Mathematics, 06.07.2019 10:00 ladybugys

Which is a counterexample for the conditional statement shown? if the numerator of a fraction is larger than the denominator of the fraction, then the fraction is greater than 1. any fraction with a denominator of 0 any fraction with a numerator of 0 any fraction with a positive numerator and a negative denominator any fraction with a negative numerator and a positive denominator

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Answer from: paaoolav

Option 2 and 3

Step-by-step explanation:

To answer the question, let's analyze each one of the statements.

* If the denominator of the fraction is 0 then the division tends to infinity and is not defined. Therefore we can discard the first option

$\frac{3}{0}$ = not defined

* If the numerator is 0 the fraction will always be equal to 0. The -3 is less than 0, therefore if we do:

$\frac{0}{-3} = 0$

0> -3

Pero 0 <1.

This case serves as a counterexample

If the numerator is negative and the denominator is positive, then the first condition of the statement is not met, and therefore nothing can be proved with this example.

If the numerator is positive and the denominator negative, then the numerator will always be greater, and since it is a division of different signs, the result will always be a negative number less than 1. Therefore this is the counterexample sought.

$\frac{10}{-2} = -5$

10> -2

-5 <1.

Answer from: amelvin41

any fraction with a positive numerator and a negative denominator

Step-by-step explanation:

The given conditional statement : If the numerator of a fraction is larger than the denominator of the fraction, then the fraction is greater than 1.

For the counterexample let's check all the options:-

Any fraction with a denominator of 0 .

Since, it contradicts the definition of fraction so it will not considered as fraction.

Any fraction with a numerator of 0 .

Here the denominator is not defined it can be negative or positive number.

Any fraction with a positive numerator and a negative denominator .

Let the fraction be $\frac{x}{y}$ , where x is the positive numerator and y be a negative number . When we simplify it, it will become a negative fraction.

Since all the negative fractions are less than 0.

Therefore the fraction will be less than 1.

Hence, it is the counter example of the given conditional statement.

Any fraction with a negative numerator and a positive denominator.

Here numerator is less than denominator. Hence does not follow the hypothesis of conditional statement.

Answer from: Quest

chicken chicken chicken

step-by-step explanation:

Answer from: Quest

step-by-step explanation:

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Which is a counterexample for the conditional statement shown? if the numerator of a fraction is la...