### Detailed Step-by-Step Solutions
a) [tex]\(7 + 5\)[/tex]
1. Start with the first number, which is [tex]\(7\)[/tex].
2. Add the second number, which is [tex]\(5\)[/tex].
3. To add these two numbers, we simply combine them.
4. So, [tex]\(7 + 5 = 12\)[/tex].
Therefore, [tex]\(7 + 5 = 12\)[/tex].
b) [tex]\(-9 + 7\)[/tex]
1. Start with the first number, which is [tex]\(-9\)[/tex].
2. The second number to add is [tex]\(7\)[/tex].
3. When adding a positive number to a negative number, you essentially find the difference between the two numbers and take the sign of the number with the larger absolute value.
4. [tex]\(|-9| = 9\)[/tex] and [tex]\(|7| = 7\)[/tex]. Since [tex]\(9 > 7\)[/tex], the result will take the sign of [tex]\(-9\)[/tex].
5. Now, subtract the smaller absolute value from the larger absolute value: [tex]\(9 - 7 = 2\)[/tex].
6. Since [tex]\(-9\)[/tex] is the number with the larger absolute value, the result is [tex]\(-2\)[/tex].
Therefore, [tex]\(-9 + 7 = -2\)[/tex].
c) [tex]\(-3 + 10\)[/tex]
1. Start with the first number, which is [tex]\(-3\)[/tex].
2. The second number to add is [tex]\(10\)[/tex].
3. When adding a positive number to a negative number, find the difference between the two numbers and take the sign of the number with the larger absolute value.
4. [tex]\(|-3| = 3\)[/tex] and [tex]\(|10| = 10\)[/tex]. Since [tex]\(10 > 3\)[/tex], the result will take the sign of [tex]\(10\)[/tex].
5. Now, subtract the smaller absolute value from the larger absolute value: [tex]\(10 - 3 = 7\)[/tex].
6. Since [tex]\(10\)[/tex] is the number with the larger absolute value, the result is [tex]\(7\)[/tex].
Therefore, [tex]\(-3 + 10 = 7\)[/tex].
d) [tex]\(-8 + (-1)\)[/tex]
1. Start with the first number, which is [tex]\(-8\)[/tex].
2. The second number to add is [tex]\(-1\)[/tex].
3. When adding two negative numbers, you add their absolute values and retain the negative sign.
4. [tex]\(|-8| = 8\)[/tex] and [tex]\(|-1| = 1\)[/tex].
5. Add the absolute values: [tex]\(8 + 1 = 9\)[/tex].
6. Since both numbers are negative, the result is also negative.
Therefore, [tex]\(-8 + (-1) = -9\)[/tex].
In summary:
- [tex]\(7 + 5 = 12\)[/tex]
- [tex]\(-9 + 7 = -2\)[/tex]
- [tex]\(-3 + 10 = 7\)[/tex]
- [tex]\(-8 + (-1) = -9\)[/tex]
