Answer :
To arrange the given integers in ascending order, we will systematically analyze and sort each set of numbers individually. Here are the steps:
### 1. List: [tex]$-6, -4, -1, 0, -3$[/tex]
1. To begin with, identify the smallest number and compare each number in the list.
2. In this list, the smallest number is [tex]$-6$[/tex].
3. Next, [tex]$-4$[/tex] is larger than [tex]$-6$[/tex] but smaller compared to others.
4. Following [tex]$-4$[/tex], [tex]$-3$[/tex] comes next because it’s larger than [tex]$-4$[/tex] but smaller than [tex]$-1$[/tex] and [tex]$0$[/tex].
5. After [tex]$-3$[/tex], [tex]$-1$[/tex] is the next value as it is larger than [tex]$-3$[/tex] but smaller than [tex]$0$[/tex].
6. Lastly, [tex]$0$[/tex] is the largest number in this list.
Hence, the sorted order for this list is:
[tex]\[ -6, -4, -3, -1, 0 \][/tex]
### 2. List: [tex]$+1, +6, +8, +3, +5$[/tex]
1. In this group, the smallest positive number is [tex]$+1$[/tex].
2. The next smallest number is [tex]$+3$[/tex].
3. Then, we consider [tex]$+5$[/tex] as it is larger than [tex]$+3$[/tex] but smaller than [tex]$+6$[/tex] and [tex]$+8$[/tex].
4. Then comes [tex]$+6$[/tex] as it is larger than [tex]$+5$[/tex].
5. The largest number in this list is [tex]$+8$[/tex].
Thus, the ascending order for this list is:
[tex]\[ +1, +3, +5, +6, +8 \][/tex]
### 3. List: [tex]$+4, +3, -10, -11, +1$[/tex]
1. Start with the smallest value, which is [tex]$-11$[/tex].
2. The next smallest number is [tex]$-10$[/tex].
3. After sorting the negative values, we move on to the positive numbers. The smallest positive among them is [tex]$+1$[/tex].
4. Next is [tex]$+3$[/tex], larger than [tex]$+1$[/tex] but smaller than [tex]$+4$[/tex].
5. Finally, [tex]$+4$[/tex] is the largest among these values.
So, the sorted order is:
[tex]\[ -11, -10, +1, +3, +4 \][/tex]
### 4. List: [tex]$-8, +8, -5, -6, +4$[/tex]
1. First, identify and list the smallest value, which is [tex]$-8$[/tex].
2. Next, [tex]$-6$[/tex] is the value larger than [tex]$-8$[/tex] but smaller than others.
3. Following [tex]$-6$[/tex], [tex]$-5$[/tex] is next as it is larger than [tex]$-6$[/tex].
4. Then, among the remaining positive numbers, [tex]$+4$[/tex] is the smallest.
5. Finally, the largest number is [tex]$+8$[/tex].
Hence, the sorted order is:
[tex]\[ -8, -6, -5, +4, +8 \][/tex]
### 5. List: [tex]$+9, -10, +6, -3, -2$[/tex]
1. Begin with the smallest number, which is [tex]$-10$[/tex].
2. Then, [tex]$-3$[/tex] is larger than [tex]$-10$[/tex] but smaller than [tex]$-2$[/tex].
3. Next comes [tex]$-2$[/tex], which is larger than [tex]$-3$[/tex] but smaller than [tex]$+6$[/tex] and [tex]$+9$[/tex].
4. Then, [tex]$+6$[/tex] takes the next position as it is the smaller positive number.
5. Finally, the largest number in this list is [tex]$+9$[/tex].
Thus, the sorted order is:
[tex]\[ -10, -3, -2, +6, +9 \][/tex]
Summarizing all the results, we have:
1. [tex]\( -6, -4, -3, -1, 0 \)[/tex]
2. [tex]\( +1, +3, +5, +6, +8 \)[/tex]
3. [tex]\( -11, -10, +1, +3, +4 \)[/tex]
4. [tex]\( -8, -6, -5, +4, +8 \)[/tex]
5. [tex]\( -10, -3, -2, +6, +9 \)[/tex]
This completes the step-by-step arrangement of each list of integers in ascending order.
### 1. List: [tex]$-6, -4, -1, 0, -3$[/tex]
1. To begin with, identify the smallest number and compare each number in the list.
2. In this list, the smallest number is [tex]$-6$[/tex].
3. Next, [tex]$-4$[/tex] is larger than [tex]$-6$[/tex] but smaller compared to others.
4. Following [tex]$-4$[/tex], [tex]$-3$[/tex] comes next because it’s larger than [tex]$-4$[/tex] but smaller than [tex]$-1$[/tex] and [tex]$0$[/tex].
5. After [tex]$-3$[/tex], [tex]$-1$[/tex] is the next value as it is larger than [tex]$-3$[/tex] but smaller than [tex]$0$[/tex].
6. Lastly, [tex]$0$[/tex] is the largest number in this list.
Hence, the sorted order for this list is:
[tex]\[ -6, -4, -3, -1, 0 \][/tex]
### 2. List: [tex]$+1, +6, +8, +3, +5$[/tex]
1. In this group, the smallest positive number is [tex]$+1$[/tex].
2. The next smallest number is [tex]$+3$[/tex].
3. Then, we consider [tex]$+5$[/tex] as it is larger than [tex]$+3$[/tex] but smaller than [tex]$+6$[/tex] and [tex]$+8$[/tex].
4. Then comes [tex]$+6$[/tex] as it is larger than [tex]$+5$[/tex].
5. The largest number in this list is [tex]$+8$[/tex].
Thus, the ascending order for this list is:
[tex]\[ +1, +3, +5, +6, +8 \][/tex]
### 3. List: [tex]$+4, +3, -10, -11, +1$[/tex]
1. Start with the smallest value, which is [tex]$-11$[/tex].
2. The next smallest number is [tex]$-10$[/tex].
3. After sorting the negative values, we move on to the positive numbers. The smallest positive among them is [tex]$+1$[/tex].
4. Next is [tex]$+3$[/tex], larger than [tex]$+1$[/tex] but smaller than [tex]$+4$[/tex].
5. Finally, [tex]$+4$[/tex] is the largest among these values.
So, the sorted order is:
[tex]\[ -11, -10, +1, +3, +4 \][/tex]
### 4. List: [tex]$-8, +8, -5, -6, +4$[/tex]
1. First, identify and list the smallest value, which is [tex]$-8$[/tex].
2. Next, [tex]$-6$[/tex] is the value larger than [tex]$-8$[/tex] but smaller than others.
3. Following [tex]$-6$[/tex], [tex]$-5$[/tex] is next as it is larger than [tex]$-6$[/tex].
4. Then, among the remaining positive numbers, [tex]$+4$[/tex] is the smallest.
5. Finally, the largest number is [tex]$+8$[/tex].
Hence, the sorted order is:
[tex]\[ -8, -6, -5, +4, +8 \][/tex]
### 5. List: [tex]$+9, -10, +6, -3, -2$[/tex]
1. Begin with the smallest number, which is [tex]$-10$[/tex].
2. Then, [tex]$-3$[/tex] is larger than [tex]$-10$[/tex] but smaller than [tex]$-2$[/tex].
3. Next comes [tex]$-2$[/tex], which is larger than [tex]$-3$[/tex] but smaller than [tex]$+6$[/tex] and [tex]$+9$[/tex].
4. Then, [tex]$+6$[/tex] takes the next position as it is the smaller positive number.
5. Finally, the largest number in this list is [tex]$+9$[/tex].
Thus, the sorted order is:
[tex]\[ -10, -3, -2, +6, +9 \][/tex]
Summarizing all the results, we have:
1. [tex]\( -6, -4, -3, -1, 0 \)[/tex]
2. [tex]\( +1, +3, +5, +6, +8 \)[/tex]
3. [tex]\( -11, -10, +1, +3, +4 \)[/tex]
4. [tex]\( -8, -6, -5, +4, +8 \)[/tex]
5. [tex]\( -10, -3, -2, +6, +9 \)[/tex]
This completes the step-by-step arrangement of each list of integers in ascending order.
