A student is trying to solve 24 ÷ 6 and cannot remember the answer. What is the most effective strategy?
ACount up from 6 one by one until reaching 24, keeping track of how many steps it took
BTry to memorize 24 ÷ 6 = 4 by repeating it many times right now
CAsk 'What number times 6 equals 24?' and use known multiplication facts to get the answer
DDraw 24 objects and circle groups of 6 to find the answer
Because division is the inverse of multiplication, every division fact can be solved by asking the corresponding multiplication question: '6 × ? = 24.' If you know 6 × 4 = 24, you immediately have 24 ÷ 6 = 4. This is much faster than counting up (option A) or drawing objects (option D), and more useful than isolated memorization (option B) because it builds on a connected understanding.
Question 2 Multiple Choice
Which set of facts forms a complete fact family using the numbers 3, 7, and 21?
A3 × 7 = 21 and 21 ÷ 3 = 7 only — you cannot get more facts from these three numbers
B3 + 7 = 10 and 10 − 3 = 7 — fact families use any operation
D3 × 7 = 21 and 21 × 1 = 21 — the identity property gives the second fact
A fact family contains all the multiplication and division facts that can be made from three related numbers. Because multiplication is commutative (3 × 7 = 7 × 3), and division 'undoes' multiplication in two ways (dividing by either factor), you always get exactly four facts. Option A misses three of the four. Option B confuses multiplication fact families with addition fact families — those are separate.
Question 3 True / False
Knowing that 8 × 4 = 32 automatically means you also know both 32 ÷ 8 = 4 and 32 ÷ 4 = 8.
TTrue
FFalse
Answer: True
Yes — this is exactly the inverse relationship. Every multiplication fact generates two division facts (and another multiplication fact with the factors swapped). The three numbers 4, 8, and 32 form a fact family. Learning one fact for free means you get three more, which is why mastering multiplication facts gives you most of your division fluency at the same time.
Question 4 True / False
Division facts is expected to be memorized largely separately from multiplication facts, since the two operations work differently.
TTrue
FFalse
Answer: False
This is the key misconception this topic addresses. Because division is the inverse of multiplication, division facts are not independent — they are derived from multiplication facts. 18 ÷ 6 = 3 because 6 × 3 = 18. Students who understand the inverse relationship don't need to memorize a separate set of division facts; they ask 'what times the divisor equals the dividend?' and use what they already know.
Question 5 Short Answer
Explain how the inverse relationship between multiplication and division helps you solve a division fact you can't immediately recall.
Think about your answer, then reveal below.
Model answer: Division and multiplication undo each other. So when you see a division problem like 42 ÷ 7, you can rephrase it as a multiplication question: '7 times what number equals 42?' If you know 7 × 6 = 42, you have your answer: 6. You don't need to memorize 42 ÷ 7 = 6 separately — you just use the multiplication fact you already know.
The inverse relationship means division facts are not isolated facts to memorize — they are multiplication facts viewed from the other direction. This understanding is more durable than rote memorization because even if you momentarily forget a division fact, you can reconstruct it from the corresponding multiplication. It also reveals why fact families (sets of three related numbers) are so useful: they show four connected facts at once.