Video: Finding Unknown Whole Numbers in Multiplication Equations

If 11 × ⬧ = 33 and ⬧ × ■ = 81, what is ■ ÷ ⬧?


Video Transcript

If 11 times diamond equals 33 and diamond times square equals 81, what is square divided by diamond?

This all looks a little bit like a puzzle. The only thing we need to do is take it one step at a time. The first step will be to find out what a diamond represents. We know that if you take 11 and multiply it by this number, you get 33. To solve this one, we’ll need to take 33 and divide it by 11. 11 goes into 33 three times. If you multiply three times 11, you get 33 with the remainder of zero. And that means our diamond represents the number three.

We’re also given the information that diamond times square equals 81. We found out that diamond equals three. So let’s take that information and plug it into the next problem. Now we know that three times the square equals 81. We can follow the same procedure and divide 81 by three to find what square is equal to.

The problem will start like this: 81 divided by three. We start with the eight and we ask how many times will three go into eight? Two times. Two times three equals six. From there, we subtract six from eight leaving us with two. Bring down the one from our 81 and you have 21. Now we need to ask how many times does three go into 21? I recognize that seven times three equals 21 and that means three goes into 21 seven times. We subtract 21 from 21 and we’re left with the remainder of zero. Three times 27 equals 81. This means that the value of the square is 27.

We can use the values of the diamond and the square to solve the final problem. Saying square divided by diamond is the same thing as saying 27 divided by three. If you remember that three times nine equals 27, then you know that 27 divided by three equals nine. And so in this case, square divided by diamond equals nine.

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