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What are fractions?
The word fraction means 'a part of the whole', it comes from the Latin word frangere which means to break. They are written with one number on top of another, the lower number tells you the size of the piece, and the upper number tells you how many pieces of that size you have. So, one piece, that is a quarter of the whole is written as 1/4 and two pieces would be written as 2/4. The lower number is called the denominator and the upper number (the 2 in 2/4) is the numerator.
One important rule with fractions is that when adding two fractions, the denominators must match. If they do, the numerators are added to get the final answer.
Example: 1/5 + 2/5 = 3/5. Only the top numbers add, and only when the bottom numbers match up.
How is this topic used in the real world?
The US Customary System of measurement is the official name for the system that uses inches, feet, and miles to measure lengths. The inch is too big for most accurate measurements (the kind you find in the building trades and in automobile repair work). Because of this, fractions of an inch often appear and have to be added and subtracted.
It is still common to find wrenches that are sized by fractions of an inch ( 5/8, 9/16 or 11/2 inch) and the standard two-by-four used in house construction is really 1 1/2 inches by 3 1/2 inches. Workers have to be able to add, subtract and multiply fractions.
A problem with fractions.
Fractions can be either proper or improper. An improper fraction has a numerator that is larger than the denominator: 6/5, 10/5 and 3/2 are all improper fractions. They are called improper because they represent an amount that is greater than one. 3/2 means three halves. Three halves is the same as one and a half. 11/2 is called a mixed fraction, because it has both a whole number (1 ) and a fraction (1/2). In mathematics, improper fractions are usually easier to use, but when talking about amounts in the real world, we usually say, "Add 1 and 1/4 cups of flour..." instead of saying, "Add 5/4 cups of flour."
A basic problem would be to convert a mixed fraction into an improper fraction.
2 1/2 = 2 + 1/2
2 = 4 X 1/2 = 4/2
finally, 4/2 + 1/2 = 5/2
Who invented fractions?
Simple fractions, like 1/2 or 1/3 are probably older than recorded history. They would have arisen naturally when some quantity had to be evenly divided. Think about how we cut a pie or a cake into equal fractions so that no one person gets more than a fair share.
Using fractions in a more formal, mathematical way is at least as old as the Egyptians (1000 BC) who only used fractions that had one as the numerator. In their system, there was no such thing as 3/4, rather, they would have to write 1/4 three times.
An interesting fact about coordinate fractions:
Zeno of Elea was famous for his paradoxes. Although he lived in the 5th century BC, the problems he posed are still talked about today, 2,400 years after his death.
Zeno said, if an arrow is shot toward a target, it first must travel half-way, and then it must travel half-way from this new place toward the target, and so on. At each step, the arrow travels half the remaining distance.
The distance traveled is 1/2 + 1/4 + 1/8 + 1/16 and so on forever.
To get to the target, the arrow has to travel all these smaller and smaller distances. Zeno claimed that since the series of fractions is infinite, the arrow can never reach the target, as it will always have just a little bit farther to go.