Final answer:
The correct missing statement for the sum of two rational numbers with different signs is their absolute difference, as when adding numbers with different signs, one subtracts the smaller absolute value from the larger and assigns the result the sign of the number with the larger absolute value.
Step-by-step explanation:
The question is asking for the missing statement regarding the sum of two rational numbers with different signs. Let's review the options provided in the light of the rules for adding rational numbers:
- When two positive numbers are added, the answer has a positive (+ve) sign, e.g., 3+2 = 5.
- When two negative numbers are added, the answer has a negative (−ve) sign, e.g., -4 + (-2) = -6.
- When two numbers with opposite signs are added, you subtract the smaller number from the larger number, and the answer has the sign of the larger number, e.g., -5 +3 = -2.
- In subtraction, change the sign of the subtracted number and then follow the addition rules, e.g., 5-(+3) = 2.
Using these rules, we can conclude that the correct missing statement is:
(a) The sum of two rational numbers with different signs is their absolute difference.
This statement corresponds to the rule that when adding numbers with different signs, we subtract the absolute values and give the result the sign of the number with the larger absolute value. Therefore, options (b), (c), and (d) are not correct as they do not consistently apply to all cases of adding rational numbers with different signs.