Respuesta :
Answer:
The possible two fractions are [tex]\frac{1}{2}[/tex] and [tex]\frac{1}{2}[/tex]
Step-by-step 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 [tex]\frac{a}{b}[/tex] and the second fraction is [tex]\frac{c}{d}[/tex]
It is given that [tex]\frac{a}{b}>\frac{2}{5}[/tex] and [tex]\frac{c}{d}>\frac{2}{5}[/tex] but [tex]\frac{a}{b}\times \frac{c}{d}<\frac{2}{5}[/tex]
Condition I:
[tex]\frac{a}{b}>\frac{2}{5}[/tex]
[tex]5a>2b[/tex]
Condition II:
[tex]\frac{c}{d}>\frac{2}{5}[/tex]
[tex]5c>2d[/tex]
Condition III:
[tex]\frac{a}{b}\times \frac{c}{d}<\frac{2}{5}[/tex]
[tex]5ac<2bd[/tex]
Substitute a = 2 in [tex]5a>2b[/tex]
[tex]10>2b[/tex]
Substitute c = 2 in [tex]5c>2d[/tex]
[tex]10>2d[/tex]
Substitute a = 2 and c = 2 in [tex]5ac<2bd[/tex]
[tex]10<bd[/tex]
Now we need to select the value of b and d so that above 3 conditions are satisfied.
For this substitute b = 4 in [tex]10>2b[/tex]
[tex]10>8[/tex] Which is true.
For this substitute d = 4 in [tex]10>2d[/tex]
[tex]10>8[/tex] Which is true.
For this substitute b = 4 and d = 4 in[tex]10<bd[/tex]
[tex]10<16[/tex] Which is true.
So, the possible two fractions are [tex]\frac{2}{4}[/tex] and [tex]\frac{2}{4}[/tex] or [tex]\frac{1}{2}[/tex] and [tex]\frac{1}{2}[/tex]
