Express as a rational number with denominator,- 28
The Correct Answer and Explanation is:
Correct Answer:
A rational number with denominator –28 can be written in the form a/–28, where a is an integer. For example, 5/–28 is a valid rational number.
Explanation:
A rational number is defined as any number that can be expressed as a fraction a/b, where a and b are integers and b is not equal to zero. The denominator, in this case, is specifically given as –28. Although it is more common to write fractions with a positive denominator, having a negative denominator does not disqualify a number from being rational.
To express any rational number with denominator –28, one must place any integer in the numerator while keeping –28 in the denominator. For example, the rational numbers 1/–28, –3/–28, 10/–28, and –7/–28 are all valid. Each of these fractions represents a rational number because both the numerator and the denominator are integers, and the denominator is nonzero.
Additionally, a fraction such as –4/–28 can be simplified. Dividing both numerator and denominator by –4 gives 1/7, which is also rational. The sign of the denominator affects the sign of the fraction. For instance, 5/–28 is equivalent to –5/28, because the negative sign can be moved to the numerator or in front of the entire fraction without changing the value.
It is also important to understand that the placement of the negative sign is a matter of convention. A fraction like a/–28 is considered the same as –a/28 or –(a/28). The key requirement is that the value must still represent a ratio of integers with a non-zero denominator. Therefore, any integer placed over –28 forms a rational number.
