Sure! Let's go through each of these math problems step by step.
1. Solving [tex]$-9 + (-8)$[/tex]:
- When you add two negative numbers, you add their absolute values and keep the result negative.
- [tex]$|-9| = 9$[/tex] and [tex]$|-8| = 8$[/tex]
- So, [tex]$-9 + (-8) = -(9 + 8) = -17$[/tex]
- Answer: [tex]$-17$[/tex]
2. Solving [tex]$-12 + 10$[/tex]
- When adding a negative number and a positive number, you subtract the smaller absolute value from the larger absolute value and take the sign of the number with the larger absolute value.
- [tex]$|-12| = 12$[/tex] and [tex]$|10| = 10$[/tex]
- [tex]$12 > 10$[/tex], so the answer will be negative.
- So, [tex]$-12 + 10 = -(12 - 10) = -2$[/tex]
- Answer: [tex]$-2$[/tex]
3. Solving [tex]$-15 - 7$[/tex]
- When you subtract a positive number from a negative number, you add the absolute values and keep the result negative.
- [tex]$|-15| = 15$[/tex] and [tex]$|7| = 7$[/tex]
- So, [tex]$-15 - 7 = -(15 + 7) = -22$[/tex]
- Answer: [tex]$-22$[/tex]
4. Solving [tex]$-13 - (-5)$[/tex]
- Subtracting a negative number is the same as adding its positive counterpart.
- So, [tex]$-13 - (-5) = -13 + 5$[/tex]
- Follow the rule of adding a negative number and a positive number.
- [tex]$|-13| = 13$[/tex] and [tex]$|5| = 5$[/tex]
- [tex]$13 > 5$[/tex], so the result will be negative.
- So, [tex]$-13 + 5 = -(13 - 5) = -8$[/tex]
- Answer: [tex]$-8$[/tex]
5. Solving [tex]$-10 + 8 - 7$[/tex]
- Follow the rules of addition and subtraction from left to right.
- First, solve [tex]$-10 + 8$[/tex]:
- [tex]$|-10| = 10$[/tex] and [tex]$|8| = 8$[/tex]
- [tex]$10 > 8$[/tex], so the result will be negative.
- [tex]$-10 + 8 = -(10 - 8) = -2$[/tex]
- Then, solve [tex]$-2 - 7$[/tex]:
- [tex]$|-2| = 2$[/tex] and [tex]$|7| = 7$[/tex]
- So, [tex]$-2 - 7 = -(2 + 7) = -9$[/tex]
- Answer: [tex]$-9$[/tex]
6. Solving [tex]$(-12)(13)$[/tex]
- Multiplying a negative number by a positive number results in a negative product.
- [tex]$(-12) \times 13 = - (12 \times 13) = -156$[/tex]
- Answer: [tex]$-156$[/tex]
7. Solving [tex]$(-4)(-5)(-6)$[/tex]
- First, multiply the first two numbers: [tex]$(-4)(-5)$[/tex]
- Multiplying two negative numbers results in a positive product.
- [tex]$(-4) \times (-5) = 20$[/tex]
- Then, multiply this result by the third number:
- [tex]$20 \times (-6)$[/tex]
- Multiplying a positive number by a negative number results in a negative product.
- So, [tex]$20 \times (-6) = -120$[/tex]
- Answer: [tex]$-120$[/tex]
So, here are the final answers for each problem:
1. [tex]$-9 + (-8) = -17$[/tex]
2. [tex]$-12 + 10 = -2$[/tex]
3. [tex]$-15 - 7 = -22$[/tex]
4. [tex]$-13 - (-5) = -8$[/tex]
5. [tex]$-10 + 8 - 7 = -9$[/tex]
6. [tex]$(-12) \times 13 = -156$[/tex]
7. [tex]$(-4) \times (-5) \times (-6) = -120$[/tex]
