Question Video: Finding the Missing Numbers in Multiplication and Division Fact Families | Nagwa Question Video: Finding the Missing Numbers in Multiplication and Division Fact Families | Nagwa

# Question Video: Finding the Missing Numbers in Multiplication and Division Fact Families Mathematics • Third Year of Primary School

Find all the missing numbers in these related facts. 6 × 3 = ?, 3 × ? = 18, 18 ÷ 6 = ?, ? ÷ 3 = 6.

04:13

### Video Transcript

Find all the missing numbers in these related facts. Six times three equals what, three times what equals 18, 18 divided by six equals what, and what divided by three equals six.

In this question, we’re given four number facts. And we’re told these aren’t just any number facts. These are related. They’re part of a family. What’s the same and what’s different about these facts? Well, firstly, as we’ve heard already, each of the facts has a missing number. They’re all in different places, though, so we need to think carefully about what numbers are missing. Two of the calculations are multiplications, and two are divisions. And although these may seem like different sorts of number sentences, they are related because we know that division is the inverse or the opposite of multiplication.

You know, there’s one other interesting thing about these number facts. Can you spot it? The same numbers keep cropping up again and again. We can see the numbers six, three, and also 18. These are the only numbers that are being used in our number sentences. I wonder why this is. Well, the key to the whole thing really is our first number fact. Six times three equals what. Let’s model this calculation using counters. We can think of six times three as being worth six lots of three. And this is the same as three, six, nine, 12, 15, 18 altogether. Our missing number is the third of our three numbers. Six times three equals 18.

Do you think maybe all of our number facts have the same three numbers in them? Let’s have a look at the second one. Three times what equals 18. Well, we know that we’ve got 18 in this group, but 18 is worth three lots of what? To help us find the missing number, we’re going to have to use some division, even though this is a multiplication question. We’re going to need to start with 18 and split it into three equal groups. There are six counters in each group. As though if we know six lots of three are 18, we also know three lots of six equal 18, too. And of course, this is something we know about multiplications, isn’t it? We can swap the numbers that we’re multiplying around and they’ll still make the same product.

Our next fact is a division. And because the missing number is the answer, the number that comes after the equal sign, we can just work out the division. 18 divided by six equals what. Now, we could do one of two things here. We could find out how many sixes there are in 18, or we could split 18 into six equal groups and see how many there are in each group. Let’s do the second one. One, two, three, four, five, six. Now, I’m guessing you probably knew what the answer was going to be before we started spitting up this number. If we know that six times three equals 18, then we also know the inverse. 18 divided by six equals three.

And what number do we divide by three to get six? The missing number in our last division is 18. We know that multiplication and division are inverse operations; they’re opposites. And so, with the number six times three equals 18, we can find four related number facts. Six times three equals 18, three times six equals 18, 18 divided by six equals three, and 18 divided by three equals six. Our missing numbers are 18, six, three, and 18 again.

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