Question

Using the numbers 3, 5, and 8, can you write nine proper fractions and nine improper fractions? You may use each number only once within a fraction.

Answer 1

3/5

2/8

5/8

3/58

3/85

5/38

5/83

8/35

8/53

•••

8/5

8/3

5/3

85/3

58/3

38/5

35/8

83/5

Answer 2

Answer: yes we can write nine proper and nine improper fraction with help of these given numbers.

Explanation: Since, a proper fraction is a fraction which has the value less than 1, that is, the value of numerator is less than the value of denominator.

For example p/q is a proper fraction if p<q.

On the other hand, In Improper fraction numerator is greater than denominator.

Since, given numbers are 3,5 and 8

So, the possible proper fractions=
`(3)/(5),(3)/(8) (5)/(8),(3)/(5.8),(5)/(3.8), (8)/(5.3),(3)/(5+8),(5)/(3+8), (5-3)/(8)`⇒
`(3)/(5),(3)/(8) (5)/(8),(3)/(40),(5)/(24), (8)/(15),(3)/(13),(5)/(11), (1)/(4)`

Similarly, the possible improper fraction=
`(5)/(3),(8)/(3) (8)/(5),(40)/(3),(24)/(5), (15)/(8),(13)/(3),(11)/(5), (19)/(3)` ( Here,
`8-(5)/(3)=(19)/(3)` )