1/2 of the above rectangle is shaded. The same rectangle
can be divided again so that it is
broken into 4 pieces:
The same area is shaded, but now we have two out of four
or 2/4 of the rectangle shaded.
It is clear, then, that 1/2 and 2/4 are equal. Similarly, we could have taken
the same rectangle
and cut it into six equal pieces:
We still have exactly half ( 1/2) of the rectangle shaded,
but now there are three of the six
equal pieces shaded. So 1/2 and 3/6 are equal. We could cut this rectangle into
of equal pieces and then shade half of them, and each one would give us another
represent 1/2 . Some other ways are 5/10, 22/44, 500/1000, 37/74. Notice that in
the denominator (that is, the bottom number) is twice as large as the numerator.
The simplest way to write this particular fraction is 1/2 because the numerator and
don’t have any factors incommon other than 1. When you are asked to reduce a
your goal is to write the fraction this way. To do this, you simply divide the
and denominator by the same number until there are no common factors left.
multiplying) the numerator and denominator of a fraction by the same number does
not change thevalue of the fraction .
Example 1: Reduce 3/15
Since 3 and 15 are both divisible by 3, we can divide the
top and bottom of this fraction to
get 1/5 .
Example 2: Reduce 24/32
Since 24 and 32 are both divisible by 2, we can divide the
top and bottom to get 12/16. Notice,
though, that this fraction is not reduced completely: the numerator and
have factors in common. Since 12 and 16 are both divisible by 4, we can divide
the top and
bottom to get 3/4 . 3 and 4 don’t have any factors in common, so we’re done. Of
could be reduced in one step simply by dividing the top and bottom by 8 to get
Multiplication and Division of Fractions Multiplying fractions is the simplest of operations to perform because it is
the way one might guess: multiply the tops and multiply the bottoms.
Addition and subtraction of fractions takes a little more
finesse than multiplication and
division. To add two fractions, the fractions must have the same denominator. We
know that if we divide the top and bottom of any fraction by the same number the
the fraction does not change (we saw this when we reduced fractions). We can
the top and bottom by any number ( except zero , of course) and it won’t change
of the fraction. This fact is used to do fraction addition and subtraction.
Example 5: Perform the following addition and
First we get a common denominator by multiplying the
numerator and denominator of the
second fraction by 2. Once we have a common denominator, we add the numerators
keep the denominator.
Subtraction works exactly the same way as addition. Here
we had to change both denominators.
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