Lesson Video: Multiplying a Two-Digit Number by a One-Digit Number: Column Method with Regrouping Mathematics • 4th Grade

In this video, we will learn how to use the standard algorithm to multiply a two-digit number by a one-digit number for calculations where there is regrouping.

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Video Transcript

Multiplying a Two-Digit Number by a One-Digit Number: The Column Method with Regrouping

In this video, we will learn how to multiply a two-digit number by a one-digit number using the standard written method for calculations where there is regrouping. 23 is a two-digit number, and we have to multiply it by five which is a one-digit number. In this video, we’re going to learn how to multiply two-digit numbers by one-digit numbers using the standard written method.

To help us understand how this method works, we’ve modeled this multiplication. The number 23 has been modeled using two 10s and three ones. There are five rows of 23 because we’re multiplying 23 by five. When we use a standard written method to add, subtract, or multiply, we always start in the ones column. We know the number 23 has three ones, and we have to multiply them by five. Let’s count in threes five times. Three, six, nine, 12, 15. Because we’ve got more than 10 ones, we’re going to need to regroup. We can take 10 of our ones and exchange them for one 10. Now, we can record our five ones under one 10 that we exchanged.

Step two is to multiply in the tens column. We know the number 23 has two 10s. We have to multiply them by five because we’re multiplying 23 by five. If you multiply two 10s by five, we get two, four, six, eight, 10, and the one we exchanged makes 11 10s. Because we have more than 10 10s, again, we have to regroup. We need to exchange our 10 10s for 100. So two 10s times five gives us 10 10s plus the one we exchanged makes 11. 11 10s is the same as one 10 and one 100. 11 10s are 110. We put the one 100 in the hundreds column and the one 10 in the tens column. 23 multiplied by five is 115.

We start by multiplying the ones and record any regrouping. Then we multiply the tens and write any regrouping in the hundreds column. Let’s practice what we’ve learned now by answering some questions.

Find the result of the following: 29 multiplied by three equals what.

In this question, we have to multiply a two-digit number, the number 29, by a single digit, three. And we can tell by the way the question’s been set out that we have to use the standard written method. We know that two-digit numbers have a tens digit and a ones digit. The number 29 has two 10s and nine ones. When we multiply using the standard written method, we always start by multiplying the ones first. So our first step is to multiply nine by three. Nine times three is 27. We can write our seven ones in the ones column and the two 10s in the tens column because 27 has two 10s and seven ones. Because we’ve regrouped two 10s, we need to remember to add those on when we’ve multiplied in the tens column.

So our next step is to multiply the tens. Number 23 has two 10s, and we need to multiply them by three. Two 10s multiplied by three gives us a total of six 10s. And we need to add on the two 10s that we regrouped earlier. Six 10s and two more 10s gives us a total of eight 10s. 29 multiplied by three equals 87. When we multiply a two-digit number by a one-digit number using the standard written method, first we multiply their ones and regroup if we need to, and then we multiply the tens. We found the result of 29 multiplied by three using the standard written method. The result is 87.

Find the number that can replace the question mark in the following: 56 multiplied by three.

In this question, we’re shown the calculation 56 multiplied by three. But one of the digits is missing. When we’re multiplying a two-digit number by a one-digit number using the standard written method, we always start by multiplying the ones first. The number 56 has six ones, and we have to multiply them by three. We know that six times three equals 18. And we know that the number 18 has one 10 and eight ones. So we can write the ones digit in the ones column. This is the missing digit. We know that 18 has eight ones and one 10, so we would need to regroup 10 of our ones and exchange them for one 10. We’ve written the 10 in the tens column.

Although the rest of the calculation has been done for us, we can work through it to make sure the answer’s correct. Our next step is to multiply our five 10s by three. Five 10s multiplied by three gives us 15 10s. But we need to add the one that we regrouped. 15 10s and one more gives us 16 10s. We can write the six in the tens column and the one in the hundreds column. So 56 multiplied by three equals 168. The missing digit which replaces the question mark is eight. All we had to do to find the missing digit was multiply the ones. The missing digit is eight.

Look at this multiplication with an error in the answer: 34 multiplied by four equals 126. Which digit in the answer is wrong and needs to be replaced to make the answer correct? Write the correct answer.

In this question, we have to calculate 34 multiplied by four to find the correct answer. We know that one of the digits in the answer given is incorrect. So let’s calculate the answer. When we multiply a two-digit number by a one-digit number using the standard written method, we always start by multiplying the ones first. We know the number 34 has four ones, and we need to multiply them by four. Four times four is 16. We can write the six in the ones column. And we need to regroup 10 of our ones and exchange them for one 10.

Next, we need to multiply the tens. We got three 10s, and we need to multiply them by four. We know that three times four is 12, so three 10s multiplied by four gives us 12 10s. And we need to add the one that we regrouped earlier. 12 10s plus one more 10 gives us a total of 13 10s. We can write three 10s in the tens column and regroup 10 of our tens for 100. So 34 multiplied by four is 136.

So the digit in the calculation we were given, which is incorrect, is the tens digit. It looks like whoever did the calculation forgot to add the 10 that we’d regrouped. So the digit which is wrong is the two. We need to replace that with a three to make the answer correct. The correct answer should be 136 not 126. We found the error in the calculation by working out 34 multiplied by four using the standard written method. First, we multiplied the ones and regrouped. Then we multiplied the tens. The digit which is wrong is the two, which needs to be replaced with a three. And the correct answer is 136.

What have we learned in this video? We have learned how to multiply a two-digit number by a single digit using the standard written method. We learned that we multiply the ones first and regroup if needed, and then we multiply the tens.

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