Missing Numbers in Multiplication

Contributor: Erika Wargo. Lesson ID: 12393

Often, "How many?" questions mean there is some information missing. This is called the "missing factor" in multiplication. If you solved 30 problems in 3 days, how many did you solve each day? Hmm...


Arithmetic, Operations and Algebraic Thinking

learning style
personality style
Grade Level
Intermediate (3-5)
Lesson Type
Quick Query

Lesson Plan - Get It!

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A box of cookies contains 12 cookies.

  • If 4 people are eating cookies, how many cookies does each person get, if each person eats the same amount of cookies?

A multiplication number sentence is made up of factors and a product.

  • A factor is a number multiplied by another number to get a product.
  • A product is the answer to a multiplication problem, or the number that is the result of multiplying two or more factors.

In some multiplication problems, one of the factors might be missing. A multiplication problem that has one factor and a product is missing a factor.

Factor x Factor = Product

To find the missing factor in a multiplication problem, you can:

  1. use a multiplication table.
  2. use multiplication facts.
  3. divide.

The fastest way to find the missing factor in a multiplication problem is to use multiplication facts. When you think of multiplication facts, you can work backwards, which is similar to dividing.

Learn about other strategies as you watch a video about finding missing factors. As you watch Multiplication Lesson 3: Finding Missing Factors, answer these questions on a piece of paper:

  1. What three strategies are discussed in the video?
  2. Which strategy do you think you will use? Explain why you chose that strategy.

Discuss the questions above with a parent or teacher after you have watched the video:

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Example 1 Find the missing factor: 5m = 25

The expression "5m" means “5 times m.” Remember that in some problems, multiplication can be shown without a multiplication symbol. To find the missing factor, figure out “5 times what number is 25.” This problem can be solved using any of the ways above, but two of the ways are shown below:

Method 1 Use the factor given and skip count. Start at 5 and count how many 5s add up to 25: 5, 10, 15, 20, 25. It took five 5s to reach 25.

Method 2 Use multiplication facts. What number times 5 equals 25? 5 x 5= 25, so the missing factor is 5.

Example 2 6 x 2 = 3 x P

In this problem, there are numbers on both sides of the equal sign.

First, solve the multiplication problem on the left side of the equal sign: 6 x 2=12.

Next, rewrite the problem, 12 = 3 x P.

Finally, solve for the missing factor. What number can be multiplied by 3 to get a product of 12? 3 x 4 = 12, so P is equal to 12.

Example 3 At the beginning of the lesson, you were asked the following question:

A box of cookies contains 12 cookies. If 4 people are eating cookies, how many cookies does each person get, if each person eats the same amount of cookies?

Draw a picture for this problem. There are 4 people eating cookies and there are 12 cookies total. Put one cookie in each box until all of the 12 cookies are divided among the 4 people. Since 3 x 4 = 12, the missing factor is 3.

Discuss with a parent or teacher:

  • What is a factor?
  • What are two ways you can use to find the missing factor in a multiplication problem?

In the Got It? section, you will practice finding the missing factor as you play interactive games.

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