Reducing Fractions to Lowest Terms (a/k/a Simplest Form)
Writing Fractions in Simplest Form (also known as Reducing Fractions to Lowest Terms)
 Sometimes you just look at it and you know right away. Many people can do
The Usual Short Way
Find a common factor between
numerator and denominator.
Divide it out. Repeat as needed.
14÷2
56÷2
70÷2
22÷2
28
→
→
,
35
7
11
28÷7
35÷7
Example:
→
4
5
No common factors, already in
lowest terms.
99÷3
33
33÷3
11
→ ,
→
108÷3
36
72÷3
39÷3
8÷8
80÷8
18÷6
30÷6
→
36÷3
24
→
→
13
1
10
3
5
When you don’t know the
answer right away, use one
of these methods to
reduce the fraction.
12
Example:
Example:
Example:
Example:
Example:
Example:
14
22
56
70
20
63
99
108
72
39
8
80
18
30
15
20
3
→ instantly.
4
The Long Way when you need it
Make the prime factorizations of
the numerator and denominator.
Cancel out common prime factors.
2∙7
7
→
2 ∙ 11 11
2∙2∙2∙7 4
→
2∙5∙7
5
2 ∙ 2 ∙ 5 20
→
3 ∙ 3 ∙ 7 63
3 ∙ 3 ∙ 11
11
→
2 ∙ 2 ∙ 3 ∙ 3 ∙ 3 12
2 ∙ 2 ∙ 2 ∙ 3 ∙ 3 24
→
3 ∙ 13
13
2∙2∙2
1
→
2 ∙ 2 ∙ 2 ∙ 2 ∙ 5 10
2∙3∙3 3
→
2∙3∙5 5
ReduceFractions.docx 6/18/2014 3:20:00 PM -
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- D.R.S.
Some Tips and Tricks
If you have
If you have
If you have
If you have
𝑒𝑣𝑒𝑛 𝑛𝑢𝑚𝑏𝑒𝑟
𝑒𝑣𝑒𝑛 𝑛𝑢𝑚𝑏𝑒𝑟
,…
𝑒𝑛𝑑𝑠 𝑖𝑛 0
,…
𝑒𝑛𝑑𝑠 𝑖𝑛 0
𝑒𝑛𝑑𝑠 𝑖𝑛 5 𝑜𝑟 0
𝑒𝑛𝑑𝑠 𝑖𝑛 5 𝑜𝑟 0
,…
𝑠𝑢𝑚 𝑜𝑓 𝑑𝑖𝑔𝑖𝑡𝑠 𝑑𝑖𝑣 𝑏𝑦 3
𝑠𝑢𝑚 𝑜𝑓 𝑑𝑖𝑔𝑖𝑡𝑠 𝑑𝑖𝑣 𝑏𝑦 3
Some of them are obscure!
,…
… you know that 2 divides into each
of the numbers
156
… lop off matching trailing zeros,
because that’s like dividing by 10.
33500
228
→
78
114
→
39
57
…
and it goes further, div by 3 →
→
335
13
19
… and it continues
in the next row…
335
65
… you know that 5 divides into each
→ … and maybe more
470
94
of the numbers
but this one stops here.
867
289
… you know that 3 divides into each
→
… and maybe more
441
147
of the numbers
but this one stops here.
273
21
You might have to check 7, 11, 13,
→
because 13 divides
377
29
17, 19, or higher prime numbers.
into 273 and 377, too.
47000
470
Your Calculator’s Fraction Features Can Help
 On many calculators, just type the fraction in (as a fraction) and the calculator will display the lowest-terms
name for the fraction.
 On a TI-84 in Classic mode (that is, not in MathPrint mode), type the fraction using the division key for the
fraction bar and then MATH ENTER ENTER to ask for a lowest-terms name for the fraction.
ReduceFractions.docx 6/18/2014 3:20:00 PM -
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- D.R.S.