Relating Multiplication and Division, Part 2
Relating multiplication and division is a Grade 4 foundational math skill in Saxon Math Intermediate 4 (Chapter 5). Students learn the inverse relationship between the two operations: multiplying and then dividing by the same number returns to the starting value. This connection between fact families helps students solve missing-factor problems and underpins understanding of division as the inverse of multiplication.
Key Concepts
New Concept Together, all four facts form a multiplication and division fact family.
$$6 \times 4 = 24 \quad 24 \div 4 = 6$$ $$4 \times 6 = 24 \quad 24 \div 6 = 4$$.
What’s next Next, you'll use this relationship to solve division problems and write your own fact families.
Common Questions
How are multiplication and division related?
They are inverse operations. If 4 x 5 = 20, then 20 divided by 5 = 4 and 20 divided by 4 = 5. Knowing one multiplication fact gives you two related division facts.
What is a fact family in multiplication and division?
A fact family is a set of related equations using the same three numbers. For 3, 7, and 21: 3x7=21, 7x3=21, 21/7=3, 21/3=7. These four equations form a complete family.
How does the multiplication-division relationship help solve missing-factor problems?
To solve 5 x n = 40, use division: n = 40 / 5 = 8. Knowing division is the inverse of multiplication lets you find the missing number by dividing the product by the known factor.
Why is understanding inverse operations important in Grade 4?
It builds the foundation for algebra. Missing-factor equations like 5n = 40 are students' first exposure to solving for an unknown variable using inverse operations.
How do you check if your multiplication answer is correct using division?
Divide the product by one of the factors. If the result equals the other factor, the multiplication is correct. For 6 x 8 = 48: 48 / 8 = 6 confirms it.