Explanation:
The possible two fractions are \frac{1}{2}
2
1
and \frac{1}{2}
2
1
Explanation:
Consider the provided information.
We need to determine two fractions that are each greater than 2/5 whose product is less than 2/5.
Let the first fraction is \frac{a}{b}
b
a
and the second fraction is \frac{c}{d}
d
c
It is given that \frac{a}{b} > \frac{2}{5}
b
a
>
5
2
and \frac{c}{d} > \frac{2}{5}
d
c
>
5
2
but \frac{a}{b}\times \frac{c}{d} < \frac{2}{5}
b
a
×
d
c
<
5
2
Condition I:
\frac{a}{b} > \frac{2}{5}
b
a
>
5
2
5a > 2b5a>2b
Condition II:
\frac{c}{d} > \frac{2}{5}
d
c
>
5
2
5c > 2d5c>2d
Condition III:
\frac{a}{b}\times \frac{c}{d} < \frac{2}{5}
b
a
×
d
c
<
5
2
5ac < 2bd5ac<2bd
Substitute a = 2 in 5a > 2b5a>2b
10 > 2b10>2b
Substitute c = 2 in 5c > 2d5c>2d
10 > 2d10>2d
Substitute a = 2 and c = 2 in 5ac < 2bd5ac<2bd
10 < bd10<bd
Now we need to select the value of b and d so that above 3 conditions are satisfied.
For this substitute b = 4 in 10 > 2b10>2b
10 > 810>8 Which is true.
For this substitute d = 4 in 10 > 2d10>2d
10 > 810>8 Which is true.
For this substitute b = 4 and d = 4 in10 < bd10<bd
10 < 1610<16 Which is true.
So, the possible two fractions are \frac{2}{4}
4
2
and \frac{2}{4}
4
2
or \frac{1}{2}
2
1
and \frac{1}{2}
2
1