Math Antics - Long Division

Summary

This Math Antics lesson introduces long division, a method for breaking down complex division problems into manageable steps. The script guides viewers through the process, emphasizing the importance of digit-by-digit division, starting from the highest place value. It illustrates the technique using examples like dividing 936 by 4 and 315,270 by 5, highlighting the need for practice and organization. Tips are provided for mastering long division, such as memorizing multiplication tables and using graph paper for neatness.

Takeaways

• 📘 Long division is a method to break down complex division problems into simpler steps, similar to basic division.
• 🔢 The process involves dividing numbers digit-by-digit, starting from the leftmost digit and working towards the right.
• 📉 Division is the reverse of multiplication and addition; instead of starting from the rightmost digit, you start from the left.
• 📈 In long division, if the divisor is too large to divide into the first digit of the dividend, you combine it with the next digit.
• 📝 It's important to write neatly and keep the division process organized to avoid mistakes and to easily follow the steps.
• 🔄 Each step of long division involves dividing, multiplying the result to find the partial product, and then subtracting to get the new remainder.
• 🎯 Practice is essential for mastering long division, as it can be complex and requires familiarity with the process.
• 🧠 Memorizing the multiplication table is beneficial for performing long division efficiently.
• 📊 After completing a long division problem, it's recommended to check the answer with a calculator to ensure accuracy and learn from any mistakes.
• 📐 Using graph paper can help keep the division process neat and organized, especially for those who struggle with alignment.
• 📚 Start practicing with smaller dividends and gradually progress to more complex problems to build confidence and skill in long division.

Q & A

What is the main topic of the Math Antics lesson?

The main topic of the lesson is long division, which is a method for dividing large numbers by breaking the problem into a series of smaller division steps.

Why is it suggested to watch the basic division video before this lesson?

It is suggested to watch the basic division video first because understanding basic division makes learning long division a lot easier, as long division builds upon the concepts introduced in basic division.

How does long division differ from basic one-step division?

Long division differs from basic one-step division in that it involves breaking down a larger division problem into multiple steps, working digit-by-digit from left to right, rather than solving the entire problem in one step using the multiplication table.

What is the first step in performing long division according to the script?

The first step in performing long division is to divide the first digit of the dividend by the divisor, ignoring the other digits for now, and placing the result directly above that digit.

Why is it important to place the answer digit directly above the digit being divided?

It is important to place the answer digit directly above the digit being divided to keep the division process organized and to ensure that each step of the division is correctly aligned with the corresponding digit in the dividend.

What should you do when you have a remainder from the previous division step and need to divide the next digit?

When you have a remainder from the previous division step, you should combine that remainder with the next digit by bringing down a copy of the next digit and placing it beside the remainder, then proceed with the division as if they were a single number.

How does the script illustrate the process of long division with the example of 936 divided by 4?

The script illustrates the process by breaking down the division of 936 by 4 into three steps: first dividing the hundreds digit (9), then combining the remainder with the tens digit (3), and finally combining the new remainder with the ones digit (6), solving each step using basic division principles.

What is the significance of the zero in the dividend when performing long division?

The zero in the dividend is significant as it serves as an important placeholder. When brought down in the division process, it can change the remainder significantly, affecting the subsequent division steps.

Why is it recommended to practice long division problems starting with smaller dividends?

It is recommended to start with smaller dividends because they involve fewer division steps, making it easier for learners to grasp the process and build confidence before tackling more complex problems.

What tips are provided in the script to help with long division practice?

The tips provided include memorizing the multiplication table, writing neatly and staying organized, starting with smaller dividends, and checking answers with a calculator to learn from mistakes.

How does the script demonstrate the difference in steps between dividing 72 by 8 and dividing 72 by 3?

The script demonstrates that dividing 72 by 8 is a one-step problem because 72 is a multiple of 8, whereas dividing 72 by 3 requires a two-step process, using the digit-by-digit method to find the quotient.

What does the script suggest for checking long division answers?

The script suggests checking long division answers with a calculator to immediately identify any mistakes, learn from them, and also to gain practice using a calculator.

Outlines

00:00

📚 Introduction to Long Division

This paragraph introduces the concept of long division as a method to break down complex division problems into simpler steps. It emphasizes the importance of understanding basic division before proceeding to long division, as the process involves a digit-by-digit approach. The example of dividing 936 by 4 is used to illustrate the step-by-step process, starting with dividing the highest place value digit and then incorporating the remainder with subsequent digits. The explanation includes the reasoning behind placing the answer digit directly above the divided digit and the importance of multiplication and subtraction in finding the remainder. The paragraph concludes with the solution to the example, demonstrating that 936 divided by 4 equals 234.

05:04

🔍 Understanding Long Division Steps and Examples

This paragraph delves deeper into the long division process, explaining that the number of steps is not always equal to the number of digits in the dividend due to the size of the divisor. Two side-by-side examples, 72 divided by 8 and 72 divided by 3, are used to illustrate this point. The first example shows a straightforward one-step division, while the second requires a two-step process due to the divisor's size relative to the dividend's digits. The paragraph also discusses the strategy of dealing with remainders and how to combine them with subsequent digits for further division. The process is reiterated with a larger problem, dividing 315,270 by 5, to demonstrate the application of long division with a multi-digit number, concluding with the final answer of 63,054.

10:06

🛠️ Tips for Mastering Long Division

The final paragraph offers advice for those learning long division, starting with the suggestion to memorize the multiplication table to facilitate the division process. It stresses the importance of neat and organized writing to prevent mistakes in column alignment. The paragraph advises starting with smaller dividends to build confidence and understanding before tackling more complex problems. It also recommends checking answers with a calculator to identify and learn from errors. The summary concludes with an invitation to learn more on the Math Antics website, encouraging continued practice and exploration of mathematical concepts.

Keywords

💡Long Division

Long Division is a mathematical process used to divide larger numbers that cannot be divided using simple mental calculation or the multiplication table. It is the main theme of the video, as it is the technique being taught. The script explains that long division involves breaking down a complex division problem into a series of simpler steps, starting from the highest place value and moving to the right, as demonstrated with the division of 936 by 4.

💡Dividend

The dividend is the number that is being divided in a division operation. In the context of the video, the dividend is the large number, such as 936 in the example, which is being divided by a divisor to yield a quotient. The script emphasizes that when dealing with long division, the dividend can have many digits, requiring multiple steps to find the quotient.

💡Divisor

The divisor is the number by which the dividend is divided. It is a key concept in the script, as the process of long division involves determining how many times the divisor can fit into the dividend. For instance, in the script, the divisor '4' is used to divide the dividend '936'.

💡Quotient

The quotient is the result obtained after dividing the dividend by the divisor. The script illustrates how to find the quotient through the long division process, such as when dividing 936 by 4, which results in a quotient of 234.

💡Remainder

A remainder is what is left over after division, when the dividend cannot be evenly divided by the divisor. The script explains that in long division, if the divisor cannot divide into the current number, a remainder is carried over to the next step, as shown when dividing 72 by 3, where the remainders are 1 and then 12 before reaching a final remainder of 0.

💡Digit-by-Digit

The term 'digit-by-digit' refers to the step-by-step process of long division, where each digit of the dividend is considered individually in sequence from left to right. The script uses this term to describe the method of breaking down the division process to make it more manageable, as seen when dividing 936 by 4, starting with the '9' and then moving to '36'.

💡Multiplication Table

A multiplication table is a set of facts that show the result of multiplying two numbers. The script mentions that for simple one-step divisions, the multiplication table can be used to find the answer quickly, but for long division, especially with larger numbers not found on the table, a different approach is necessary.

💡Place Value

Place value refers to the value of a digit based on its position in a number. The script explains that in long division, the process starts with the highest place value, which is the leftmost digit of the dividend, and then moves to the right, emphasizing the importance of place value in the division process.

💡Steps

In the context of the video, 'steps' refers to the individual division operations within the long division process. The script clarifies that the number of steps in long division does not always correspond to the number of digits in the dividend, as it also depends on the size of the divisor, as illustrated with the examples of dividing 72 by 8 and 3.

💡Practice

Practice is emphasized in the script as an essential part of mastering long division. The video suggests starting with smaller dividends and gradually moving to more complex problems, checking answers with a calculator to learn from mistakes, which is a key part of the learning process.

💡Graph Paper

Graph paper is recommended in the script as a tool to help keep the division process neat and organized. Writing neatly and keeping columns aligned can prevent mistakes in long division, and graph paper can assist with this by providing a structured grid to write on.

Highlights

Introduction to long division as a method for breaking down complex division problems into simpler steps.

The importance of understanding basic division before attempting long division.

Long division allows for the division of very large numbers by breaking the process into manageable parts.

The concept of digit-by-digit division in long division, starting from the highest place value.

Illustration of long division with a simple example: 936 divided by 4.

Explanation of how to handle remainders by combining them with the next digit in the dividend.

The process of bringing down the next digit to increase the remainder for further division.

Demonstration of how to complete a division problem with no remainder, as shown with 936 divided by 4.

Comparison of the number of division steps to the number of digits in the dividend.

Example of a two-step division problem: 72 divided by 3, emphasizing the digit-by-digit approach.

The possibility of skipping steps in long division when the divisor is too large for the current digit.

A complex long division example: dividing 315,270 by 5, showcasing the step-by-step process.

The significance of zero as a placeholder in long division and its impact on the remainder.

Strategies for practicing long division, including the use of multiplication tables and graph paper.

Advice on starting with smaller dividends and gradually progressing to more complex problems.

The recommendation to check answers with a calculator to identify and learn from mistakes.

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

Transcripts

Hi! Welcome to Math Antics. In this lesson, we are gonna learn about long division.

If you haven’t already watched our video about basic division, then be sure to go back and watch that first.

It will make learning long division a lot easier.

Long division is just a way of breaking up a bigger division problem into a series of short division steps

like the ones that we did in the basic division video.

The nice thing about long division is that once you know the procedure,

you can divide up all kinds of numbers, even if they are REALLY big.

The key to long division is to think about our division problem digit-by-digit.

If our dividend (the number we’re dividing up) has a lot of digits,

then that means that there will be a lot of division steps to do.

When we learned basic one-step division, all of the dividends were small enough

that we could just use the multiplication table to help us find the answer.

But what if we have a division problem like this? 936 divided by 4

936 is definitely NOT on our multiplication table!

In fact, there’s not anything even close to 936, so what do we do?

Well, instead of trying to divide the entire 936 by 4 all at once,

let’s break this problem up into smaller steps by just trying to divide each digit by 4,

one digit at a time …digit-by-digit.

Do you remember how with multi-digit multiplication and addition,

we always start with the smallest digit (the ones place digit) and we work from right to left?

Well division is backwards! We still go digit by digit, but the other way.

We start by trying to divide up the digit in the biggest number place first and we work our way from left to right.

So the first step in this problem is to divide the FIRST digit of our dividend by 4.

We’ll just ignore the other digits for now, and that makes it look like we have the division problem 9 divided by 4.

Great! That’s easy! It’s just a basic division problem like in the last video.

So we ask, “How many ‘4’s will it take to make 9 or almost 9?”

Well, two ‘4’s would be 8, and that’s almost 9.

So just like before, we put the 2 in our answer spot on top of the line.

But wait a minute… there’s a lot of room up there. Where exactly do we put it?

Well, the answer digit should always go directly above the digit we’re dividing.

Since we’re dividing the digit 9, our 2 should go right above the 9.

Okay, now we multiply… 2 times 4 is 8, and the 8 goes below the 9 so that we can subtract to get our remainder.

9 minus 8 is 1, so our remainder is 1.

Now at this point in our basic one-step division problems, we would re-write our remainder up in our answer with a little ‘r’ next to it.

But we aren’t going to do that yet because this is long division and we still have more digits to divide (the ones we’ve been ignoring).

Since we’re going digit-by-digit, let’s stop ignoring the next digit in our dividend (the 3).

Now you might think that our next division step is to divide that 3 by the 4. But it’s not quite that simple.

We had a remainder from our last division step, and we can’t just forget about that.

We need to combine that remainder with our next digit and divide them both together.

We do that by bringing down a COPY of the next digit (the 3) and put it right beside the remainder (which is 1).

When we do that, it looks like our remainder is 13. It’s kind of like our remainder is teaming up with the next digit over.

And if you think about it, that makes sense because

the digits that we were ignoring during our first division step really are part of the remainder, because we still need to divide them.

Okay, so bringing down that next digit makes our remainder bigger.

And that’s good because before, the remainder was so small that 4 couldn’t divide into it.

But now it’s 13, and 4 will divide into 13.

So we ask, “How many ‘4’s will it take to make 13?”

Well, three ‘4’s would be 12, and that’s really close without being too big. So let’s put 3 in our answer line.

Yep - it goes right over the 3 because that is the next digit we were dividing in this digit-by-digit process.

And then 3 times 4 is 12 which we put right below the 13 so that we can subtract to get the next remainder which will also be 1.

See how we’re just repeating the basic division procedure? But we’re going further down the screen as we do.

Alright, now that we have a new remainder, it’s time for our next division step.

Let’s stop ignoring the last digit in the dividend (the 6) and bring down a copy of it to team up with our new remainder.

Together, they form a remainder of 16.

Ah ha! That’s good because it’s gonna be easy to divide 4 into 16 because 16 is a multiple of 4.

It takes exactly fours ‘4’s to make 16. So we put a 4 in the last place of our answer line,

and then we write the 16 below our new remainder.

Now if we subtract 16 from 16, we see that our last remainder will be zero, which means there’s no remainder left.

That’s great! We solved the whole division problem digit-by-digit by breaking it up into three basic division steps.

And now we know that 936 divided by 4 equals 234.

And we also know why they call it long division!!

In fact, that was so long, I think I need a coffee break…

Oh man…

that was some looooooooooooong division!

Wheew… let’s see…

Okay, so that problem had a three-digit dividend and it also had three division steps.

But the number of steps isn’t always the same as the number of digits we have.

And that’s because the number of steps also depends on how big our divisor is.

To see what I mean, let’s work two division problems side by side.

These both look like the basic one-step division problems that you did in the last video, don’t they?

But as you‘ll see, one of them is actually a two-step problem.

Let’s start with the first problem: 72 divided by 8.

We just ask, “How many ‘8’s does it take to make 72 (or almost 72)?”

Well that’s easy! On our multiplication table you can see that 72 is a multiple of 8.

8 × 9 = 72 So we put 9 in our answer line, and we write 72 below, and we see that we have no remainder.

Now let’s try the next problem: 72 divided by 3.

If we ask, “How many ‘3’s will it take to make 72 (or almost 72)?”, we can see that the answer is not on our multiplication chart.

The biggest multiple of three listed there is 30 which isn’t even close.

The reason is that this should really be a two-step problem.

Let’s try using the new digit-by-digit method we just learned.

Instead of asking, “How many ‘3’s make 72?”, let’s just focus on the first digit and ask,

“How many ‘3’s does it take to make 7?”

Ah - that’s easy. Two ‘3’s would give us 6, which is very close.

So let’s put a 2 in the answer line right above the 7.

Then we multiply 2 times 3, and that makes 6.

And we subtract 6 from 7 to get a remainder of 1.

Now for the second step…

We bring down a copy of the next digit (the 2) and we combine it with the 1 to get a new remainder of 12.

Then we ask, “How many ‘3’s does it take to make 12?”

and the answer to that is exactly 4.

So we write a 4 in the answer line, and 3 × 4 = 12.

12 − 12 = 0 So we have no remainder!

We’re done! 72 divided by 3 is 24.

Now here’s the interesting thing about these examples.

The first problem could have been a two-step problem also.

If we had taken it digit-by-digit, we would have first asked, “How many ‘8’s does it take to make 7 (or almost 7)?”

But the answer would have been zero since 8 is too big to divide into 7.

We would have put zero in our answer line and the remainder would have just been 7.

So basically, we just skipped that step. And that’ll happen with digit-by-digit division sometimes.

If the number is too small to divide into, you just put a zero in the answer line and you move on to the next digit.

Okay, now that you know the procedure for long division, are you ready to see a really long problem?

Good - I thought so!

Let’s divide 315,270 by 5.

Now don’t worry… it’s really not that hard if you just go digit-by-digit.

I’m gonna work the problem pretty fast, so don’t worry if you don’t follow all the math.

Just focus on the repeating division process as we go along. Are you ready?

The first digit is 3. How many times will 5 divide into 3? Zero.

5 is too big. So let’s just skip that step and combine our first digit with our next digit.

So how many times does 5 divide into 31? Six.

6 times 5 is 30. And 31 minus 30 gives us a remainder of 1.

Now on to the third digit… We bring a copy of it down to join with the remainder.

And we ask how many times will 5 divide into 15? Three.

3 times 5 is 15. And 15 minus 15 is zero.

On to the next digit…

Now even though our previous remainder was zero, we still bring down a copy of the next digit.

Now we ask how many times will 5 divide into 2? Zero.

5 is too big, so we need to move on to the next digit and bring a copy of it down also.

There, that’s better.

Now we ask, how many times will 5 divide into 27? Five.

5 times 5 is 25. And 27 minus 25 gives a remainder of 2.

…now for that last digit, which is a zero.

And you might wonder, “Why do we even have to bring a copy of a zero down? Isn’t that nothing?”

But the zero is an important place holder… and when we bring a copy of it down,

it changes our remainder of 2 into a remainder of 20. Now that’s a big difference!

Now we ask, how many times will 5 divide into 20? Four.

4 times 5 is 20. And 20 minus 20 is zero.

Yes! We’re done! There’s no more digits to divide.

And you can see that our final answer is: 63,054.

Alright… that’s the procedure for long division.

As you can see, it’s kinda complicated, so don’t get discouraged if you’re confused at first.

Like almost everything, it just takes practice.

So, as you get ready to practice some long division problems on your own, here’s a few tips that will help you out.

First: If you haven’t already done it, memorizing your multiplication table will really help with division.

Second: When you’re working problems, it’s really important to write neatly and stay organized.

If your writing is messy, it might be hard to keep your columns lined up and that could lead to mistakes.

And if that’s the case, try using graph paper to help keep things lined up.

Third: Start with some smaller two or three-digit dividends so you only have a few division steps to do.

Then work up to the longer problems.

And last of all: After each practice problem you do, check your answer with a calculator.

That will let you know right away if you’ve made any mistakes so you can correct them, and most importantly, learn from them.

And it will give you practice with a calculator, which is also important.

Alright, that’s all for this lesson.

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

Learn more at www.mathantics.com