Saturday, July 11, 2015

Segment 3 of Dr Rules Notes- Division and Fractions to Enjoy

Division and Fractions

Division is to multiplication what subtraction iss to addition. They undo one another.
Fractions are a special case of division. Here are some things to remember and talk about one at a time with a child to build numeracy skills:

  • 1 and 0 are special numbers
  • All real numbers can be expressed as fractions
  • Fractional parts are between 0 and 1
    • ½, ¼, 1/8 all between 0 and 1
  • Zero is the line of demarcation which divides the positive from the negative numbers
    • It would fall into the category of an even number but it's not divisible by two
  • 0 cannot divide because the answer is undefined. I am going to explain why it's undefined in a minute.
  • As the number in the denominator gets small er the fraction gets larger
    • 1/4<1/3/<1/2<1/1<1/1/2( one over one half) 1/1/2=2 (one over one half equals 2)
    • 1/1/4 =4 (read one divided by one fourth equals four)
    •  1/1/10000=10000 - one divided by one ten thousandth equals one ten thousand
    •  1/1/10000000=10000000 One over one-millionth equals one million
  • As the denominator gets smaller the value gets greater
    • So 1/0 would be infinitely large
We call 1/0 undefined because we cannot comprehend infinity.
If you have 2/0 you would have 2 X infinity which we just can't wrap our mind around.

Another cool things about about fractions to remember. Fractions allow you to divide by multiplying. Its an advantage of fractions over decimals. You can multiply the reciprocal of the second fraction to divide.

Example: One half divided by One fourth = 1/2 X 4/1

I hope you enjoy thinking about these math curiosities this week and testing them as I have.  Next week I will share his thoughts on advanced Math and Math as a philosophy.

Can't stand to wait a week?  I understand.  Try: I love Theoni Papas books.  Her work is perspective changing.  A great math teacher.

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