Addition (symbol +) combines two groups into one total. Subtraction (symbol −) finds what is left, or the difference between two amounts. They undo each other — if 7 + 5 = 12, then 12 − 5 = 7 and 12 − 7 = 5. Those four facts together are called a fact family.

On a number line, adding means moving right; subtracting means moving left. For bigger numbers, we add and subtract column by column (ones, then tens): carrying happens when the ones add up to 10 or more, and borrowing happens when you don't have enough ones to subtract, so you trade in a ten.

Ten ones always make exactly one ten. When adding, if your ones column reaches 10 or more, you trade 10 of those ones for one new ten and carry it into the tens column — nothing is lost, it is just repackaged.

Borrowing is the same trade in reverse: if the ones column doesn't have enough to subtract, you break one ten from the tens column back into 10 ones, giving you enough to subtract from. The total amount never changes — only how it's grouped.