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= $\frac{3}{5},\frac{3}{8} \frac{5}{8},\frac{3}{5.8},\frac{5}{3.8}, \frac{8}{5.3},\frac{3}{5+8},\frac{5}{3+8}, \frac{5-3}{8}$⇒$\frac{3}{5},\frac{3}{8} \frac{5}{8},\frac{3}{40},\frac{5}{24}, \frac{8}{15},\frac{3}{13},\frac{5}{11}, \frac{1}{4}$

Similarly, the possible improper fraction= $\frac{5}{3},\frac{8}{3} \frac{8}{5},\frac{40}{3},\frac{24}{5}, \frac{15}{8},\frac{13}{3},\frac{11}{5}, \frac{19}{3}$   ( Here, $8-\frac{5}{3}=\frac{19}{3}$ )