Fact Families: Multiplication and Division Are Related

Contributor: Ashley Nail. Lesson ID: 13415

Ever wonder how multiplication and division are related? Change some symbols and switch the numbers around, and you will quickly see these families form!


Elementary, Operations and Algebraic Thinking

learning style
Kinesthetic, Visual
personality style
Lion, Beaver
Grade Level
Intermediate (3-5)
Lesson Type
Quick Query

Lesson Plan - Get It!

  • How many relatives do you have?

Maybe a sister or brother, cousins, aunts, uncles, grandparents, and don't forget a mom or a dad! You might even have step-parents, second cousins, or great aunties.

Numbers have relatives too. However, their family trees look a lot different.

  • For example, how are 9, 1, and 10 related?

They are not cousins. Instead, those numbers are related by addition and subtraction operations!

9 + 1 = 10

1 + 9 = 10

10 - 1 = 9

10 - 9 = 1

  • Can you think of any other ways numbers can be related?

Numbers can also be related through multiplication and division!

Let's look at the numbers in the multiplication equation below:

multiplication equation

  • Notice how each number has an important name?

Much like in your family, these titles matter and help to describe the relationships.

Factors are numbers that, when multiplied, make up a product. The product is the answer in a multiplication equation.

You can display this multiplication equation with equal groups or an array:

equal groups and an array

  • How are the numbers in this multiplication equation related to division?

Let's look at the product from the equation.

The product is 6. There were 6 total dots in our equal groups drawing.

In a division equation, the product becomes the dividend. The dividend is the total amount to be divided or split up.

In this case, the total is 6:

the dividend

The divisor is how many groups the total will be split into. In this case, the dividend will be split into 2 groups:

the divisor

To find the quotient or the answer of a division equation, you will need to divide the 6 total dots into 2 equal groups. Then, count how many dots are in each group!


  • Does anything look familiar?

Compare this equal group drawing to the one above. They are the same!

  • What about the numbers and the equations? What is similar about them?

compare equations

  • Do you see the relation?

There are two more equations that complete this family.

  • Do you know what they are?

Yes! We use the commutative property of multiplication to find these equations in our fact family.

If you need to review this concept, check out our Additional Resource found in the right-hand sidebar.

For a quick review on fact families, watch Relating Multiplication to Division (Fact Families), from Alex Lochoff:

  • Ready to practice finding more multiplication and division fact families?

Click NEXT to visit the Got It? section and use your new skills!

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