 Lesson Video: Multiplying Two-Digit Numbers by One-Digit Numbers: Adding Partial Products | Nagwa Lesson Video: Multiplying Two-Digit Numbers by One-Digit Numbers: Adding Partial Products | Nagwa

# Lesson Video: Multiplying Two-Digit Numbers by One-Digit Numbers: Adding Partial Products Mathematics • 4th Grade

In this video, we will learn how to multiply two-digit numbers by one-digit numbers by calculating partial products and using expanded column multiplication.

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### Video Transcript

Multiplying Two-Digit Numbers by One-Digit Numbers Using Partial Products

In this video, we will learn how to multiply two-digit numbers by one-digit numbers by calculating partial products and using expanded column multiplication. Let’s imagine we’ve been asked to multiply 32 by three. We’ve modeled three lots of 32 using base ten blocks. Here’s one group of 32, two groups of 32, and three groups of 32. 32 is a two-digit number. We can break it apart into its tens part and its ones parts. 32 has two ones and three 10s, which are worth 30.

Now that we’ve broken our number apart, we can multiply each part by three. We need to start with the ones. We have to multiply our two ones by three, which is the same as saying two multiplied by three. And we know that two times three is six. Next, we need to multiply the tens part of the number. We have to multiply three 10s by three. And we know that three 10s are worth 30. We know that three multiplied by three is nine, so three 10s multiplied by three equals nine 10s. And we know that nine 10s are worth 90. So two ones multiplied by three gives us a total of six ones, and three 10s multiplied by three gives us a total of nine 10s or 90.

Now all we need to do is add our two products, our ones product and our tens product. 90 plus six equals 96. 32 multiplied by three is 96. So, to calculate 32 multiplied by three, first we multiplied the ones. Two times three is six. Next, we multiplied the tens part of the number. Three 10s or 30 multiplied by three. The tens product is 90. Finally, we had to add the two products together. Six ones plus no ones gives us a total of six ones, and we only have nine 10s to add in the tens column. 90 plus six is 96. Let’s try some practice questions now where we need to multiply two-digit numbers by one-digit numbers using partial products.

Calculate 32 multiplied by two.

In this question, we’re being asked to multiply a two-digit number by a one-digit number. Our two-digit number is the number 32. And we have to multiply it by two. We can model the number 32 using three tens blocks and two ones blocks. And we’ve got two lots of 32 because we’re multiplying by two. We can break the number 32 apart. The two is worth two ones, and the three is worth three 10s or 30. Let’s start by multiplying the ones part of the number. Two ones multiplied by two gives us four ones. Next, we need to multiply the tens part of the number. We’ve got three 10s, and we need to multiply them by two. Three 10s multiplied by two gives us six 10s. And we know that six 10s are 60. 30 times two is 60.

Now, all we need to do is add our two partial products. Four ones and no ones gives us a total of four. And we only have six 10s in our tens column. 32 multiplied by two is 64. To calculate 32 multiplied by two, first we broke the number apart. 30  has two ones and three 10s worth 30. First, we multiplied the ones. Two times two is four. Then we multiplied the tens. Three 10s multiplied by two gives us a total of six 10s or 60. Finally, we added our two partial products together. Four plus 60 equals 64. 32 times two is 64.

Calculate the following: 75 multiplied by six.

In this question, we’re multiplying a two-digit number by a one-digit number. Let’s start by multiplying the ones. There are five ones in the number 75, so we need to multiply five ones by six. Five times six is 30. Next, we need to multiply the tens part of the number. The tens digit in the number 75 is a seven, so we need to multiply seven 10s by six. We know that seven times six is 42. 42 10s are 420.

Finally, we just need to add together our two partial products. What is 30 plus 420? Zero plus zero is zero. Three 10s plus two 10s gives us a total of five 10s. And we only have a four in the hundreds place, which gives us a total of four 100s. 30 plus 420 gives us a total of 450.

We calculated 75 multiplied by six. The answer is 450. First, we multiplied the ones part of the number or five times six. Then we multiplied our seven 10s by six, which gave us 420. And finally, we added together our two partial products to give us the answer. 75 multiplied by six is 450.

Find the missing number.

We have to multiply 23 by four. We can see that the first part of the calculation has been done for us. And we need to find this missing number. And we already know the answer; 23 multiplied by four gives us 92. When we’re multiplying a two-digit number by a one-digit number, it helps to break apart our two-digit number. We can break the number 23 into its tens and ones parts. So 23 has three ones and two 10s worth 20. When we’re using this method, multiplying using partial products, we start by multiplying the ones. And we know that 23 has three ones. So first, we multiply three by four. And that’s where we get the product 12.

Next, we have to multiply the tens part of the number 23. We know that 23 has two 10s, which are worth 20. So we have to calculate 20 multiplied by four, which is 80. Now, we can check that 12 plus 80 equals 92. Two plus zero gives us a total of two ones. And one 10 plus eight 10s gives us a total of nine 10s. So the missing number is 80. Three times four is 12. 20 times four is 80. 12 plus 80 equals 92. So the missing number is 80.

Liam spilled ink on his multiplication homework. Help him remember what he did. Use his work to find 13 multiplied by four. What calculation should he do to find the missing number? And again, what calculation should he do to find the missing number?

This is a three-part question. First, we have to help Liam finish multiplying 13 by four. He’s already multiplied in the ones place. Three ones multiplied by four is 12. Liam has also multiplied the tens part of number 13. We know that 13 has one 10, and 10 multiplied by four is 40. Now all we need to do is add these two partial products to find the total. Two plus zero gives us a total of two ones. One 10 plus four 10s is five 10s. 13 multiplied by four is 52.

Next, we have to multiply 46 by two. We can see that Liam has already multiplied the ones. Six multiplied by two is 12. Now we need to help him multiply the tens part of the number 46. 46 has four 10s. Four 10s multiplied by two gives us a total of eight 10s. 40 multiplied by two is 80. And if we add our two partial products together, 12 plus 80 gives us 92. The missing number in this calculation is the number 80. Finally, we have to multiply 24 by three. In this calculation, the ones product is missing. The number 24 has four ones, and we need to multiply them by three. Four times three is 12, and 12 plus 60 does total 72.

We helped Liam to complete his multiplication homework. 13 multiplied by four is 52. 46 multiplied by two is 92. But Liam had spilled ink on the tens part of his calculation. And we calculated that the product of 40 and two is 80. So the missing part of his calculation was the number 80. 24 multiplied by three is 72. Liam had spilled ink on the ones part of his calculation. We multiplied four times three to give us our missing product of 12. The missing numbers are 52, 80, and 12.

What have we learned in this video? We have learned how to multiply two-digit numbers by one-digit numbers by calculating partial products and using expanded column multiplication.