1) Calculate: a) \( (-7)+3 \) b) \( (-7)+(-3) \) c) \( (12)+(-8) \) d) \( (-12)+(-8) \) e) \( (-12)+8 \)

Sure, let's solve each of these addition problems step by step: ### a) \( (-7) + 3 \) - **Understanding the Operation:** You're adding a negative number (-7) and a positive number (3). - **Calculation:** \[ (-7) + 3 = -4 \] - **Explanation:** Starting at -7 on the number line and moving 3 units to the right brings you to -4. --- ### b) \( (-7) + (-3) \) - **Understanding the Operation:** You're adding two negative numbers. - **Calculation:** \[ (-7) + (-3) = -10 \] - **Explanation:** When adding negatives, you add their absolute values and keep the negative sign. So, 7 + 3 = 10, then add the negative sign to get -10. --- ### c) \( 12 + (-8) \) - **Understanding the Operation:** You're adding a positive number (12) and a negative number (-8). - **Calculation:** \[ 12 + (-8) = 4 \] - **Explanation:** Subtract the absolute value of the negative number from the positive number: 12 - 8 = 4. --- ### d) \( (-12) + (-8) \) - **Understanding the Operation:** You're adding two negative numbers. - **Calculation:** \[ (-12) + (-8) = -20 \] - **Explanation:** Add the absolute values and keep the negative sign: 12 + 8 = 20, then add the negative sign to get -20. --- ### e) \( (-12) + 8 \) - **Understanding the Operation:** You're adding a negative number (-12) and a positive number (8). - **Calculation:** \[ (-12) + 8 = -4 \] - **Explanation:** Subtract the absolute value of the negative number from the positive number: 12 - 8 = 4, then add the negative sign to get -4. --- **Summary of Results:** a) \( (-7) + 3 = -4 \) b) \( (-7) + (-3) = -10 \) c) \( 12 + (-8) = 4 \) d) \( (-12) + (-8) = -20 \) e) \( (-12) + 8 = -4 \)