Fact Families
Fact families use three numbers to generate four related multiplication and division equations, demonstrating that multiplication and division are inverse operations. In Grade 6 Saxon Math Course 1 (Chapter 1: Number, Operations, and Algebra), students write all four facts for any set of three related numbers: if a x b = c, then b x a = c, c / a = b, and c / b = a. For the numbers 3, 5, and 15: 3 x 5 = 15, 5 x 3 = 15, 15 / 3 = 5, and 15 / 5 = 3. Knowing one fact unlocks the other three, which accelerates problem solving and fact recall.
Key Concepts
Property Multiplication and division are inverse operations. A fact family is a set of three numbers that can be used to create two related multiplication facts and two related division facts. $$ a \times b = c \quad b \times a = c \quad c \div a = b \quad c \div b = a $$.
Examples Using the numbers 8, 9, and 72, the fact family is $8 \times 9 = 72$, $9 \times 8 = 72$, $72 \div 8 = 9$, and $72 \div 9 = 8$.
If you know $6 \times 7 = 42$, you automatically know three other facts: $7 \times 6 = 42$, $42 \div 6 = 7$, and $42 \div 7 = 6$.
Common Questions
What is a fact family in multiplication and division?
A fact family is a set of three numbers that generate four related equations: two multiplication facts and two division facts.
Write the fact family for 4, 7, and 28.
4 x 7 = 28, 7 x 4 = 28, 28 / 4 = 7, 28 / 7 = 4.
How do fact families show that multiplication and division are inverse operations?
If 6 x 8 = 48, then 48 / 6 = 8. Multiplying and then dividing by the same number returns to the original value, proving they undo each other.
Write the fact family for 9, 6, and 54.
9 x 6 = 54, 6 x 9 = 54, 54 / 9 = 6, 54 / 6 = 9.
How can knowing a fact family help solve a missing number problem?
If you know 7 x n = 63, the fact family tells you n = 63 / 7 = 9 without guessing or trial and error.