Download Reducing Fractions to Lowest Terms

Divide by the greatest number that can divide
Evenly into the numerator and denominator.
Ex: 9 ÷ 9 = 1
18 ÷ 9 = 2
OR
Divide by a smaller factor but divide more than once.
9 ÷ 3= 3 ÷ 3= 1
18 ÷ 3 = 6 ÷ 3 = 2
A Fraction is in lowest terms when 1 is the only common
factor that can divide evenly into the numerator and
denominator. The following are fractions in lowest terms.
Ex:
3 , 7 ,
4
9
11 , 9 ,
12 10
12 ,
17
1
8
If the numerator or denominator is a prime number 3 or
higher, the fraction is in lowest terms.
Prime numbers: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37,
43, 47, 53, 59, 61, 71, 73, 79, 83, 89, 97
Divisibility Rules are on the next page
Divisibility Rules – Rules to help one know what number to
divide by to reduce a fraction.
1. If the numerator and denominator are even, divide by 2.
Even numbers end in 0,2,4,6, or 8. Ex: 4 ÷ 2 = 2
10 ÷ 2 = 5
2. If the numerator and denominator end in 0,
divide by 10.
30 ÷ 10 = 3
50 ÷ 10 = 5
3. If the numerator and denominator end in 0 and 5,
Divide by 5. Ex: 20 ÷ 5 = 4
35 ÷ 5 = 7
4. If 3 can divide evenly into the sum of the numerator and
the sum of the denominator, divide by 3.
Ex: 12 = 1 + 2 = 3
15 = 1 + 5 = 6
3 can divide evenly into 3
3 can divide evenly into 6
12 ÷ 3 = 4
15 ÷ 3 = 5
lowest terms
5. A number is divisible by 4 if its last two digits are
divisible by 4.
Ex1: 24
24 is divisible by 4. 24 ÷ 4 = 6
Ex2: 40
40 is divisible by 4. 40 ÷ 4 = 10
Therefore 4 can divide evenly into both 24 and 40.
6. A number is divisible by 6 if it is an even number
divisible by 3.
Ex: 36 is an even number.
3 + 6 = 9, therefore it is divisible by 3. (9 ÷ 3 = 3)
36 is also divisible by 9. 36 ÷ 6 = 6
7. A number is divisible by 9 if the digits add up to 9.
Ex: 81
8 + 1 = 9, therefore 9 divides evenly into 81
81 ÷ 9 = 9
Finding the lowest terms
steps
1. List the factors of the smaller number in the
Fraction.
2. Pick the largest factor that can be divided evenly
Into the numerator and denominator (GCF or
Greatest common factor)
3. Divide both numerator and denominator by
The GCF.
Example:
8
16
8 is the smaller number
factors of 8 are 1,2,4,8
8 is the largest number that can divide evenly in 16
8 ÷ 8=1
16 ÷ 8 = 2
lowest terms
A fraction is in lowest terms when 1 is the GCF.
When 1 is the only number that can divide evenly into both the
Numerator and denominator