You can do this a number of ways. The simplest is to decompose 4 into a sum.
4 = 1 + 3
4/5 = 1/5 + 3/5 Or
4 = 2 + 2
4/5 = 2/5 + 2/5
The ancient Egyptians (and some other civilizations) made use of what we now call "Egyptian Fractions" to write fractions with a numerator greater than 1. They would, for example, write 2/5 as the sum
2/5 = 1/3 + 1/15
They had a simple algorithm for finding such sums good with fractions of the form 2/n. In your problem, however, we have double this amount.
4/5 = 2(2/5) = 2(1/3 + 1/15) = 2/3 + 2/15
Applying the 2/n algorithm again, we find that
4/5 = 2/3 + 2/15 = (1/2 + 1/6) + (1/10 + 1/30)
Thus, a decomposition of 4/5 into Egyptian Fraction form is
4/5 = 1/2 + 1/6 + 1/10 + 1/30 ______
It is unlikely you are expected to know anything about Egyptian Fractions, but they are an interesting way to work your problem. (At the link above is a section on how to compute them when the denominator is prime (3, 5) and when it is not (15).)
4 = 1 + 3
4/5 = 1/5 + 3/5 Or
4 = 2 + 2
4/5 = 2/5 + 2/5
The ancient Egyptians (and some other civilizations) made use of what we now call "Egyptian Fractions" to write fractions with a numerator greater than 1. They would, for example, write 2/5 as the sum
2/5 = 1/3 + 1/15
They had a simple algorithm for finding such sums good with fractions of the form 2/n. In your problem, however, we have double this amount.
4/5 = 2(2/5) = 2(1/3 + 1/15) = 2/3 + 2/15
Applying the 2/n algorithm again, we find that
4/5 = 2/3 + 2/15 = (1/2 + 1/6) + (1/10 + 1/30)
Thus, a decomposition of 4/5 into Egyptian Fraction form is
4/5 = 1/2 + 1/6 + 1/10 + 1/30 ______
It is unlikely you are expected to know anything about Egyptian Fractions, but they are an interesting way to work your problem. (At the link above is a section on how to compute them when the denominator is prime (3, 5) and when it is not (15).)
