# Video: Using Equal Groups to Understand Multiplication by Zero

When we multiply, we can think about counting equal groups of objects. 3 boxes of 2 balls = 6 balls, 3 × 2 = 6. How many balls would you have if you had 3 boxes with 0 balls in each box? Find the missing number: 3 × 0 = ＿.

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### Video Transcript

When we multiply, we can think about counting equal groups of objects. Three boxes of two balls equals six balls. Three times two equals six. How many balls would you have if you had three boxes with zero balls in each box? Find the missing number: three times zero equals what.

To start within this problem, we’re reminded of a way of thinking about multiplication. When we multiply, we can think about counting equal groups of objects. And the picture shows this. We have three boxes. And in each box, there’s an equal number of balls. We can think of each of the three boxes as representing a group. And, of course, they’re all equal groups. They all contain two basketballs. Three boxes of two balls or three groups of two balls equals six balls altogether. And we can see that by counting in twos. Two, four, six.

This is why we can write the calculation three times two equals six. Three lots of two equals six. Now, we can apply this idea of counting equal groups of objects when multiplying by zero. The question asks us, how many balls would we have if we had three boxes with zero balls in each box? And we can see in the picture we have three empty boxes. We could think of these as three empty groups or three groups with nothing in them. So we don’t need to do any counting here. We can see straightaway we haven’t got any balls. When there were two balls in each box, we could count in twos. This time, we’d have to count in zeros. And the answer would be zero each time. Three groups of zero equals zero.

The final part of the question asks us to find the missing number. Three multiplied by zero equals what? Well, as we’ve seen already, three groups of nothing equals nothing. The missing number is zero. Multiplying by zero can be quite difficult to think about. So it’s useful to have this idea of counting equal groups of objects. It can help us understand why the answer is zero. If we have three boxes with zero balls in each box, then we’ll have zero balls altogether. And so, the answer to three times zero equals zero. The answers to both parts of this problem are the same; they’re zero.