Review of Introductory Mathematics
FRACTIONS
This is the simplest form the fraction can have. To eliminate the lengthy process of trial and error
used in finding the LCD, you can reduce the denominators to their prime numbers.
Least Common Denominator Using Primes
A prime number is a whole number (integer) whose only factors are itself and one. The first
prime numbers are:
1, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, . . . .
By dividing by primes, you can find that the primes of 105 are:
7 = a prime number, therefore, stop dividing.
105
3
35
35
5
7
The primes of 105 are: 3, 5, 7
A systematic way of finding the prime factors of larger positive integers is illustrated below. The
primes are tried in order, as factors, using each as many times as possible before going on to the
next. The result in this case is:
504
=(2)(252)
=(2)(2)(126)
=(2)(2)(2)(63)
=(2)(2)(2)(3)(21)
=(2)(2)(2)(3)(3)(7)
To add several fractions with different denominators, follow these steps:
Step 1:
Express denominators in prime factors.
Step 2:
Determine the least common denominator by using all of the prime
numbers from the largest denominator, and then include each prime
number from the other denominators so that each denominator can be
calculated from the list of primes contained in the LCD.
Step 3:
Rewrite using the least common denominator.
Step 4:
Add the fractions.
Rev. 0
Page 31
MA-01
