Long Division- Multi Digits by 1 Digit
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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 maths 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 (bus stop method) 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 organise dividend, divisor and quotient in a specific way; Take a look at the picture below. 
When using the bus stop method, see how many times the divisor goes into each digit in the dividend.
| Step # | Explanation |
|---|---|
| 1 | How many times does 4 goes in to 1? |
| 2 | If it is 0, carry the 1 infront of the next digit. |
| 3 | How many times does 4 go into 12? |
| 4 | Write this number on the top. |
| 5 | How many times does 4 go into 8? |
| 6 | Write this number on the top bar. |
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. The dividend is 363, we will place this first and the divisor is three (3) so we will place this in front of the dividend. Now, we are going to show all the steps one by one:
Step one: How many times does the divisor (3) fit into the first number in the dividend (3).
Three goes into three once, so we write the one above the ones place in the quotient.
Step two: How many times does the divisor (3) fit into the second number in the dividend (6)?
Step three: How many times does the divisor (3) fit into the third number in the dividend (3)?
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 # | Explanation |
|---|---|
| 1 | How many times does 3 goes in to 1? |
| 2 | If it is 0, carry the 1 infront of the next digit. |
| 3 | How many times does 3 go into 12? |
| 4 | Write this number on the top. |
| 5 | How many times does 3 go into 6? |
| 6 | Write this number on the top bar. |
So we can state that 126 divided by 3 equals 42.
Long Division Summary
Long division is a way to organise the calculation of a division problem.
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 it's really popular! Mr. Squeaks wants to work out exactly how much he has been making! We can help work out how much he earned through babysitting by using long division - multi-digit by one digit. In long division, we organise the dividend (how much we are dividing), divisor (how much we are dividing between) and quotient (the answer),like this. In long division, we find the quotient or answer by following a sequence of steps. The Field Family hired Mr. Squeaks to watch their children three times and paid him three hundred and sixty-three pounds in total. To find out how much he made for each babysitting session, we can do a division calculation. To do this, we will divide three-hundred and-sixty-three by three. Put the dividend, three hundred and sixty-three here and the divisor, three, here. We will see how many threes are in three hundred and sixty three by working through each digit one at a time. The first digit in the dividend is three, so we see how many threes go into three. Three goes into three once. So we write one above the three here. Now let's move on to the next digit, which is six. How many times does three go into six? Twice, so we write two above the six here. The last digit we need to check is three. How many times does three go into three? Three goes into three once, so we write one here. We have seen how many times three goes into each digit and written the quotient above. Our answer is one hundred and twenty one. So Mr Squeaks was paid one hundred and twenty one pounds per babysitting session. The Vole's hired Mr. Squeaks to babysit five times and paid him two hundred and forty-five pounds in total. We can divide two hundred and forty-five by five to see how much he earned each time. We need to see how many times five goes into each digit. What is our first step? Our first step is to see how many fives are in two. What do you notice when you think about how many times five goes into two? It doesn't work, as five is bigger than two. So we need to look at the first two digits together. How many times does five go into twenty-four? There are four fives in twenty-four because four times five is twenty. So we write four here. As we reached twenty and we were seeing how many fives were in twenty four, we carry the remaining four across to the next digit. We write the four here. Now we need to see how many fives are in forty five. There are nine fives in forty-five, so we write nine here. Our answer is forty-nine. The Vole's paid Mr. Squeaks forty- nine pounds for each babysitting session. Remember, long division is a way to organise the calculation of a division problem. To divide we follow these steps: Set up your division calculation with the dividend here and you divisor here. One digit at a time, see how many times your divisor goes into the dividend. If the divisor does not fit into the first digit, look at the first two digits together. Remember to carry across any remainders after seeing how many times the divisor has fit into the dividend. 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.
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 four times. Write the 4 above the 8 like this. Next, how many times does 2 go into the next digit, 4?
Solution- Step 1: Divide. How many times does 2 go into 8? Four times. Write this 4 above the 8.
- Step 2: How many times does 2 go into 4? Two times. Write this 2 above the 4.
- Step 3: How many times does 2 go into 2? One time. Write this 1 above the 2.
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 two times.
Next, how many times does 2 go into 8?
2 goes into 8 four times, so write 4 on the top. What is the next step?
Solution- Step 1: Divide. How many times does 2 go into 4? Two times. Write this 2 above the 4.
- Step 2: How many times does 2 go into 8? Four times. Write this 4 above the 8.
- Step 3: How many times does 2 go into 8? Four times. Write this 4 above the 8.
- Step 4: How many times does 2 go into 0? Zero times. Write this 0 above the 0.
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$9.
Step 1: Divide. How many times does 9 go into 7? 9 does not go into 7, so we find how many times it goes into 74. It goes in 8 times with 2 remaining, so we place the number 8 above the 4 and carry the 2 in front of the 7.
.
SolutionTo calculate how many hours Mr. Squeaks will need to work to afford his Paris trip, you will need to divide the cost of the trip by how much he charges per hour to babysit.
747$\div$9 = 83 hours
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Solve the following division problems.
HintsFor 410$\div$5...
5 goes into 41 eight times. Write this 8 above the 1.
For 639$\div$9...
9 goes into 63 seven times. Write this 7 above the 3.
SolutionWritten worked solution for 410$\div$5:
1. Divide 410$\div$5. 5 does not go into 4, so we find how many times it goes into 41. It goes in 8 times remainder 1, so we place the number 8 above the 1 in 41 and carry the 1 in front of the 0.
2. How many times does 5 go into 10? Twice. So we write 2 above the 0.
The answer is 82.
410$\div$5 = 82
5,205$\div$5 = 1,041
639$\div$9 = 71
3,393$\div$3 = 1,131
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Solve the division problem.
HintsStep 1: Divide. How many times does 4 go into 4? 4 goes into 4 one time. Write the 1 above the 4 in the dividend.
Next, how many times does 4 go into 8?
4 goes into 8 two times. Write the 2 above the 8 like this.
Solution- Step 1: Divide. How many times does 4 go into 4? One time. Write this 1 above the 4.
- Step 2: How many times does 4 go into 8? Two times. Write this 2 above the 8.
- Step 3: How many times does 4 go into 4? One time. Write this 1 above the 4.
The answer is 121.
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Complete the following mathematical expressions.
HintsFor 4,935$\div$7: 7 does not go into 4, so we see how many times it goes into 49. 7 goes into 49 seven times. How many time does 7 go into 3? Zero times.
For 3,996$\div$___ = 1,332:
3,996 divided by what equals 1,332?
One strategy to find a missing divisor is to use "guess and check". Try each possible divisor (3, 4, 5) until one of them gives you a quotient of 1,332.
Another strategy is to use the inverse. Since multiplication is the inverse of division we can see, 1,332 x what = 3,996.
SolutionWritten worked solution for 4,935$\div$7:
Step 1. Divide 49$\div$7. 7 does not go into 4, so we find how many times it goes into 49. It goes in seven times, so we place the number 7 above the 9 in 49.
Step 2. How many times does 7 go into 3? It goes in zero times so we place 0 above the 3 and carry the 3 in front of the 5.
Step 3. How many times does 7 go into 35? Five times, so we write 5 above the 5.
The answer is 705.
The answers the the questions are:
1. 248$\div$2 = 124
2. 450$\div$ 5 = 90
3. 3,996$\div$ 3 = 1,332
4. 4,935$\div$7 = 705
