Final answer:
The phrases "add the opposite" and "keep-change-change" are used when completing the operation of subtraction with integers.
Step-by-step explanation:
The phrases "add the opposite" and "keep-change-change" are used when completing the operation of subtraction with integers.
When adding or subtracting integers, the phrase "add the opposite" means that you need to change the sign of the second number and then perform the addition. For example, to subtract -3 from 5, you would change the sign of -3 to +3 and then add the two numbers: 5 + 3 = 8.
The phrase "keep-change-change" is a mnemonic for subtracting integers. The first number is kept as is, the subtraction sign is changed to addition, and the second number is changed to its opposite sign. For instance, to subtract 3 from 5, you would keep 5, change the subtraction sign to addition, and change 3 to -3, resulting in 5 + (-3) = 2.