Question Video: Finding the Missing Number in Equivalent Multiplication Expressions | Nagwa Question Video: Finding the Missing Number in Equivalent Multiplication Expressions | Nagwa

# Question Video: Finding the Missing Number in Equivalent Multiplication Expressions Mathematics • Fourth Year of Primary School

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Complete: 10 × 4 × 7 = 10 × ＿.

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### Video Transcript

Complete: 10 times four times seven equals 10 times what?

This question relies on us understanding that we can multiply numbers in different orders and still get the same answer. For instance, if we want to work out the answer to 10 times four times seven, one way to find the answer might be to work out 10 times four first and then to multiply that answer by seven. Another answer might be to work out four times seven first and then times the answer by 10. Or we could even really juggle the numbers around and multiply 10 by seven first and then multiply that answer by four. However we do it, we’re always going to get the same answer.

So let’s think about the first multiplication to start with. What does 10 multiplied by four multiplied by seven mean? Well, if we worked out this in order, then we’d calculate 10 multiplied by four first and then multiply that by seven. Let’s use this rectangle to represent the multiplication 10 times four. So if we work out 10 times four times seven, this means we need seven of these rectangles. There are two, three, four, five, six, seven. This diagram represents the first calculation, 10 multiplied by four seven times.

Now let’s think about the second part of our number sentence. 10 multiplied by what? In the same way as we’ve just done, we can draw another rectangle to represent this multiplication. The height of our rectangle is going to be worth 10 again. And we need the length to be exactly the same as the length of the other rectangle. The length of the rectangle is the same as seven fours. In other words, to find out our missing number, what we have to do is to calculate the four times seven part of our multiplication first.

Let’s count in fours seven times to find out what it’s worth. Four, eight, 12, 16, 20, 24, and 28. The missing number is 28. All we’ve done is multiply the four times seven part of the calculation first. This leaves us with 10 times 28 to find the overall answer. 10 times four times seven equals 10 times 28.

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