Problem: Solve the given arithmetic problems involving sums and differences with negative numbers.
####
Step-by-Step Solutions:
1.
\( 10 + (-5) \)
- Adding a negative number is the same as subtracting its positive counterpart.
- \( 10 + (-5) = 10 - 5 = 5 \)
-
Answer: \( 5 \)
2.
\( -8 + 12 \)
- Adding a positive number to a negative number involves finding the difference between their absolute values and keeping the sign of the larger number.
- Absolute values: \( | -8 | = 8 \) and \( | 12 | = 12 \)
- Difference: \( 12 - 8 = 4 \)
- Since \( 12 \) (positive) is larger, the result is positive.
-
Answer: \( 4 \)
3.
\( 18 - 6 \)
- Subtracting a positive number is straightforward.
- \( 18 - 6 = 12 \)
-
Answer: \( 12 \)
4.
\( 10 - 20 \)
- Subtracting a larger positive number from a smaller positive number results in a negative number.
- \( 10 - 20 = -10 \)
-
Answer: \( -10 \)
5.
\( -4 - 12 \)
- Subtracting a positive number from a negative number is the same as adding the negative of that number.
- \( -4 - 12 = -4 + (-12) = -16 \)
-
Answer: \( -16 \)
6.
\( 25 + (-4) \)
- Adding a negative number is the same as subtracting its positive counterpart.
- \( 25 + (-4) = 25 - 4 = 21 \)
-
Answer: \( 21 \)
7.
\( -4 + 4 \)
- Adding a number to its opposite (negative) results in zero.
- \( -4 + 4 = 0 \)
-
Answer: \( 0 \)
8.
\( 3 + (-14) \)
- Adding a negative number is the same as subtracting its positive counterpart.
- \( 3 + (-14) = 3 - 14 = -11 \)
-
Answer: \( -11 \)
9.
\( (-8) + 10 \)
- Adding a positive number to a negative number involves finding the difference between their absolute values and keeping the sign of the larger number.
- Absolute values: \( | -8 | = 8 \) and \( | 10 | = 10 \)
- Difference: \( 10 - 8 = 2 \)
- Since \( 10 \) (positive) is larger, the result is positive.
-
Answer: \( 2 \)
10.
\( (-4) + (-10) \)
- Adding two negative numbers results in a negative number whose magnitude is the sum of their absolute values.
- \( (-4) + (-10) = -(4 + 10) = -14 \)
-
Answer: \( -14 \)
11.
\( 25 + (-5) \)
- Adding a negative number is the same as subtracting its positive counterpart.
- \( 25 + (-5) = 25 - 5 = 20 \)
-
Answer: \( 20 \)
12.
\( 25 - 10 \)
- Subtracting a positive number is straightforward.
- \( 25 - 10 = 15 \)
-
Answer: \( 15 \)
---
Final Answers:
1. \( 5 \)
2. \( 4 \)
3. \( 12 \)
4. \( -10 \)
5. \( -16 \)
6. \( 21 \)
7. \( 0 \)
8. \( -11 \)
9. \( 2 \)
10. \( -14 \)
11. \( 20 \)
12. \( 15 \)
Boxed Final Answer:
\[
\boxed{
\begin{aligned}
1. & \ 5 \\
2. & \ 4 \\
3. & \ 12 \\
4. & \ -10 \\
5. & \ -16 \\
6. & \ 21 \\
7. & \ 0 \\
8. & \ -11 \\
9. & \ 2 \\
10. & \ -14 \\
11. & \ 20 \\
12. & \ 15
\end{aligned}
}
\]
Parent Tip: Review the logic above to help your child master the concept of adding and subtracting negative numbers worksheet with answers.
