I have borrowed material used in the blog from from internet (it is not my original creation). But added annotations to make kids understand.
My task was to teach kids about rational numbers. And then how to divide and multiply rational numbers?
I started off with an example like this. This lead to the concepts of factors and primes. I am pretty sure there are many applications of prime numbers. This is one simple example where kids can apply their knowledge about prime numbers to reduce fractions using prime factorization.
Factors are numbers you can multiply together to get another number.
Starting from factor concept, introduce the concept of prime numbers:
A number (except 1) with only two factors is called a PRIME number. Others are called composite numbers.
So our original number 36 has many factors (see above), but only 2 and 3 are prime factors. Can we write 36 in terms of just its prime factors? Consider one factorization of 36:
Once you have your prime factorization, division becomes lot simpler.
The beauty of using the prime factorization method is that you can be sure that the fraction’s reduction possibilities are exhausted — that is, you can be certain that you haven’t missed any factors that the numerator and denominator may have in common.