The task involves solving a series of addition and subtraction problems involving positive and negative integers. Let's solve each problem step by step.
Problem 1: \(-5 + 12\)
- Start at \(-5\) on the number line.
- Move 12 units to the right (since we are adding a positive number).
- The result is \(7\).
Answer: \(7\)
Problem 2: \(6 - 10\)
- Start at \(6\) on the number line.
- Move 10 units to the left (since we are subtracting a positive number).
- The result is \(-4\).
Answer: \(-4\)
Problem 3: \(-8 + 13\)
- Start at \(-8\) on the number line.
- Move 13 units to the right (since we are adding a positive number).
- The result is \(5\).
Answer: \(5\)
Problem 4: \(-6 - 17\)
- Start at \(-6\) on the number line.
- Move 17 units to the left (since we are subtracting a positive number).
- The result is \(-23\).
Answer: \(-23\)
Problem 5: \(6 + (-8)\)
- Adding a negative number is the same as subtracting its positive counterpart.
- This is equivalent to \(6 - 8\).
- Start at \(6\) on the number line.
- Move 8 units to the left.
- The result is \(-2\).
Answer: \(-2\)
Problem 6: \(-6 - (-4)\)
- Subtracting a negative number is the same as adding its positive counterpart.
- This is equivalent to \(-6 + 4\).
- Start at \(-6\) on the number line.
- Move 4 units to the right.
- The result is \(-2\).
Answer: \(-2\)
Problem 7: \(-9 + (-14)\)
- Adding a negative number is the same as subtracting its positive counterpart.
- This is equivalent to \(-9 - 14\).
- Start at \(-9\) on the number line.
- Move 14 units to the left.
- The result is \(-23\).
Answer: \(-23\)
Problem 8: \(14 + (-5)\)
- Adding a negative number is the same as subtracting its positive counterpart.
- This is equivalent to \(14 - 5\).
- Start at \(14\) on the number line.
- Move 5 units to the left.
- The result is \(9\).
Answer: \(9\)
Problem 9: \(-12 + 4\)
- Start at \(-12\) on the number line.
- Move 4 units to the right (since we are adding a positive number).
- The result is \(-8\).
Answer: \(-8\)
Problem 10: \(-12 - (-20)\)
- Subtracting a negative number is the same as adding its positive counterpart.
- This is equivalent to \(-12 + 20\).
- Start at \(-12\) on the number line.
- Move 20 units to the right.
- The result is \(8\).
Answer: \(8\)
Final Answers:
1. \(7\)
2. \(-4\)
3. \(5\)
4. \(-23\)
5. \(-2\)
6. \(-2\)
7. \(-23\)
8. \(9\)
9. \(-8\)
10. \(8\)
Boxed Answer:
\[
\boxed{7, -4, 5, -23, -2, -2, -23, 9, -8, 8}
\]
Parent Tip: Review the logic above to help your child master the concept of adding and subtracting positive and negative integers worksheet.
