Video: Verifying Mathematical Equations Involving Multiplication

Is the calculation 2 × 4 × 629 = 5012 correct?


Video Transcript

Is the calculation two multiplied by four multiplied by 629 equals 5012 correct?

The answer to this problem is either yes or no. Either two times four times 629 does equal 5012 or doesn’t. To find out which one is true, we’re going to have to calculate the answer for ourselves. To find the answer, we need to multiply three numbers together. The first two numbers in the multiplication are single-digit numbers. They’re easy to deal with. But then, we have a three-digit number. So to find the answer, we’re gonna have to give this a little bit of thought.

The first thing we can do is to make the multiplication simpler. Two times four equals eight. And so, two times four times 629 is exactly the same as eight times 629. One thing we know about multiplications, which is the same as additions, is that we can multiply in any order and the answer will always be the same. And so, we could swap the two numbers that we’ve got in our multiplication and rewrite it as 629 multiplied by eight. It makes no difference to the answer, but it might help us to have the larger number first. There are several different ways we could multiply 629 by eight. Multiplying by eight is the same as doubling, then doubling, then doubling again. So we could double 629, then double it, and then double it a third time.

Another method we could use is short multiplication. Let’s use this method to find the answer. Is it going to be the same as 5012? We can begin by multiplying our ones digit by eight. What is nine times eight? Well, we know that 10 eights are 80. So nine eights must be eight less than 80. 80 take away eight equals 72, which is the same as seven tens and two ones. Next, we need to multiply our tens digit. Two tens multiplied by eight equals 16 tens. But we already have seven tens underneath. So that takes us to 23 tens or 230. Let’s pause the calculation for a moment.

We’ve solved the problem. Can you see why? Look at the tens digit in our answer, and then compare it with the tens digit in 5012. We’ve calculated that the number is going to have three tens in it. But 5012 only contains one ten. So we can see that two times four times 629 is not going to equal 5012. It’s not correct.

Well, we’ve only got one more digit to multiply, and it would be a shame to stop there. So, let’s continue and to find the actual answer. Six hundreds multiplied by eight equals 48 hundreds. We’ve also got two hundreds underneath, so that takes us to 50 hundreds or five thousands. The actual answer to the calculation two times four times 629 is 5032. As soon as we got to the tens digit, we could see that the calculation was not correct. And so as our answer, we just need to give the word no. The calculation in the problem is not correct.

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