When adding two rational numbers with different signs, you can determine the sign of the sum by comparing the magnitudes of the numbers.
• If the absolute value of the first number is greater than the absolute value of the second number, the sum will have the same sign as the first number.
• If the absolute value of the second number is greater than the absolute value of the first number, the sum will have the same sign as the second number.
To determine whether the sum will be positive or negative, you can also compare the signs of the numbers:
• If one number is positive and the other is negative, the sum will be negative if the positive number is smaller than the negative number and positive if it is greater.
• If the numbers have different signs, the sum will be positive if the numbers have opposite signs and negative if they have the same sign.
• If the sum of the two rational numbers is zero, it means that the two numbers cancel each other out, which happens when the absolute value of the first number is equal to the absolute value of the second number with opposite signs.
It's important to note that if you are adding two rational numbers with different signs, you also have to keep in mind that the order of the numbers matters and you might get different results depending on the order.
I hope this helps :)