Question
The product of a positive and its negative is 3 1/16, what is the number
Answers
Answered by
GPT-4o mini
Let the positive number be \( x \). The negative of that number is \( -x \). According to the problem, the product of the positive number and its negative is given by:
\[
x \cdot (-x) = 3 \frac{1}{16}
\]
We can convert \( 3 \frac{1}{16} \) to an improper fraction:
\[
3 \frac{1}{16} = \frac{3 \times 16 + 1}{16} = \frac{48 + 1}{16} = \frac{49}{16}
\]
Now, we can rewrite the equation:
\[
-x^2 = \frac{49}{16}
\]
To solve for \( x^2 \), we multiply both sides by -1:
\[
x^2 = -\frac{49}{16}
\]
Since \( x \) represents a positive number, \( x^2 \) must be positive. Here, we notice that there is an inconsistency because \( -\frac{49}{16} \) cannot represent the square of a real number.
Therefore, the statement in the problem is not possible. The product of a positive number and its negative cannot equal a positive value.
If we recheck the equation, we find:
\[
-x^2 = 3 \frac{1}{16} \implies x^2 = -\frac{49}{16}
\]
This indicates that we cannot have a positive real solution. Thus, there is no positive number whose product with its negative equals \( 3 \frac{1}{16} \).
\[
x \cdot (-x) = 3 \frac{1}{16}
\]
We can convert \( 3 \frac{1}{16} \) to an improper fraction:
\[
3 \frac{1}{16} = \frac{3 \times 16 + 1}{16} = \frac{48 + 1}{16} = \frac{49}{16}
\]
Now, we can rewrite the equation:
\[
-x^2 = \frac{49}{16}
\]
To solve for \( x^2 \), we multiply both sides by -1:
\[
x^2 = -\frac{49}{16}
\]
Since \( x \) represents a positive number, \( x^2 \) must be positive. Here, we notice that there is an inconsistency because \( -\frac{49}{16} \) cannot represent the square of a real number.
Therefore, the statement in the problem is not possible. The product of a positive number and its negative cannot equal a positive value.
If we recheck the equation, we find:
\[
-x^2 = 3 \frac{1}{16} \implies x^2 = -\frac{49}{16}
\]
This indicates that we cannot have a positive real solution. Thus, there is no positive number whose product with its negative equals \( 3 \frac{1}{16} \).