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Fractions - Part I
Fraction Addition
Fractions are not that difficult to understand.
They are written with a number on top (numerator), a line underneath, and
a number on the bottom (denominator).
Here's a typical fraction:
In this fraction, 3 is the numerator, 4 is the denominator, and it has
the value of three fourths or 3 ÷ 4.
The easiest way to show how fractions work is with money.
In the United States and Canada, money is expressed in dollars and we can
think of coins as fractions of a dollar.
A common coin is the quarter,
so-called because it is worth a quarter of one
dollar. (Look at a U.S. Quarter and you will see
the words "quarter dollar").
From the Latin word "decimus" (meaning one tenth) we get the word
dime which
is one tenth of one dollar.
If we had 3 quarters, their total value would be
3/4 of one dollar. Three dimes would equal 3/10 of one dollar. If we wanted to
find the total value of all 6 coins, we could easily add up 75¢ and
30¢ and find it equals $1.05.
However, this is exactly the same as a
math problem in which you have to find the sum of 3/4 and 3/10.
Notice that in each fraction, the bottom number denotes
the type of coin it is, hence the term
denominator. Also, you might
have heard paper money (for example $50 and $100 bills) referred to as
bills of large denominations.
Also notice that the top number in each fraction shows the amount, quantity or
number of each
coin we have, hence the term numerator.
We could add the tops of the fractions and we would be correct in saying
that it equals six coins but this does NOT give us the value.
So now we have to look for something that quarters and dimes have in
common. We have to find a
whole number into which we could convert quarters and dimes. The
quarter does NOT work because a quarter equals 2 and a half dimes. However,
nickels will work because a quarter equals 5 nickels and a dime equals
2 nickels. A nickel is one twentieth of a dollar (1/20) and so 3 dimes
equal 6 nickels and three quarters have a value of 15 nickels.
So, the nickel is the common denominator
we had to find.
We can
show this mathematically as:
3 + 3 = 15 + 6 = 21 = 1 plus 1
4 10 20 20 20 20
Yes, that was a long way to go just to add up six coins, but it does
demonstrate how fractions work and now you know what the terms
numerator, denominator and
common denominator mean.
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