Multiplication and division are inverse operations. This means they undo each other, just like addition and subtraction. If you know a multiplication fact, you automatically know two related division facts.
Think of a rectangle. The total number of squares (product) can be divided by the number of rows to find the columns, or by the number of columns to find the rows.
A fact family is a group of four related math facts created from the same three numbers. For multiplication and division, these three numbers are the two factors and their product.
Every fact family shows the same relationship in four different ways. Knowing one fact helps you know all four.
An array is an arrangement of objects in rows and columns. It is a powerful tool to visualize how multiplication and division are connected.
The array doesn't change. Whether you count the total (multiplication) or split the total into equal groups (division), you are describing the same arrangement.
If a number in a multiplication or division equation is missing, you can use the inverse operation to find it. This is often called solving for an unknown.
Ask yourself: "What operation would undo this problem?" Use the fact family to help you rearrange the numbers and find the answer.
Recognizing patterns can make working with multiplication and division facts up to 7×7 easier and faster.
These special rules are consistent for all numbers. Memorizing them helps you solve problems quickly and check your work for reasonableness.