Question

Ułamki : 1/2 , 1/3 , 1/4 , 1/5... nazywają się ułamkami egipskimi.Każdy ułamek można przedstawić jako sumę różnych ułamków egipskich , np 3/4 = 1/2 + 1/4 lub 13 /12 = 1/2 +1/3 +1/4.

a) przedstaw 9/20 za pomocą sumy ułamków egipskich

Answer 1

Explanation:

An Egyptian fraction may be defined as a finite sum of some distinct unit fractions. Some example of the Egyptian fractions are

`$(1)/(3)+(1)/(5)+(1)/(9)$` ,

`$(1)/(4)+(1)/(6)+(1)/(13)$`

In this type of fractions, there is always a numerator in in the form of 1 and a denominator as a positive integer.

So every fraction can be written as sum of the fraction in Egyptian fraction form.

a). The given fraction
`$(9)/(20)$` cab be written in the form of Egyptian fraction form as the sum of

`$\Rightarrow (1)/(4) + (1)/(5)$`

`$\Rightarrow (5)/(20) + (4)/(20)$`

`$\Rightarrow (9)/(20) $`