Problem Analysis:
The task involves understanding and applying the rules for adding positive and negative numbers. The table provided outlines the rules and provides examples to illustrate them. Let's break down the rules and solve any potential problems step by step.
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Addition Rules:
1.
Pos. + Pos. = Pos.
- Adding two positive numbers results in a positive number.
- Example: \( 4 + 8 = 12 \)
2.
Neg. + Neg. = Neg.
- Adding two negative numbers results in a negative number.
- Example: \( -6 + (-3) = -9 \)
3.
Pos. + Neg. = Use the sign of the larger absolute value number
- When adding a positive number and a negative number, the result takes the sign of the number with the larger absolute value.
- Example:
- \( 12 + (-7) = 5 \) (Absolute values: \( |12| = 12 \), \( |-7| = 7 \); 12 is larger, so the result is positive.)
- \( 10 + (-14) = -4 \) (Absolute values: \( |10| = 10 \), \( |-14| = 14 \); 14 is larger, so the result is negative.)
4.
Neg. + Pos. = Use the sign of the larger absolute value number
- This rule is essentially the same as the previous one but written in reverse order.
- Example:
- \( -13 + 16 = 3 \) (Absolute values: \( |-13| = 13 \), \( |16| = 16 \); 16 is larger, so the result is positive.)
- \( -9 + 7 = -2 \) (Absolute values: \( |-9| = 9 \), \( |7| = 7 \); 9 is larger, so the result is negative.)
Solution Explanation:
The rules are designed to handle all possible combinations of adding positive and negative numbers. Here’s a summary of how to apply them:
1.
Same Signs:
- If both numbers have the same sign (both positive or both negative), simply add their absolute values and keep the common sign.
- Examples:
- \( 5 + 3 = 8 \)
- \( -7 + (-2) = -9 \)
2.
Different Signs:
- If the numbers have different signs, subtract the smaller absolute value from the larger absolute value. The sign of the result will be the same as the number with the larger absolute value.
- Examples:
- \( 8 + (-3) = 5 \) (Larger absolute value is 8, so the result is positive.)
- \( -10 + 4 = -6 \) (Larger absolute value is 10, so the result is negative.)
Final Answer:
The rules provided in the table are comprehensive and cover all scenarios for adding positive and negative numbers. By following these rules, you can accurately determine the sum of any pair of numbers.
\[
\boxed{\text{The rules are correct and complete for solving addition problems involving positive and negative numbers.}}
\]
Parent Tip: Review the logic above to help your child master the concept of adding and subtracting signed numbers.
