Video: Using the Standard Algorithm to Multiply Two-Digit by Two-Digit Numbers

Write the missing digits to complete the standard algorithm.

04:07

Video Transcript

Write the missing digits to complete the standard algorithm.

And then, we’re shown a calculation for 93 multiplied by 22. And as part of the working for the calculation, we can see that there’s a number missing. The arrow’s pointing to it. And we’re given five possible answers. Five sets of digits, 1800, 1860, 1878, 1980, or 2232. How can we work out the missing digits?

There are two methods we can use, and they both involve understanding how the algorithm works or how the method works. The number that we see in equal signs at the end is the answer to the multiplication. So, we know 93 multiplied by 22 equals 2046. And how we get there is, first of all, we multiply both digits in the top number by the ones digit in the second number. So, in other words, we work out 93 times two.

The second step, then, is to multiply the digits in the top number by the tens digit in the second number. So, we need to multiply by 20. And this is our missing number, the answer to 93 times 20. So, our first method to find the missing digits might be to work out what 93 times 20 is. But, because we know that 186 plus our missing digits equals 2046, we could rearrange this and work backwards. 2046 take away 186 will leave us with our missing digits. Let’s try these two methods and hopefully they’ll both give us the same answer.

Firstly, we could work out 93 times 20. Before we do that, spend 10 seconds looking at the calculation to see if there’s a quick way to find out what 93 times 20 is. Is there something we already know that could help us? Yes, in a way, it’s already been done for us. We know already what 93 multiplied by two is. If 93 multiplied by two is 186, then 93 multiplied by 20, or 10 lots of two, will be 10 lots of 186. It’ll be 1860. And if we look across to our possible answers, we can see that 1860 is there. We didn’t even have to work out the multiplication. We just shifted the digits one place to the left and turn 186 into 1860.

Just to be sure and to check our answer, let’s try the subtraction method, 2046 take away 186. And, we’ll use column subtraction to find the answer. Six take away six equals zero. We can’t subtract eight from four, so we’re going to need to exchange. And, there’s a zero in the hundreds column, so we’re gonna have to exchange from the thousands.

Instead of two thousands, we now have one thousand. And we could exchange that for 10 hundreds. We’ll take one of those hundreds. Now, we have nine hundreds, and we’ll exchange that for 10 tens. 14 tens, then, take away eight equals six. Nine hundreds take away one hundred equals eight hundreds. And, then one thousand take away zero equals one thousand. We’ve checked our answer, and it’s correct. The missing digits to complete this standard algorithm are one, eight, six, zero, or 1860.

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