Answer :
To understand the statement [tex]\(-30 < -5\)[/tex], let's break down the concept of comparing negative numbers:
1. Understanding Negative Numbers: On the number line, numbers increase in size from left to right. Negative numbers are on the left side, and the further left you go, the smaller the number.
2. Comparing Negative Numbers: For any two negative numbers, the one with the larger absolute value is actually smaller. For example, between the numbers [tex]\(-30\)[/tex] and [tex]\(-5\)[/tex], [tex]\(-30\)[/tex] has a larger absolute value (absolute value is the number without its sign), meaning [tex]\(-30\)[/tex] is further left on the number line compared to [tex]\(-5\)[/tex].
3. Applying to the Statement: The statement [tex]\(-30 < -5\)[/tex] reads as "negative 30 is less than negative 5." This means that on the number line [tex]\(-30\)[/tex] is to the left of [tex]\(-5\)[/tex].
Now, looking at your options:
- A. 30 is greater than 5: This relates to positive numbers, not negative ones.
- B. 30 is less than minus 5: This involves comparing a positive and a negative number, not two negative ones.
- C. Minus 30 is less than minus 5: This correctly describes the relationship between [tex]\(-30\)[/tex] and [tex]\(-5\)[/tex].
- D. Minus 30 is greater than minus 5: This is incorrect because [tex]\(-30\)[/tex] is actually smaller than [tex]\(-5\)[/tex].
Thus, the correct interpretation of the statement [tex]\(-30 < -5\)[/tex] is captured by option C: minus 30 is less than minus 5.
1. Understanding Negative Numbers: On the number line, numbers increase in size from left to right. Negative numbers are on the left side, and the further left you go, the smaller the number.
2. Comparing Negative Numbers: For any two negative numbers, the one with the larger absolute value is actually smaller. For example, between the numbers [tex]\(-30\)[/tex] and [tex]\(-5\)[/tex], [tex]\(-30\)[/tex] has a larger absolute value (absolute value is the number without its sign), meaning [tex]\(-30\)[/tex] is further left on the number line compared to [tex]\(-5\)[/tex].
3. Applying to the Statement: The statement [tex]\(-30 < -5\)[/tex] reads as "negative 30 is less than negative 5." This means that on the number line [tex]\(-30\)[/tex] is to the left of [tex]\(-5\)[/tex].
Now, looking at your options:
- A. 30 is greater than 5: This relates to positive numbers, not negative ones.
- B. 30 is less than minus 5: This involves comparing a positive and a negative number, not two negative ones.
- C. Minus 30 is less than minus 5: This correctly describes the relationship between [tex]\(-30\)[/tex] and [tex]\(-5\)[/tex].
- D. Minus 30 is greater than minus 5: This is incorrect because [tex]\(-30\)[/tex] is actually smaller than [tex]\(-5\)[/tex].
Thus, the correct interpretation of the statement [tex]\(-30 < -5\)[/tex] is captured by option C: minus 30 is less than minus 5.
