Answer :
To understand the statement [tex]\(-30 < -5\)[/tex], let's break it down:
1. Negative Numbers and Number Line: Negative numbers are positioned to the left of positive numbers on the number line. The further left a number is, the smaller it is.
2. Understanding [tex]\(-30 < -5\)[/tex]:
- Consider numbers on the number line. [tex]\(-30\)[/tex] is located to the left of [tex]\(-5\)[/tex].
- Therefore, [tex]\(-30\)[/tex] is smaller than [tex]\(-5\)[/tex], because being further left means being less.
3. Analyzing the Options:
- Option A: "30 is greater than 5" is not related to the negative numbers [tex]\(-30\)[/tex] and [tex]\(-5\)[/tex].
- Option B: "30 is less than minus 5" incorrectly refers to comparing positive 30 with negative numbers.
- Option C: "Minus 30 is less than minus 5" correctly captures the expression [tex]\(-30 < -5\)[/tex].
- Option D: "Minus 30 is greater than minus 5" is incorrect because we know [tex]\(-30\)[/tex] is to the left of [tex]\(-5\)[/tex] on the number line, meaning it is less.
The correct interpretation of the statement [tex]\(-30 < -5\)[/tex] is Option C: Minus 30 is less than minus 5.
1. Negative Numbers and Number Line: Negative numbers are positioned to the left of positive numbers on the number line. The further left a number is, the smaller it is.
2. Understanding [tex]\(-30 < -5\)[/tex]:
- Consider numbers on the number line. [tex]\(-30\)[/tex] is located to the left of [tex]\(-5\)[/tex].
- Therefore, [tex]\(-30\)[/tex] is smaller than [tex]\(-5\)[/tex], because being further left means being less.
3. Analyzing the Options:
- Option A: "30 is greater than 5" is not related to the negative numbers [tex]\(-30\)[/tex] and [tex]\(-5\)[/tex].
- Option B: "30 is less than minus 5" incorrectly refers to comparing positive 30 with negative numbers.
- Option C: "Minus 30 is less than minus 5" correctly captures the expression [tex]\(-30 < -5\)[/tex].
- Option D: "Minus 30 is greater than minus 5" is incorrect because we know [tex]\(-30\)[/tex] is to the left of [tex]\(-5\)[/tex] on the number line, meaning it is less.
The correct interpretation of the statement [tex]\(-30 < -5\)[/tex] is Option C: Minus 30 is less than minus 5.
