Mathematics from zero
Four operations: free-recall review
Saying an answer out loud from memory locks it in far better than reading it again. For each prompt, give a full answer in your own words before you open the model answer — then compare and patch any gaps.
Reconstruct the unit’s spine from memory — what each operation means, the two meanings of difference, why carrying and borrowing work, why order matters for only two operations, how division undoes multiplication, and the two limits of division.
- 01Subtraction answers two everyday questions. Name both, and show they give the same difference.
- 02Why does the order of the numbers matter for subtraction and division but not for addition and multiplication?
- 03Carrying (in addition) and borrowing (in subtraction) feel like opposite tricks. What single fact makes both of them work?
- 04Explain why multiplication is repeated addition, and why you are allowed to split a factor by place to multiply larger numbers.
- 05What does it mean to say division undoes multiplication, and how do you use that to check a division?
- 06State the two limits of division: the rule for remainders, and why dividing by zero is undefined.
If you could rebuild each answer from memory, you hold the unit’s spine: each operation answers a question about amounts; subtraction names both what is left and the gap; carrying and borrowing are one regrouping rule run two ways; multiplication is shorthand for repeated addition and shares out over addition so you can split factors by place; division undoes multiplication, which is how you check it; and division has two limits — remainders stay below the divisor, and dividing by zero has no answer.