Equivalent Fractions: Simplifying And Building With Answers Page 6
ADVERTISEMENT
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
168
Since 120 ÷ 15 = 8 , the form of 1 to use is
c.
. Instead of multiplying the
8
8
first fraction by
, we can alternatively divide the second fraction:
8
96
8
12
÷
=
120
8
15
The missing numerator is a = 12. Note how we used the idea that division is
the inverse of multiplication to do this problem.
40
Since 200 ÷ 5 = 40 , the form of 1 to use is
d.
. Again, we do this problem
40
“backwards” by dividing the second fraction:
200
40
5
!
÷
= !
320
40
8
The missing denominator is b = 8.
This last example leads to the idea of simplifying (or reducing) fractions. That is, given a
32
fraction such as
, can we apply the Fundamental Property of Fractions to reduce the numbers
40
8
to a “simpler” form? Using the form of 1 as
, we can write:
8
32
4 • 8
4
=
=
40
5 • 8
5
32
4
4
We say that
reduces to
. Note that
does not reduce further, since there is no other form
40
5
5
8
of 1 we can use in the Fundamental Property of Fractions. But where did
come from? Recall
8
from Chapter 1 that the greatest common factor (GCF) of 32 and 40 is the largest number that
will divide into both 32 and 40, which is precisely the number 8. In other words, using the GCF
of the numerator and denominator as the common factor will always result in the form of 1 to
use. In the past, you may have learned to reduce fractions by dividing the numerator and
denominator by the same number (this is the same as our form of 1). The big problem, however,
is knowing when to stop.
150
ADVERTISEMENT
0 votes
Related Articles
Related forms
Related Categories
Parent category: Education