Long Division- Multi digits by 1 digit
Basics on the topic Long Division- Multi digits by 1 digit
Long Division – Definition
One of the most basic lessons in mathematics are the four operations: addition, subtraction, multiplication, and division. At the beginning of learning mathematics, all of those four operations were used with small numbers like ten, twenty, fifty, etc. Then, when you start solving more complex math problems, the numbers become bigger and bigger. To be able to calculate with big numbers accurately, it is important to know the best ways to do it. That is why in this learning text we are going to teach you how to divide numbers that are bigger than a hundred.
In this learning text, we will be learning about long division. But what is long division exactly? Let’s take a look at the definition of long division:
Long division is a mathematical method for dividing large numbers by partitioning the dividend into smaller parts. It helps to break down long division problems into simple and easy steps. Division always features these terms: dividends, divisors , and quotients.
In this text, we will use long division with no remainders. In a long division problem, the dividend is the large number that is divided by another number called the divisor. The quotient is the result of the division.
Steps for Solving Long Division Problems – Explanation
In order to solve long division problems, you must set up the numbers first – the dividend and the divisor.
First you must identify the dividend (the number that is being divided), and divisor (the number that divides it) as well as the quotient (the answer and remainder or leftover). Long division is written with a division bar symbol that separates the dividend and the quotient.
In long division we organize dividend, divisor and quotient in a specific way; Take a look at the picture below.
In long division we use the following steps:
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- Divide
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- Multiply
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- Subtract
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- Bring down
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- Repeat
| Step # | Explanation |
|---|---|
| 1 | Divide the numbers in the dividend by the divisor. Start with the hundreds. |
| 2 | Multiply the number in the quotient by the divisor. |
| 3 | Subtract the number from the multiplication from the hundreds digit. |
| 4 | Bring down the next number from the dividend. |
| 5 | Repeat the steps for the tens place (or ones place) in the dividend. |
Long Division – Example 1
Now, we will go over a couple of examples of solving long division problems. We will go step by step, making sure you understand fully the whole long division process.
Let’s look at the first example: we are going to divide 363 by 3.
Firstly, we will place the numbers in the correct position: dividend which is 363 we will place first and the divisor which is three (3) we will place in front of the dividend.
Now, we are going to show all the steps one by one:
Step one is division. We divide hundreds in the dividend (the number 363) by the divisor (3).
Three is one group of three hundreds in the hundreds place. We write the one above the hundreds place in a quotient.
Step two is multiplication. We multiply the number one (1) by the divisor three (3). Then we write the answer, which is three (3) below the hundreds in the dividend.
Step three is subtraction. Three (3) minus three(3) equals zero. We write the zero below, and then we move to the next step.
Step four is bring down. We bring down the number from the tens place.
Step five repeating. We repeat the same steps over again for the tens and the ones place.
There are two (2) groups of 3 tens in sixty (60). We write the two (2) above the tens place and then multiply by the three (the divisor). Two (2) times three (3) is six (6). Write the six (6) below the previous six (6) and subtract. Six (6) minus six (6) equals zero (0). We have one more number to bring down from the one's place. We bring down the three (3) from the ones and repeat the steps one more time.
Finally, we have an answer: the quotient is 121. So, we can answer 363 divided by 3 is 121.
Long Division – Example 2
Now we will look at another example. This time, we are going to divide 126 by 3.
We are going to follow the same steps as in the first example.
| Step # | What to do |
|---|---|
| 1 | Divide |
| 2 | Multiply |
| 3 | Subtract |
| 4 | Bring down |
| 5 | Repeat |
We start with the hundreds place when dividing the dividend 126 by the divisor 3.
What do you notice when you think about how many groups of 3 make 1? Since 3 is bigger than 1, it cannot be divided evenly. So, we must look at two place values in our first step! So, this time we would like to know how many groups of 3 can we fit into 12 (using the hundreds and tens place together). The answer is 4 times. We write the four (4) above the tens place in a quotient.
Our next step is to multiply the number four by the divisor three.
So we write the answer twelve below the twelve and follow up the next step.
The next step is to subtract 12 from 12.
Twelve minus twelve equals zero (0). We write the zero below, and then we move to the next step.
Now we need to bring down the next number and repeat the steps from above.
We bring down the number 6 and we repeat the process again. There are two groups of 3 in 6. Therefore, we write the 2 above the ones’ place and then multiply by the 3 (the divisor). 2 x 3 = 6 – Write the 6 below the other 6 and subtract. We have zero (0) after subtraction.
Now we have an answer: the quotient is 42. So we can state that 126 divided by 3 equals 42.
Long Division – Summary
Long division is a way to organize the calculation of a division problem. To divide using long division, we follow these simple steps:
| Step # | Explanation |
|---|---|
| 1 | We divide hundreds (or tens) in the dividend by the divisor. |
| 2 | We multiply the number in a quotient by the divisor. |
| 3 | We subtract the number from the multiplication from the hundreds digit. |
| 4 | We bring down the next number from the dividend. |
| 5 | We repeat the steps again, we divide tens (or ones) in the dividend by the divisor, etc. |
Now you should be able to solve long division problems without remainders. If you need more help on how to do long divisions step by step, be sure to watch the video explaining each individual problem and complete the downloadable long division worksheets that are available for this topic.
Frequently Asked Questions about Long Division – Multi-Digit by 1-Digit
Transcript Long Division- Multi digits by 1 digit
Mr. Squeaks needs funds for his next historical adventure, so he's starting a business to raise money! He starts a babysitting service and boy does it take off! Mr. Squeaks wants to calculate exactly how much he has been making! We can help calculate the earnings per babysitting duty with... "Long Division - Multi-Digit by 1 Digit" In long division, we organize the dividend, divisor, and quotient like THIS. In long division, we find the quotient using these steps... Divide, multiply, subtract, bring down, repeat The Field Family hired Mr. Squeaks to watch their kids three times and paid him three hundred sixty-three dollars. We can divide to calculate how much he made EACH time he babysat. To do this, we will divide three-hundred-sixty-three by three. Put the dividend, "three hundred sixty-three" HERE… And the divisor, three, HERE. First, we divide the hundreds in the dividend, by the divisor. Three goes into three, one time. We write the one ABOVE the hundreds place in the quotient. Next, we multiply this number by the divisor. One times three equals three… and write this answer BELOW the hundreds in the dividend. Then, we subtract. Three minus three equals zero. Now, we bring down the number from the tens place... and REPEAT these steps. THREE goes into six, TWO times… so, we write the two above the tens place and multiply it by the divisor. Three times two equals six. write the six HERE... and subtract. Six minus six equals zero. There is still the number in the ones place to bring down... so, we have to repeat the steps ONE MORE time. Three goes into three one time. One times three equals three… and three minus three equals zero. The quotient is one hundred twenty-one. The Field Family paid Mr. Squeaks one hundred, twenty-one dollars each time he babysat. The Vole's hired Mr. Squeaks to babysit five times and paid him "two hundred forty-five" dollars in all. We can divide two hundred forty-five by five to see how much he earned each time. What is our first step? We need to divide the hundreds place by the divisor. What do you notice when you think about how many times five goes into two? Since five is MORE than two, it can not be divided evenly. This time, we need to look at the first two place values TOGETHER. How many times does five go into twenty-four? There are FOUR groups of five in twenty-four. We write the four above the TENS PLACE in the quotient... and multiply the four to the divisor, five. Four times five is twenty. Where do we write the twenty? We put it UNDER the twenty-four. Now, subtract, twenty-four minus twenty equals four. What is our next step? Bring down the next number. What number do we bring down? Five and now we have forty-five HERE. We need to repeat the steps again. How many times does five go into forty-five? Nine times. What do we multiply the nine by? The divisor, five. What is nine times five? Forty-five Write forty-five here... and subtract leaving zero. What is the quotient? Forty-nine. The Vole's paid Mr. Squeaks forty-nine dollars each time. Remember... long division is a way to organize the calculation of a division problem. To divide we follow these steps: Divide Multiply Subtract Bring down next place value in the dividend. Repeat these steps until all digits in the dividend have been used. Mr. Squeaks has earned enough money to go on his long-awaited adventure. Mr. Squeaks! Mr. Squeaks! Mr. Squeaks, it’s time for you to go on your trip. [Mr. Squeaks closes his eyes again…too exhausted to move.]
Long Division- Multi digits by 1 digit exercise
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Find the quotient.
HintsStep 1: Divide.
How many times does 2 go into 8? Write this number above the 8.
2 goes into 8 4 times.
Step 2: Multiply 2$\times$4.
2$\times$4 = 8. Place this 8 under the 8 in the dividend.
Subtract.
Bring down the 4 and repeat the steps twice.
Solution- Step 1: Divide. How many times does 2 go into 8? 4 times. Write this 4 above the 8.
- Step 2: Multiply. 2$\times$4 = 8. Place this 8 under the 8 in the dividend.
- Step 3: Subtract the 8s.
- Step 4: Bring down the 4.
- Step 5: Repeat the steps twice.
The answer is $\$$421.
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Complete the division problem.
HintsStep 1: Divide
How many times does 2 go into 4? Write this number above the 4.
2 goes into 4 2 times.
Step 2: Multiply 2$\times$2.
2$\times$2 = 4. Place this 4 under the 4 in the dividend.
Subtract.
Bring down the 8 and repeat the steps 3 times.
Solution- Step 1: Divide. How many times does 2 go into 4? 2 times. Write this 2 above the 4.
- Step 2: Multiply. 2$\times$2 = 4. Place this 4 under the 4 in the dividend.
- Step 3: Subtract the 4s.
- Step 4: Bring down the 8.
- Step 5: Repeat the steps 3 times.
The answer is 2,440.
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Solve the division problem.
HintsTo calculate how many hours Mr. Squeaks will need to work to afford his Paris trip, you will need to divide the cost of the trip by how much he charges per hour to babysit.
The cost of the Paris trip is $\$$747. The amount Mr. Squeaks charges per hour to babysit is $\$$9. Therefore, we calculate 747$\div$9.
Step 1: Divide. How many times does 9 go into 7? 9 does not go into 7, so we find how many times it goes into 74. It goes in 8 times, so we place the number 8 above the 4.
Step 2: Multiply 9$\times$8, and place this number below the 74.
Step 3: Subtract.
SolutionTo calculate how many hours Mr. Squeaks will need to work to afford his Paris trip, you will need to divide the cost of the trip by how much he charges per hour to babysit.
747$\div$9 = 83 hours
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Solve the following division problems.
HintsFor 410$\div$5...
5 goes into 41 8 times. Write this 8 above the 1.
For 639$\div$9...
9 goes into 63 7 times. Write this 7 above the 3.
Remember the steps of long division:
1. Divide
2. Multiply
3. Subtract
4. Bring down
5. Repeat
SolutionWritten worked solution for 410$\div$5:
1. Divide 41$\div$5. 5 does not go into 4, so we find how many times it goes into 41. It goes in 8 times, so we place the number 8 above the 1 in 41.
2. Multiply 5$\times$8.
3. Subtract the product: 41-40.
4. Bring down the next digit.
5. Repeat these steps with this new number (in this case, 10).
The answer is 82.
410$\div$5 = 82
5,205$\div$5 = 1,041
639$\div$9 = 71
3,393$\div$3 = 1,131
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Solve the division problem.
HintsStep 1: Divide. How many times does 4 go into 4? 4 goes into 4 1 time. Write the 1 above the 4 in the dividend.
Step 2: Multiply 4 $\times$ 1, and place this number below the 4 in the dividend.
Step 3: Subtract.
Step 4: Bring down the 8.
Step 5: Repeat the steps twice.
Solution- Step 1: Divide. How many times does 4 go into 4? 1 time. Write this 1 above the 4.
- Step 2: Multiply. 4$\times$1 = 4. Place this 4 under the 4 in the dividend.
- Step 3: Subtract the 4s.
- Step 4: Bring down the 8.
- Step 5: Repeat the steps twice.
The answer is 121.
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Complete the following mathematical expressions.
HintsFor 4,935$\div$7:
For 3,996$\div$___ = 1,332:
3,996 divided by what equals 1,332?
One strategy to find a missing divisor is to use "guess and check." Plug in each possible divisor (3, 4, 5) until one of them gives you a quotient of 1,332.
SolutionWritten worked solution for 4,935$\div$7:
1. Divide 49$\div$7. 7 does not go into 4, so we find how many times it goes into 49. It goes in 7 times, so we place the number 7 above the 9 in 49.
2. Multiply 7$\times$7.
3. Subtract the product: 49-49.
4. Bring down the next digit.
5. Repeat these steps with this new number (in this case, 3). 7 does not go into 3, so we place a 0 above the 3 in the dividend, and continue the steps.
The answer is 705.
The answers the the questions are:
1. 248$\div$2 = 124
2. 450$\div$ 5 = 90
3. 3,996$\div$ 3 = 1,332
4. 4,935$\div$7 = 705
