FRAME 2-30.
Solution to
Frame 2-29.
Instead of looking for the biggest number that divides into both the
numerator and denominator evenly (called the "largest common
denominator"), you can divide by prime numbers. A prime number is a
4
2
=
number that cannot be divided by any whole number other than itself and
10
5
1 without leaving a remainder. Prime numbers include 2, 3, 5, 7, 11, 13,
17, 19, 23, 29, 31, and so on. Begin with "2." If "2" divides into both the
3
1
=
numerator and denominator evenly (no remainder), then reduce the
6
2
fraction by two. Take the new fraction and try to reduce the new
numerator and denominator by "2" again. Continue until the fraction can
6
1
=
no longer be reduced by 2. Then do the same with the next prime
24
4
number ("3"). Continue until there is no whole number (other than 1) that
will divide into both the numerator and the denominator evenly. For
7x4
28
7
=
=
example:
8x1
8
2
2
2
2
3
48
48
24 ; 24
12 ; 12
6 ; 6
2
=
=
=
=
=
72 2
36 2
18 2
93
72
36
18
9
3
NOTE: On 6/9, 2 will divide evenly into 6 but not into 9. Therefore, you
go to the next prime number.
A variation is to break both the numerator and the denominator down into
prime factors (prime numbers that yield the original number when
multiplied). If the same factor appears in both the numerator and
denominator, mark it out. Mark out factors one at a time. [For example,
if you have "2" as a factor 3 times in the numerator but only twice in the
denominator, you can only mark out two of the "2's" in the numerator.]
When you are finished, multiple the remaining factors to obtain the
reduced fraction. For example:
48
2x2x2x2x3
2x2x2x2x3
2
=
=
=
72
2x2x2x3x3
2x2x2x3x3
3
Reduce 200/375 by this method.
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MD0900
2-13