Chapter 5: Fractions 61You can go the other way, too, taking a fraction to a simpler appearance. This is officially called
simplifying, but you’ll often hear it called reducing to lowest terms, or just reducing.MATH TRAP
The expression “reducing a fraction” is a dangerous way to describe simplifying.
It makes it sound like the fraction is getting smaller, but it’s not. The appearance
of the fraction is changing, but its value is not. If you must use “reduce”—and most
people do—remember that the fraction hasn’t changed. 53 may look smaller than 405243 ,
but it’s the same number.The fraction
16
36 can be written in a much simpler form. Find a number that divides both the
numerator and denominator, preferably the GCF. In this case, that’s 4. Think of the fraction
with the numerator and denominator factored:
16
3644(^5943)
3
. Can you see the disguised 1 in there?
16
36
44
944
94
44
9 14
9(^55335353). The fraction^4
9
is a simpler name for^16
36
.
If you don’t know, or don’t want to look for, the GCF of the numerator and denominator, you can
start the process with any number that divides both. Divide the numerator and denominator by
the same number. Repeat until there are no other numbers that will divide both. It may take a
while, but you’ll get there. If you start with the GCF, you’ll only need one try.CHECK POINT- Change^1
5
to a fraction with a
denominator of 40. - Change^3
4
to a fraction with a
denominator of 28. - Change^5
7
to a fraction with a
denominator of 147. - Simplif y^35
40
.
- Simplify^63
84
.
Multiplying and Dividing Fractions
Since you’ve already had a preview of the rule for multiplying fractions, let’s start the conversa-
tion about arithmetic there. The basic rule for multiplication of fractions calls for multiplying
numerator times numerator and denominator times denominator, then simplifying if possible.
To m u l t i p l y^1
93
7
3 , multiply 1 × 3 and 9 × 7. This gives you^3
63
, which simplifies to^1
21
, because
3
6313
21 31
213
31
55521 1(^333)
3