Question

Find a counterexample to show that the conjecture is false. The product of two positive numbers is always greater than either number.

Answer 1

Answer:

$\frac{1}{2}$×$\frac{1}{4}$=$\frac{1}{8}$

Step-by-step explanation:

This sentence isn't always true.

• here is a counter example :

The trick is to use fractional numbers .

• $\frac{1}{2}$ ×$\frac{1}{4}$ = $\frac{1}{8}$

let's analyse this example :

• $\frac{1}{2}$$\geq$$\frac{1}{8}$   and  $\frac{1}{4}$$\geq$$\frac{1}{8}$

1/2=0.5 and 1/4=0.25 but 1/8=0.125

0.125<0.25<0.5

• here is another example : (1/2)*(1/3)=1/6
• the same thing : 1/6<1/3<1/2