Missing values in number sentences using multiplication and division: Explanation

Seven multiplied by something equals 35. How can we find the missing value in this number sentence? Let’s start with the known number, seven. Here are seven dots in a row. Now let’s keep adding rows of seven until we reach our product, 35.

Seven more gives us 14. Seven more gives us 21. Seven more gives us 28. And seven more gives us 35! Now we can simply count how many rows of seven we needed to get to 35.

One, two, three, four, five. Seven multiplied by five is 35! These groups of dots are called an array. What if we want to find missing values in multiplication another way? Well, look again at our array.

It shows us something that can help us. We have 35 dots shared equally into seven columns. Shared equally… that’s another way to say divide! To share a larger number equally into smaller groups is to divide. So we could make two different kinds of number sentences from this array.

We could say seven times five equals 35, or 35 divided by seven equals five. Let’s go back to our original number sentence. Seven multiplied by something equals 35. We know now that this can be rewritten as 35 divided by seven equals something. The answer is five, and that’s the missing value in our multiplication.

We’ve learned that, to find a missing value in a multiplication problem, we can do the opposite, or inverse, of multiplication – division. Let’s try another example. Something multiplied by nine equals 72. We know that the inverse of multiplication is… The inverse of multiplication is division. We also know when we divide, we share… When we divide we share a larger number equally into smaller groups.

So, something multiplied by nine equals 72 can be rewritten as what? Something multiplied by nine equals 72 can be rewritten as 72 divided by nine equals something. Now all we need to do is complete the division problem! Seventy-two divided by nine equals… eight. So our missing value is eight.

Eight multiplied by nine equals 72. Here’s one more example to try on your own. Nine multiplied by nine equals 81. Now you know how to find a missing value in a number sentence using multiplication and division!