Understanding some basic math concepts is necessary before understanding what "simplify a fraction" means. The first thing needed is a solid knowledge of the multiplication tables. Practicing the various combinations of any two numbers multiplied together and recognizing the resulting number indicates readiness for further understanding.
An understanding of the concept of a prime number is also necessary. A prime number has only two factors. The factors are the number itself and the number one. Prime numbers cannot be divided by any other numbers than the two factors. This knowledge helps students understand the concept of factoring, finding the divisors of numbers and recognizing when there are no other divisors possible.
A simple fraction is where the numerator, the number on the top half of the fraction, and the denominator, the number on the bottom half of the fraction are both reduced as low as possible. This means that both the numerator and denominator must be factored (broken down to list all possible numbers that when multiplied together yield that number). By examining the factors in the numerator and denominator and recognizing any that are the same, the fraction can be reduced.
Fractions where the numerator and the denominator can be reduced by removing factors can be simplified to the lowest terms. For example, the fraction 2/4 when simplified becomes 1/2. The numerator 2 is a prime number and has the factors 2 and 1. The number 4 has the factors 2 and 4. By dividing the number 2 into both the numerator and denominator, the fraction will be simplified. 2 divided by 2 equals 1, and 4 divided by 2 equals 2. The fraction 1/2 cannot be further simplified. This is known as simplifying or reducing to lowest terms.