Facts about Fractions

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When one is young, the biggest lesson learnt at home is that of sharing. While growing up with a sibling, we are always taught that everything at home belongs equally to both.
The concept of equal allocation is reinforced at regular intervals following fights that occur and recur faster than a sneeze, and before the blink of an eye, we master the math behind fractions through the graceful art of sharing.
As Robert Brault rightfully said, “The advantage of growing up with siblings is that you become very good at fractions”.
Be it the last slice of pizza or the last bar of chocolate, fractions to be divided and shared are calculated to utmost precisions. This legacy continues forever and the most carefully calibrated fraction equations remain in the working memory of our brains ready to be employed at all required times.

The facts given below elucidate the knowledge of fractions that I gained over the last few years.

1. Origin of the word fractions.
The word ‘Fraction’ came to be used as a math term sometime after the early 15th Century. It originated from the Latin word ‘Fractio’ meaning “a breaking.”

2. History of fractions.
History suggests that the first noted evidences of the use of fractions dates back to 2000 BC in Egypt, where fractions were used to calculate taxes. The land belonging to an individual was divided into sections, and each section was taxed a certain amount.
The same idea was adopted by the British in 1550 AD for profits of voyage that had to be paid.

3. The earliest representation of fractions differed from the presently used ones.

As the concept of fractions first originated in Egypt, its initial representations were in the form of pictures called hieroglyphs. For example, the picture of a mouth was drawn above a number to represent a unit fraction.

4. Fractions help explain the infinite chocolate trick.

As per the infinite chocolate trick, on dividing a whole bar of chocolate into two trapezoids, one rectangle and a smaller square, an extra piece of chocolate is obtained when rearranging the divided sections. The explanation to this trick is that on rearranging the divided sections, the extra piece obtained is equal to the tiny fraction of chocolate lost while aligning the sides of the trapezoid.

5. The mind blowing 1/998001 fraction.

The fraction 1/998001 when converted to its equivalent decimal, gives every three digit number except 998.
1/998001= 0.000001002003004……….995996997999000001002….

6. There is no fraction exactly equal to pi.
Pi is an irrational number and its decimal expansion never terminates. The value of pi though represented as 22/7 in fractions, is precise only to two decimal places. 355/113 is a better approximation as it is precise to 6 decimal places.
There is however no fraction that exactly equals the decimal expansion of pi.

7. Characteristics of fractions.
The characteristics of fractions can be explained as follows:
i. a/b where a<b is a proper fraction.
ii. a/b where a>b is an improper fraction.
iii. A fraction written with a whole number is called a mixed fraction.
iv. An improper fraction may be written as a mixed fraction and vice versa.

8. Equivalent fractions.
Equivalent fractions are those which have different numbers in the numerator and denominator, but the same final value.
An example of equivalent fractions: 1/2= 5/10=100/200

9. Reciprocal fractions.

Any fraction a/b, forms its reciprocal fraction when flipped over such that the denominator and numerator exchange places. The reciprocal fraction of a/b is thus b/a. Product of reciprocal fractions is 1.

10. Dividing fractions.

When dividing two fractions, the answer is obtained by simply reciprocating the divisor and multiplying the two fractions.
(a/b)/(c/d) = (a/b)*(d/c)

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