I admit, I don’t understand very well…)

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