Question Video: Finding the Missing Number in a Multiplication Sentence Mathematics • 4th Grade

What is the missing number? 34 × _ = 68


Video Transcript

What is the missing number? 34 times what equals 68.

In this question, we can see a multiplication calculation. Did you know often this multiplication might be written like this? 34 multiplied by something equals 68. We need to find the missing number. Now these are two ways of writing exactly the same multiplication. But can you see how it’s been written in the question? The numbers have been written on top of each other, vertically. They’re all in columns, and we call this way of working the column method. Another way to describe it is short multiplication. And it’s a helpful way of multiplying two-digit numbers, sometimes even three-digit numbers, by a one-digit number, because it helps us to split these two-digit numbers into separate parts.

We know that the number 34 is made up of four ones and three tens. And just by writing our number like this, we can see those tens and those ones, can’t we, in separate columns? Now, often when we’re using the column method, we know what we need to multiply and what we need to multiply by. And we need to find the answer. But with this problem, we know the first number of our multiplication, 34. We know what the answer is going to be, which is 68, but we just don’t know what we’re multiplying by. Perhaps it might be a good idea to imagine we’re going to work out this multiplication using the column method and think about what we need to do to get from our first number to the answer.

So if we’re going to work out this column multiplication, the first thing we do is we look at our ones digit, which is four. And then we’d multiply it by whatever we’re multiplying by. We don’t know. And then we’d write the answer at the bottom. And we can see that the answer is eight. So here’s our first clue as to what our missing number is going to be. What do we multiply four by to get eight? Well, we know that four doubled is eight, isn’t it? Four times two equals eight. So it looks like our missing number might be two. Let’s complete the digit card with a two, and we’ll see whether it works when we multiply our tens digit.

Now in the tens place of our number 34, we have the digit three. Three 10s are 30, aren’t they? And we think that our missing number is two. So what is 30 times two? Well, there is a smaller number fact that we could use to help us here. We know that three times two equals six, and so three 10s times two or 30 equals six 10s or 60. Can you see the digit six is in the tens place in our answer? We’ve used our understanding of how the column method works to find out the missing number. 34 times two equals 68. Our missing number is two.

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