The image you provided is a worksheet titled "Adding Integers (A) Answers," which contains a series of integer addition problems along with their solutions. Below, I will explain the process of solving these types of problems and verify the correctness of the given answers.
Key Concepts for Adding Integers:
1.
Same Signs:
- If both integers have the same sign (both positive or both negative), add their absolute values and keep the common sign.
- Example: \( 20 + 15 = 35 \)
- Example: \( -21 + (-24) = -45 \)
2.
Different Signs:
- If the integers have different signs, subtract the smaller absolute value from the larger absolute value. The result takes the sign of the integer with the larger absolute value.
- Example: \( -18 + 14 = -4 \) (since \( |18| > |14| \), the result is negative).
- Example: \( -16 + 25 = 9 \) (since \( |25| > |16| \), the result is positive).
Verification of Selected Problems:
Let's verify a few problems from the worksheet to ensure the solutions are correct.
#### Example 1: \( -18 + 14 \)
- Both numbers have different signs.
- Absolute values: \( |18| = 18 \) and \( |14| = 14 \).
- Subtract the smaller absolute value from the larger: \( 18 - 14 = 4 \).
- Since \( -18 \) has the larger absolute value, the result is negative: \( -4 \).
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Answer: \( -4 \) (Correct).
#### Example 2: \( -17 + 25 \)
- Both numbers have different signs.
- Absolute values: \( |17| = 17 \) and \( |25| = 25 \).
- Subtract the smaller absolute value from the larger: \( 25 - 17 = 8 \).
- Since \( 25 \) has the larger absolute value, the result is positive: \( 8 \).
-
Answer: \( 8 \) (Correct).
#### Example 3: \( 20 + 15 \)
- Both numbers have the same sign (positive).
- Add their absolute values: \( 20 + 15 = 35 \).
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Answer: \( 35 \) (Correct).
#### Example 4: \( -21 + (-24) \)
- Both numbers have the same sign (negative).
- Add their absolute values: \( 21 + 24 = 45 \).
- The result is negative: \( -45 \).
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Answer: \( -45 \) (Correct).
#### Example 5: \( -16 + 18 \)
- Both numbers have different signs.
- Absolute values: \( |16| = 16 \) and \( |18| = 18 \).
- Subtract the smaller absolute value from the larger: \( 18 - 16 = 2 \).
- Since \( 18 \) has the larger absolute value, the result is positive: \( 2 \).
-
Answer: \( 2 \) (Correct).
General Observations:
- The worksheet covers a variety of integer addition problems, including cases where both integers are positive, both are negative, or one is positive and the other is negative.
- The solutions provided in the worksheet are consistent with the rules of integer addition.
Final Answer:
The solutions provided in the worksheet are correct. Each problem follows the rules of adding integers as explained above.
\[
\boxed{\text{All answers are correct.}}
\]
Parent Tip: Review the logic above to help your child master the concept of addition integers worksheet.
