Missing values in number sentences using any operation: Explanation

Thirty-three add something equals 94. How can we find the missing number? We can use the opposite of addition: subtraction. Addition and subtraction are inverse operations. Thirty-three add something equals 94 can be rewritten as 94 subtract 33 equals something.

Ninety-four subtract 33 equals… 61. And that’s our missing number! Thirty-three add 61 equals 94. Here’s one for you to try. Twenty-seven add 56 equals 83.

We can use inverse operations to find the missing value in subtraction problems, too. Let’s investigate. Something subtract 21 equals 46. When we subtract, we start with a larger value and take away a smaller value. So we know that we’re looking for a value larger than 21.

We also know that the inverse of subtraction is addition. So we can add 21 to 46 to find our missing value. Twenty-one add 46 equals… 67. And 67 subtract 21 equals 46! Try the next one yourself.

Forty-nine subtract 37 equals 12. What if our subtraction sentence looked a little different? Like this: 72 subtract something equals 31. Here, we are missing the second number in the subtraction. We know we need to take a smaller number from 72 to get the answer of 31.

We also know that addition and subtraction are inverse operations. We can’t add two numbers to get a smaller number, but we can see what two numbers added together would give us the larger number. We can rewrite our problem as 31 add something equals 72. How do we find the missing number now? We’ve done this before!

Thirty-one add something equals 72 can be rewritten as 72 subtract 31 equals something. That’s 41. Seventy-two subtract 41 equals 31! Try the next example. Ninety-three subtract 45 equals 48.

What happens if we have a missing value in a multiplication problem? Like this one: Three multiplied by something equals 78. We can use the inverse of multiplication: division. Three multiplied by something equals 78 can be rewritten as 78 divided by three equals something. Seventy-eight divided by three equals… 26.

And three multiplied by 26 equals 78! Here’s one for you to try. Six multiplied by 14 equals 84. Let’s try using inverse operations to find the missing value in a division problem. Something divided by six equals eight.

When we divide, we share a larger number into smaller, equal groups. So we know that we’re looking for a value larger than six or eight. We also know that the inverse of division is multiplication. So we can multiply eight by six to find our missing value. Eight multiplied by six equals… 48.

48 divided by six equals eight! Try the next one yourself. Ninety-nine divided by 11 equals nine. What if our division problem looked a little different? Like this: Fifty-six divided by something equals eight.

Here, we are missing the second number in the division. We know we need to divide 56 by a smaller number to get the answer of eight. We also know that multiplication and division are inverse operations. We can’t multiply two numbers to get a smaller number, but we can see what two numbers multiplied would give us the larger number. We can rewrite our problem as eight multiplied by something equals 56.

Now we know how to find the missing number! We can rewrite eight multiplied by something equals 56 as 56 divided by eight equals something. The answer is seven and 56 divided by seven equals eight! Over to you! Try this last example yourself.

Twenty-eight divided by four equals seven. Now you know how to find a missing value in a number sentence using any operation!