Multiplication-Division Relationship

Arithmetic · Axiom Academy

LESSON Multiplication-Division Relationship Multiplication and division are inverse operations — each one undoes the other. 1. Two Operations, One Relationship Knowing a single multiplication fact hands you its division facts for free. If 3 × 4 = 12 , then 12 ÷ 3 = 4 — the division simply undoes the multiplication. Multiplication assembles the whole A fact family is a group of related multiplication and division facts that use the same three numbers. The three numbers 3, 4, and 12 generate four facts. Every multiplication fact carries its division facts along with it. Here are four more families — each multiplication fact paired with one of its division facts. 4. Use One Operation to Check the Other Because they undo each other, you can check a division by multiplying back . Take the family 6, 8, 48 : if 48 ÷ 8 = 6, then 6 × 8 should return 48 — and it does, so the division is correct. Division and multiplication run in opposite directions over the same three numbers. If the product you get back is the number you started with, your quotient must have been right. You've seen how multiplication and division are two sides of one relationship — and how that relationship hands you whole fact families and a built-in way to check your work. Scroll up to revisit any step.

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