## Friday, June 5, 2015

### How to Add or Subtract Two Fractions by the Butterfly Method

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The butterfly method is used in Japan to teach addition or subtraction of two fractions. Japanese schools teach this method and encourage students to "forget" the butterfly drawing as they get better using the method.

To add or subtract fractions the butterfly way,

1. Write the fractions side-by-side as usual and draw two wings along the diagonals made by the numerator of one fraction and the denominator of the other fraction and draw an antenna on each wing.

2. As suggested by the wings, that look like a multiplication sign, multiply the numbers in each wing and put the product in the antenna for the wing.

3. Think or say: “This poor butterfly needs a body.” To give it a body, connect the bottom parts of the wings with a body-like loop and multiply the two denominators it connects, putting the product inside the body.

4. Add or subtract the numbers in the antennae in keeping with what is being done to the fractions and put the result over the number in the body.

5. If necessary, reduce or simplify the result.

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## Wednesday, June 3, 2015

### Large Numbers With Names

The following table lists names of large numbers which are found in many English dictionaries and thus have a special claim to being "real words". The "Traditional British" values shown are not used in American English and are becoming very rare in British English, but their other-language variants are dominant in many non-English-speaking areas, including continental Europe and Spanish speaking countries in Latin America.

## Standard dictionary numbers

NameShort scale
modern British)
Long scale
(continental Europe,
older British)

Million106106

Milliard109

Billion1091012

Trillion10121018

Quintillion10181030

Sextillion10211036

Septillion10241042

Octillion10271048

Nonillion10301054

Decillion10331060

Undecillion10361066

Duodecillion10391072

Tredecillion10421078

Quattuordecillion10451084

Quindecillion10481090

Sexdecillion (Sedecillion)10511096

Septendecillion105410102

Novemdecillion (Novendecillion)106010114

Vigintillion106310120

Centillion1030310600

## The googol Family

### The names googol and googolplex were introduced in Kasner and Newman's 1940 book, Mathematics and the Imagination, in the following passage: The name "googol" was invented by a child (Dr. Kasner's nine-year-old nephew) who was asked to think up a name for a very big number, namely 1 with one hundred zeroes after it. He was very certain that this number was not infinite, and therefore equally certain that it had to have a name. At the same time that he suggested "googol" he gave a name for a still larger number: "Googolplex". A googolplex is much larger than a googol, but is still finite, as the inventor of the name was quick to point out. It was first suggested that a googolplex should be 1, followed by writing zeros until you got tired. This is a description of what would actually happen if one actually tried to write a googolplex, but different people get tired at different times and it would never do to have Carnera a better mathematician than Dr. Einstein, simply because he had more endurance. The googolplex is, then, a specific finite number, equal to 1 with a googol zeros after it. ValueNameAuthority                    10100GoogolKasner and Newman, dictionaries 10googol = $\,\!10^{10^{100}}$GoogolplexKasner and Newman, dictionaries If you wish to see a googolplex written out, here's a link you can click on, http://www.googolplexwrittenout.com/ . Of course it comes in multiple volumes, each containing 1 million digits (mostly zeros) of the written out number. A googolplex is so big that if you could read 1 million volumes of 1 million digits in only a 1/1000 of a second, it would still take you MUCH longer than the age of the universe to finish.

Citations:http://en.wikipedia.org/w/index.php?title=Names_of_large_numbers&oldid=665322020