Mathematics from zero
Four operations: multiple-choice review
Six questions across all four operations. None of them asks you to recite a definition — each one asks you to use what an operation means to pick the right move, the way you would when the numbers are too big to count on your fingers.
Confirm you can connect the four operations: what each one does, why carrying and borrowing work, why order matters for subtraction and division but not addition and multiplication, and the two limits — remainders and dividing by zero.
Adding 36 + 27, the ones place comes to 6 + 7 = 13. What do you write, and why?
In 53 − 28, the ones column asks 3 − 8. The top digit is smaller. What is the correct move?
You know 7 + 9 = 16 and 7 × 9 = 63. Which statement is guaranteed by the order rule, with no recounting?
To multiply 24 × 3 in your head, you split 24 into 20 + 4. Why is splitting a factor by place allowed?
A child writes 23 ÷ 4 = 4 remainder 7. Something is wrong. Which rule is being broken?
Why is 12 ÷ 0 left undefined, while 0 ÷ 12 has a perfectly good answer?
Across the unit the through-line is that each operation answers a question about amounts. Addition and multiplication are order-free because joining groups or counting equal groups does not care which number you name first; subtraction and division are not, because they ask a directed question — what is left, or how many groups fit. Carrying and borrowing both work because ten ones and one ten are the same amount, just written in different places. And division has two edges to respect: the remainder must stay smaller than the divisor, and dividing by zero has no answer at all.