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Greater than 2/5 with a product less than 2/5​

User Smoak
by
4.0k points

1 Answer

5 votes

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

User EisenbergEffect
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