Math Antics - Multi-Digit Multiplication Pt 1

Summary

In this Math Antics video, viewers are introduced to the basics of multi-digit multiplication. The lesson emphasizes the importance of memorizing multiplication facts and suggests using a multiplication table for practice. The presenter demonstrates the process by breaking down the multiplication of a three-digit number by a one-digit number into smaller steps, starting from the ones place and carrying over when necessary. The video uses clear examples, such as multiplying 137 by 5 and 2,617 by 4, to illustrate the method. It concludes with encouragement to practice and hints at upcoming lessons for more complex multiplication scenarios.

Takeaways

• 📚 Start by mastering basic multiplication facts to simplify multi-digit multiplication.
• 📈 Practice is key to getting comfortable with multi-digit multiplication.
• 🔢 Always align the ones place when setting up a multiplication problem.
• ↕️ The order of numbers in multiplication doesn't affect the result, but it's conventional to place the larger number on top.
• 📝 Break down the problem into smaller steps, multiplying each digit of the smaller number by the larger number from right to left.
• 🔄 Carry over numbers when the multiplication result exceeds ten.
• 🔢 Add the carried-over number to the next multiplication result in the same place value.
• 📉 Work from the ones place to the highest place value in the top number.
• 📈 Use the examples provided in the script to understand the process of carrying and adding in multi-digit multiplication.
• 💻 Visit www.mathantics.com for more resources and exercises to practice multi-digit multiplication.

Q & A

What is the main topic of the Math Antics video lesson?

The main topic of the Math Antics video lesson is basic multi-digit multiplication.

Why is it suggested to have a multiplication table handy when doing multi-digit multiplication?

It is suggested to have a multiplication table handy when doing multi-digit multiplication because it can help if you haven't memorized basic multiplication facts.

What is the recommended order of numbers when setting up a multi-digit multiplication problem?

It is recommended to put the number with the most digits on the top and the one with the fewest digits on the bottom when setting up a multi-digit multiplication problem.

How many small multiplication steps are there in the example 137 × 5?

There are three small multiplication steps in the example 137 × 5.

What is the first step in the multiplication process for the number 137?

The first step in the multiplication process for the number 137 is to multiply the bottom digit (5) by the digit in the ones place of the top number (7).

Why do you carry over a digit in the multiplication process?

You carry over a digit in the multiplication process to ensure that the carried digit is added to the subsequent multiplication result in the correct place value.

What is the final result of the multiplication problem 137 × 5?

The final result of the multiplication problem 137 × 5 is 685.

How many small multiplication steps are there in the example 2,617 × 4?

There are four small multiplication steps in the example 2,617 × 4.

What is the purpose of carrying a digit in the multiplication of 2,617 by 4?

The purpose of carrying a digit in the multiplication of 2,617 by 4 is to add it to the next multiplication result in the correct place value, ensuring accuracy in the multiplication process.

What is the final result of the multiplication problem 2,617 × 4?

The final result of the multiplication problem 2,617 × 4 is 10,468.

What is the advice given at the end of the video for mastering multi-digit multiplication?

The advice given at the end of the video for mastering multi-digit multiplication is to practice the printable exercises and then move on to learning multiplication with multiple digits in both numbers.

Outlines

00:00

📘 Introduction to Multi-Digit Multiplication

This paragraph introduces the concept of multi-digit multiplication, emphasizing that while it may be challenging initially, practice will lead to proficiency. It highlights the importance of memorizing basic multiplication facts and having a multiplication table on hand for reference. The video demonstrates the multiplication of a three-digit number by a one-digit number, explaining the process of aligning numbers in stacked form and the significance of order in multiplication. The paragraph outlines the step-by-step method of breaking down the multiplication into smaller steps, starting with multiplying the bottom digit by the ones place of the top number and carrying over as necessary. The example of multiplying 137 by 5 is used to illustrate the process, including carrying over and adding the carried number to subsequent steps, culminating in the final answer of 685.

05:04

📘 Advanced Multi-Digit Multiplication Example

This paragraph builds upon the previous by introducing a more complex example of multi-digit multiplication, involving a four-digit number (2,617) multiplied by a one-digit number (4). It reiterates the importance of aligning the ones places and starting from the rightmost digit. The paragraph walks through each multiplication step, detailing how to handle carrying over digits and adding them to subsequent results. The process is illustrated through the multiplication of each digit of 2,617 by 4, including carrying over and adding the carried number to the next step's result. The final answer of 10,468 is reached after completing all four steps. The paragraph concludes with encouragement to practice and a preview of upcoming content, which will cover multiplication involving two multi-digit numbers.

Keywords

💡multi-digit multiplication

Multi-digit multiplication refers to the process of multiplying numbers that have more than one digit. In the video, this concept is central as it is the main operation being taught. The script explains that while it can be tricky at first, with practice, one can master it. The video provides a step-by-step guide on how to multiply a three-digit number by a one-digit number, emphasizing the importance of breaking down the problem into smaller, manageable steps.

💡memorize

To memorize, in the context of the video, means to commit to memory the basic multiplication facts. The script suggests that memorizing these facts will make multi-digit multiplication easier. It implies that having these facts readily available in one's memory can streamline the multiplication process, reducing the need to constantly refer to a multiplication table.

💡multiplication table

A multiplication table is a mathematical table used to define the product of two numbers. In the video, it is mentioned as a handy tool for those who have not memorized their basic multiplication facts. The script advises that if one is not confident with the multiplication facts, having a multiplication table at hand can assist in solving practice problems more efficiently.

💡stacked form

Stacked form, as used in the video, refers to the way numbers are aligned when written for multiplication, with the ones places lined up vertically. This format is crucial for ensuring that each digit in the multiplicand (the number being multiplied) is correctly aligned with the corresponding digit in the multiplier. The script demonstrates that this alignment is essential for performing the multiplication steps accurately.

💡ones place

The ones place is the rightmost digit in a number, representing the units. In the context of the video, the ones place is significant because the multiplication process starts from this position and moves leftward. The script explains that when multiplying, one begins by multiplying the bottom digit by the digit in the ones place of the top number, as demonstrated in the examples provided.

💡carrying

Carrying is the process of transferring a digit to the next column when the sum of digits in a column exceeds the base of the numeral system (usually 10 in the decimal system). In the video, carrying is a key step in the multiplication process, especially when the product of a multiplication step is a two-digit number. The script illustrates carrying with examples, such as when multiplying 5 by 7 in the first example, which results in carrying the '3' to the tens place.

💡multiplication steps

Multiplication steps refer to the individual multiplication operations performed when multiplying larger numbers. The video breaks down the process of multi-digit multiplication into a series of these smaller steps, each involving the multiplication of a single digit from the multiplicand by each digit of the multiplier. The script uses this term to describe the systematic approach to solving the multiplication problem, which involves moving from the ones place to higher places as the steps progress.

💡order of the problem

The order of the problem in multiplication refers to the arrangement of the numbers being multiplied. The video script clarifies that the order does not affect the result of the multiplication, which is a fundamental property of multiplication (commutative property). However, the script also suggests a conventional approach to writing the problem with the larger number on top for ease of calculation.

💡practice problems

Practice problems are exercises designed to help individuals apply and reinforce their understanding of a mathematical concept through repetition and application. In the video, the presenter encourages viewers to practice the skills learned through the provided exercises. The script emphasizes the importance of practice in mastering multi-digit multiplication and becoming proficient in the technique.

💡printable exercises

Printable exercises are written materials that can be printed out for practice or study. The video script mentions these as a resource for viewers to use after watching the lesson. These exercises are meant to provide additional practice to reinforce the concepts taught in the video, allowing learners to apply what they've learned in a hands-on manner.

Highlights

Introduction to basic multi-digit multiplication and its potential challenges.

Emphasis on the importance of memorizing basic multiplication facts for easier multi-digit multiplication.

Advice to have a multiplication table handy for practice problems.

The recommendation to place the number with the most digits on top in multiplication problems.

Explanation of the multiplication procedure by breaking down the problem into smaller steps.

Instruction to start multiplication from the ones place and move leftward.

How to handle carrying over when the multiplication result is a two-digit number.

Example of multiplying 137 by 5, demonstrating the step-by-step process.

Clarification on adding carried digits to subsequent multiplication results.

Final answer to the example problem 137 × 5, which is 685.

Introduction of a second example, multiplying 2,617 by 4.

Guidance on multiplying each digit of the bottom number by the top number, starting from the ones place.

Process of carrying over and adding carried digits in the second example.

Final answer to the second example problem 2,617 × 4, which is 10,468.

Encouragement to practice multi-digit multiplication with printable exercises.

预告下一节视频内容：学习多位数乘法，当两个数都包含多个数字时的乘法方法。

Conclusion of the lesson and invitation to visit www.mathantics.com for more information.

Transcripts

Hi and welcome to Math Antics.

In this video lesson, we’re gonna learn how to do basic multi-digit multiplication.

Now this can be tricky at first, but don’t get discouraged.

It just might take some extra time and practice, but you’ll get the hang of it.

One thing I want to mention before we start is that

multi-digit multiplication will be much easier for you if you memorize your basic multiplication facts.

But if you don’t have them memorized, then be sure to have a multiplication table handy when you’re doing your practice problems.

Okay, the best way to learn this it to jump right in. Let's try 137 × 5.

Now as you can see, this is a three-digit number times a one-digit number.

When you’re given a problem like this (where the numbers are written side by side),

you need to re-write it in stacked form with the ones places lined up the way we did with addition and subtraction.

Now you might remember with multiplication, that the order of the problem doesn’t matter,

so we could put whichever number we want on the top or the bottom.

BUT… it’s always best to put the number with the most digits on the top, and the one with the fewest digits on the bottom.

There, now we draw our answer line below, and we put our times symbol to the left so we don’t forget that we’re multiplying.

Okay, now we’re ready to learn the procedure for multiplying.

Basically what we’re gonna do is break up this big multiplication problem into a series of small multiplication problems or steps.

Those small steps involve multiplying a digit in the bottom number by a digit in the top number.

Now in our problem, we only have one digit on the bottom, and we’re gonna multiply it by each of the digits in the top number.

And since the top number has three digits, that means that our problem will have three small multiplication steps.

For the first step, we multiply the bottom digit (5) by the digit in the ones place of the top number (which is 7).

We always start with the ones place and work our way from right to left. So 5 × 7 gives us 35.

Now just like with addition, when we get a two-digit answer, we have to carry the first digit to the top of the next column,

because it will be in the way of the next answer digit if we don’t.

So the ‘5’ stays down here in the ones place of the answer,

but the ‘3’ gets carried up to the top of the tens place column.

Now it’s time for the second step.

We multiply the bottom digit (5) by the next digit to the left in our top number (3). So, 5 × 3 = 15.

But wait a second!… there’s that ‘3’ we carried up to the top from the last answer… what do we do with that?

Well we need to add it to the answer that we just got.

That’s because that ‘3’ was supposed to go in the tens place of the answer, but just not all by itself.

We had do the second multiplication step first and see what else needed to go in that answer spot with it.

And it turned out to be a ‘5’ (the second digit of the answer 15),

so we have to combine the two digits that both go in that answer place.

That’s why we add the digit we carried, and we end up with 18.

But once again, our answer is a two-digit number,

so we leave the ‘8’ in our answer line, and we carry the ‘1’ up to the top of the hundreds place column.

Now for our third and last multiplication step. We have 5 × 1 which is just 5.

But again, there’s the digit we carried up above so it wouldn’t be in the way.

What do you think we do with that digit?

Yep, we add it to the answer we got from the multiplication step.

So 5 + 1 gives us 6, and that’s what goes in our answer line.

Okay then… we’ve done all three of our multiplication steps and the answer to our problem (5 × 137) is 685.

Now that wasn’t so bad, was it.

Let’s try one more example before you practice some on your own. Let’s multiply 2,617 by 4.

Again, we stack our problem with the ones places lined up, and we make sure that the number with the most digits is on top.

Because our top number has four digits this time, it means we will break this problem up into four small multiplication steps.

We’ll multiply the bottom digit by each digit in the top number, starting with the ones place on the right and working our way left.

Okay, here we go with the first step.

We multiply the bottom digit by the top digit in the ones place: 4 × 7 = 28

Because we have a two-digit answer, we need to carry the digit that will be in the way.

We’re gonna add it back in after we complete the next multiplication step.

So we carry the ‘2’ to the top of the tens column and we leave the ‘8’ where it is.

Now we can do the second step. We multiply the bottom digit by the next digit in the top number: 4 × 1 = 4.

That was easy! But don’t forget about that digit we carried. We need to add that to our answer from the second step.

So, 4 plus 2 gives us 6, and that’s what we put in our answer place.

And this time, we have a one-digit answer, so we don’t need to carry.

We can just move on to the next step.

For our third multiplication step, we’ll multiply 4 × 6, and that gives us 24.

Yep - it’s a two-digit answer so we’ll need to carry again.

The ‘4’ stays in the answer and the ‘2’ moves up to the top of the thousands column.

Now it’s time for the fourth and last step.

We multiply 4 × 2 which is 8, but then we need to add the digit we carried (which is a ‘2’),

so 8 + 2 gives us 10 and that can go down in our answer line.

And even though it’s a two-digit number, we don’t have to carry, because we’re all done with our multiplication steps

and we have our final answer. 4 × 2,617 = 10,468.

Alright, that’s the basics of multi-digit multiplication.

But it’s really important to practice so you get good at it. Be sure to do the printable exercises for this section.

Then, once you think you have it down,

you’ll be ready to move on to the next video and learn how to do multiplication when both of the numbers have multiple digits.

Thanks for watching Math Antics, and I’ll see ya next time.

Learn more at www.mathantics.com