Reducing Fractions to Lowest Terms
METHOD
I
-
Prime Foctoring
Reduce 36 to lowest terms.
o
60
Foctor the numerotor ond denominotor into prime foctors.
36
60
z\
z\t
2. lB
z\r
2, g
IZ\I
3.3
I
36
60
-=-
2
.30
z\
2,15
Z\
3.5
2.2.3.3
2.2.3.s
Concel common foctors in numerotor ond denominotor, ond multiply the remoining foctors.
/ /./ z
7W.s=i
3
METHOD 2
-
Divisibiliry
36 ,o lowest terms.
Reduce
60
o
Using the divisibility hints on sheet 2,check for the even divisibility of prime numbers into boffi
the numeralor ond denominolor. Since 2 divides into bolh 36 & 60 evenly:
36+2 _18
60+2
o
o
30
Continue using the divisibility rules. Since 2 divides into bolfi
l8+2
9
30+2
15
Finolly, since 3 divides into bolfi 9
9+3
3
l)+J
)
& l5
l8 & 30 evenly:
evenly:
There ore no remoining common prime foctors, so the finol onswe,
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www.ucc.edu
i, :.
5
Reducing Fractions to Lowest Terms
HINTS FOR DIVISIBITITY OF SOME COMMON PRIME FACTORS*
Exomple
lf even {0,2,4,6,8)
Check rhe losr digit
lf the
Add oll digits
ls
Then number is
76
divisible by 2
sum is
divisible by 3 The number
is
divisible by 3
ihe lost digit O or 5?
I
123
6
415
The number is divisible by 5
I=
6 is even
2
123:41
+2+3=6
is divisible
Lost
19
by 3
J
415
digh is 5
5
=83
All digits ore the
Are oll of the digits the
some?
Add up every other digii.
lf there
is on even number
number is divisible by I
l.
of digits, the
lf the
sums ore lhe some, fhe number
divisible by I l.
is
66
some, ond there
ore on even
number of dioits.
66
_=6
2+3=5
5=5
253
253
* A seporote help sheet lists o complete explonotion of Divisibility
11
1l
Rules
Answers
Now, try fhe procfice problems below.
5
1.
PRACTICE PROBLEMS: Reduce the following froctions
l.
20
6.
36
-=
30
42
-=
to lowest terms.
2.
9
7
1l
J
3.
5
2. 42
66
-=
7.
E
4.
85
5.
24
3.
40
t4
4.=9,-=
J.
5l
98
70
90
--
66
6.
102
7.
8.
75
ll0
9.
10.
Thank you to the Academic Learning Centers at Union County College
www.ucc.edu
5
7
J
5
114
10.-=
7
7
9
_27
_
I
9
20
t7
t9
l5
-22
=23