Building Multiplication and Division Fact Families

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If you know that $4 \times 6 = 24$, what other three facts from this family do you automatically know?

$$\begin{array}{c} \Large 24 \\[-0.1em] \Huge \triangle \\[-0.9em] \Large 4 \hspace{1.5em} 6 \end{array}$$You also know $6 \times 4 = 24$, $24 \div 4 = 6$, and $24 \div 6 = 4$.

The product is $48$ and one factor is $6$. What are the three members of this fact family?

$$\begin{array}{c} \Large 48 \\[-0.1em] \Huge \triangle \\[-0.9em] \Large 6 \hspace{1.5em} 8 \end{array}$$The other factor is $8$ (since $6 \times 8 = 48$). The members are $6$, $8$, $48$.

Create the complete fact family for the numbers $11$, $5$, $55$.

$$\begin{array}{c} \Large 55 \\[-0.1em] \Huge \triangle \\[-0.9em] \Large 11 \hspace{1.5em} 5 \end{array}$$$11 \times 5 = 55$, $5 \times 11 = 55$, $55 \div 11 = 5$, and $55 \div 5 = 11$.

The members of a fact family are $3$, $4$, $12$. What are the two multiplication facts?

$$\begin{array}{c} \Large 12 \\[-0.1em] \Huge \triangle \\[-0.9em] \Large 3 \hspace{1.5em} 4 \end{array}$$$3 \times 4 = 12$ and $4 \times 3 = 12$.

The members of a fact family are $3$, $4$, $12$. What are the two division facts?

$$\begin{array}{c} \Large 12 \\[-0.1em] \Huge \triangle \\[-0.9em] \Large 3 \hspace{1.5em} 4 \end{array}$$$12 \div 3 = 4$ and $12 \div 4 = 3$.

What property of multiplication allows you to write two different multiplication facts for most fact families?

The Commutative Property of Multiplication, which states that changing the order of the factors does not change the product (e.g., $a \times b = b \times a$).

Create the complete, four-equation fact family for the numbers $2$, $8$, $16$.

$$\begin{array}{c} \Large 16 \\[-0.1em] \Huge \triangle \\[-0.9em] \Large 8 \hspace{1.5em} 2 \end{array}$$$2 \times 8 = 16$, $8 \times 2 = 16$, $16 \div 2 = 8$, and $16 \div 8 = 2$.

Create the complete, four-equation fact family for the numbers $5$, $7$, $35$.

$$\begin{array}{c} \Large 35 \\[-0.1em] \Huge \triangle \\[-0.9em] \Large 5 \hspace{1.5em} 7 \end{array}$$$5 \times 7 = 35$, $7 \times 5 = 35$, $35 \div 5 = 7$, and $35 \div 7 = 5$.

The numbers are $6$, $9$, $54$. Write the four related facts.

$$\begin{array}{c} \Large 54 \\[-0.1em] \Huge \triangle \\[-0.9em] \Large 6 \hspace{1.5em} 9 \end{array}$$$6 \times 9 = 54$, $9 \times 6 = 54$, $54 \div 6 = 9$, and $54 \div 9 = 6$.

When writing the division facts for a fact family, which number always comes first?

The largest number, which is the dividend (and the product from the multiplication facts), always comes first.

Create the complete fact family for the numbers $10$, $4$, $40$.

$$\begin{array}{c} \Large 40 \\[-0.1em] \Huge \triangle \\[-0.9em] \Large 4 \hspace{1.5em} 10 \end{array}$$$10 \times 4 = 40$, $4 \times 10 = 40$, $40 \div 10 = 4$, and $40 \div 4 = 10$.

Can the numbers $5$, $6$, $31$ form a fact family? Why or why not?

No, because $5 \times 6 = 30$, not $31$. The numbers are not related by multiplication and division.

Create the fact family for $3$, $9$, $27$.

$$\begin{array}{c} \Large 27 \\[-0.1em] \Huge \triangle \\[-0.9em] \Large 3 \hspace{1.5em} 9 \end{array}$$$3 \times 9 = 27$, $9 \times 3 = 27$, $27 \div 3 = 9$, and $27 \div 9 = 3$.

Create the fact family for $8$, $7$, $56$.

$$\begin{array}{c} \Large 56 \\[-0.1em] \Huge \triangle \\[-0.9em] \Large 8 \hspace{1.5em} 7 \end{array}$$$8 \times 7 = 56$, $7 \times 8 = 56$, $56 \div 8 = 7$, and $56 \div 7 = 8$.