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What is the rule for adding two rational numbers with the same sign?

The sum keeps the sign the same as the addends; the absolute value is the sum of the absolute values.

What is the rule for adding two rational numbers with different signs and unequal absolute values?

The sum takes the sign of the larger absolute value, and the absolute value equals the larger minus the smaller.

What is the sum of two numbers that are opposites of each other?

The sum of two opposites is always 0.

What is the result when any rational number is added to 0?

The result is unchanged; 0 is the additive identity.

What does the Commutative Property of Addition state?

Changing the order of the addends does not change the sum.

What does the Associative Property of Addition state?

Changing the grouping of the addends does not change the sum.

What is the result of adding (−5) + (−3)?

The result is -8.

What is the result of adding (−3) + 5?

The result is +2.

What is the result of adding (−5) + 3?

The result is -2.

Is the sum of two rational numbers always a rational number?

Yes, rational number addition is closed; the sum of two rational numbers is still rational.

What is the final displacement if an object moves 5 m left and then 5 m right?

The final displacement is 0 m.

What strategies can be used to simplify additions of multiple numbers using the Commutative and Associative properties?

1. Group same sign numbers for simplification. 2. Cancel pairs of opposites to make 0. 3. Rearrange order to combine for convenience.

Fill in the blanks for the rules of addition of rational numbers: Same sign addition, keep the sign {{c1::unchanged}}, absolute value {{c2::added}}; different signs, take the sign of the {{c3::larger absolute value}}, the absolute value {{c4::subtracted}}; adding 0 results in {{c5::no change}}.

1. Same sign: sign unchanged, absolute value added; 2. Different signs: take larger absolute value's sign, subtract; 3. Adding 0: result unchanged.