Give a counterexample to this statement:
"The quotient of two fractions between 0 and 1 is always a whole number."
Example:
Consider the fractions \(\frac{1}{2}\) and \(\frac{1}{3}\).
The quotient is:
\[ \frac{\frac{1}{2}}{\frac{1}{3}} = \frac{1}{2} \times \frac{3}{1} = \frac{3}{2} \]
Since \(\frac{3}{2}\) is not a whole number, this serves as a counterexample.
Answer (3)
There are many counter examples to this. People seem to think multiplying two fractions will get you a whole number but it definitely isn't the case. Just take 1/2 and 2/3 as an example:
1/2 ÷ 2/3 (dividing is the same as multiplying by the reciprocal)
1/2 * 3/2 is 3/4 and that is not a whole number. Hope this helped.
0 < 6 1 < 1 0 < 3 1 < 1 3 1 6 1 = 6 3 = 2 1
A counterexample to the statement is that the quotient of 4 1 and 2 1 results in 2 1 , which is not a whole number. Therefore, the statement is false. This demonstrates that the quotient of two fractions between 0 and 1 can result in a non-whole number.
;
