Long Division Using Partial Quotients
- Long Division Using Partial Quotients – Introduction
- Long Division with Partial Quotients – Explanation
- Long Division Using Partial Quotients – Example
- Long Division Using Partial Quotients – Guided Practice
- Long Division Using Partial Quotients – Summary
- Long Division Using Partial Quotients – Frequently Asked Questions
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Basics on the topic Long Division Using Partial Quotients
Long Division Using Partial Quotients – Introduction
Long division can seem like a complex process, but it becomes more manageable when we break it down into smaller steps. The method of long division using partial quotients simplifies the task by allowing us to take it one piece at a time, making it a user-friendly approach for students learning division.
Long Division with Partial Quotients – Explanation
Long division with partial quotients is a systematic way of dividing larger numbers (the dividend) by smaller numbers (the divisor) to find the quotient and remainder. This method is similar to standard long division but focuses on estimating and subtracting multiples of the divisor from the dividend.
The partial quotients method involves dividing the dividend into parts that the divisor can easily multiply into, then subtracting these parts from the dividend step by step until what's left is too small to be divided by the divisor. The final quotient is the sum of all these partial quotients, and any remaining number becomes the remainder.
This method is particularly helpful for students who are intimidated by the traditional long division method or have difficulty with multiplication facts.
Long Division Using Partial Quotients – Example
Let's solve a division problem using partial quotients with the following example:
Example: Divide 452 by 3 using the partial quotients method.
| Step | Action | Result |
|---|---|---|
| 1. Set up the problem | Place $452$ inside the division box and $3$ outside. | |
| 2. Estimate a first partial quotient | How many times does $3$ go into $452$? Estimate $100$. | $3 \times 100 = 300$ |
| 3. Subtract this first product from $452$ | $452 - 300 = 152$ | Remaining $152$ |
| 4. Estimate a second partial quotient | $3$ goes into $152$ about $50$ times. | $3 \times 50 = 150$ |
| 5. Subtract this second product | $152 - 150 = 2$ | Remaining $2$ |
| 6. Finish with a remainder | $2$ is too small for $3$ to go into, so it remains. | Remainder $2$ |
| 7. Add the partial quotients | Sum of $100$ and $50$ gives the final quotient. | Final quotient $150$ |
The answer is 150 with a remainder of 2, which we write as 150 R2.
Long Division Using Partial Quotients – Guided Practice
Let's go through another example together:
Example: Divide 627 by 4 using the partial quotients method.
| Step | Action | Result |
|---|---|---|
| 1. Set up the problem | Place $627$ inside the division box and $4$ outside. | |
| 2. Estimate and subtract | Consider $4$ multiplying into $627$. Start with $100$. | $4 \times 100 = 400$ |
| 3. Subtract the first product from $627$ | $627 - 400 = 227$ | Remaining $227$ |
| 4. Estimate the next partial quotient | $4$ goes into $227$ about $50$ times. | $4 \times 50 = 200$ |
| 5. Subtract the second product | $227 - 200 = 27$ | Remaining $27$ |
| 6. Continue with smaller partial quotients | $4$ goes into $27$ about $6$ times. | $4 \times 6 = 24$ |
| 7. Subtract and find the remainder | $27 - 24 = 3$, which is our remainder. | Remainder $3$ |
| 8. Add the partial quotients | Sum of $100$, $50$, and $6$ gives the final quotient. | Final quotient $156$ |
Thus, 627 divided by 4 is 156 with a remainder of 3, or 156 R3.
Try some division on your own using this method!
Long Division Using Partial Quotients – Summary
Key Learnings from this Text:
- Partial quotients break down the division process into smaller, more manageable steps.
- This method requires estimation and subtraction to find the quotient.
- The final answer is the sum of the partial quotients, with any leftover amount as the remainder.
- It's important to go through the steps carefully to ensure accuracy.
Dive into other division strategies and boost your maths skills with our interactive practice problems, engaging videos and helpful worksheets on our educational platform.
Long Division Using Partial Quotients – Frequently Asked Questions
Transcript Long Division Using Partial Quotients
The victory in the Great Beetle War would not have been possible without the help of hometown heroes like Airman Squeaks, who used the strategy of chunking in division to help deliver groups of supplies behind enemy lines. One method for solving long division problems is to use chunking. This method divides a problem into smaller, more manageable parts using multiples of ten or simple numbers. We'll use Airman Squeaks' supply deliveries to demonstrate how to divide three and four digit numbers. He has four hundred and thirty-two corn kernels to take to six battallions. We need to calculate how many kernels would be given to each. We set up the problem exactly as we would with the traditional long division method. First, estimate how many times six goes into four hundred and thirty-two. Ask yourself "what multiple of ten can we multiply by six to get close to this number?" Six times seventy equals four hundred and twenty. We have found seventy lots of six, so seventy goes here. Six times seventy equals four hundred and twenty so we write this below the dividend. Four hundred and thirty two subtract four hundred and twenty equals twelve. Now ask yourself "how many groups of six are in twelve?" Two sixes are twelve, so we write two here, and twelve below. We subtract again and get zero. We add the seventy and two together, which equals seventy-two. Airman Squeaks will deliever seventy-two corn kernels to each battalion. He must also ensure that the troops are adequately supplied with insect repellent. He has seven hundred and sixty-five cans that need to be delivered to five different locations. We set up the problem like this. What multiple of ten can we multiply five by to get close to seven hundred and sixty-five? Although there are many multiples we could choose, here we can say five times one hundred equals five hundred. What do we get when we subtract five hundred from seven hundred and sixty-five? Two hundred and sixty-five. What multiple of ten can we multiply five by to get close to two hundred and sixty-five? Five times fifty equals two hundred and fifty. Subtract again. What is left? Fifteen. How many groups of five are in fifteen? Three. Three times five is fifteen. How many lots of five are in seven hundred and sixty five altogther? One hundred and fifty-three. Finally, Airman Squeaks had to deliver two thousand, three hundred and sixty-seven sticks to build three barracks. How many sticks would each one receive? Pause the video and solve this one on your own, then press play when you are ready to check your answer. Although there are many ways to begin multiplying this problem by using different multiples, we chose the largest number that would get us the closest. Three times seven hundred is two thousand one hundred. After we subtract, we have two hundred and sixty-seven. Three times eighty is two hundred and forty. We are left with twenty-seven. And three times nine equals twenty-seven. Altogether we have found seven hundred and eighty nine lots of three are in the dividend. While our hero returns from his daring mission, let's review. Remember, another method for solving long division problems is to use chunking. This method divides a problem into smaller, more manageable parts using multiples of ten or simple numbers. Using multiples of ten or other simple numbers, we estimate how many times the divisor goes into the dividend. Airman Harry Squeaks has returned from a daring mission deep in enemy territory after weeks of anticipation. Welcome home Airman Squeaks!
Long Division Using Partial Quotients exercise
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How many first aid kits should go to each squad?
HintsSubtract the 500 from 985. What's left?
What has been multiplied by 5 to give 400?
Place this answer to underneath the $\times$ 100.
The next multiple is 10.
What is 5 $\times$ 10?
Put this under 85.
What multiple of 5 is needed to make 35?
What is the total of all the chunks?
SolutionThe 1st step in the calculation was 5 $\times$ 100. So you need to subtract 500 from 985. This leaves 485.
Next, you think about what multiple was used to make 400. 5 $\times$ 80 = 400 so 80 goes in the next gap.
After subtracting, you're left with 85, and the next multiple is 10. 5 $\times$ 10 = 50, so you put 50 underneath.
Subtracting 50 leaves 35 and 5 $\times$ 7 = 35, so $\times$ 7 is the next one to fill in.
Finally, subtracting leaves 0, so you can now add all your chunks, giving 197 as the final solution.
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How many food packets should go to each troop?
HintsFirst, fill in the divisor in the right place.
You are dividing by 7 so where does that go?
Think about your 7 times table and multiply each one by 10.
70, 140, 210, 280 etc.
The first dividend is 560, so how many sevens are needed to make 560?
Subtract 560 from 623, how much is left?
How many sevens are needed to make your next dividend?
9 $\times$ 7 = 63, so subtracting 63 leaves you with 0.
Now you can add all of your chunks together for the final answer.
Solution- 7 $\times$ 80 = 560, so 80 is the first chunk.
- 623 - 560 = 63, 63 is your next dividend.
- 7 $\times$ 9 = 63.
- 63 - 63 = 0, so now we can add together all of the chunks.
- 80 + 9 = 89
- 623 $\div$ 7 = 89
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Work out how many tablets will go to each batallion.
HintsYou need to work out 1794 $\div$ 23. Set out the problem like the others. Think of a multiple of 10 that you can multiply by 23. A good starting place would be 23 $\times$ 50.
Subtract this amount and then think of another multiple of 23.
Maybe 23 $\times$ 20. How many are left? How many 23's do you need now?
If you're left with 184, then you could do 23 $\times$ 8 = 184 as a final multiplication. Subtracting this leaves 0, so now what's the final step to get to your answer?
SolutionOne method of getting to the answer would be as follows:
23 $\times$ 50 = 1150
subtracting leaves 644
23 $\times$ 20 = 460
subtracting leaves 184
23 $\times$ 8 = 184
Adding together all the chunks gives an answer of 78.
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How many bottles will Airman Squeaks be delivering each day?
HintsLet's look at 228 $\div$ 6 first. Try starting with 6 $\times$ 30 = 180 Now subtract and see what's left. How many 6's do you need?
To do 441 $\div$ 3, start with 3 $\times$ 100.
1272 $\div$ 8
Make the 1st multiple as easy as possible. 8 $\times$ 100 = 800, so this would work nicely.
696 $\div$ 12
Double digits work in the same way. Think of a multiple of 10 that you can multiply by 12, to get close to 696.
Try 12 $\times$ 50 to start.
SolutionOn Monday, he delivered 38 bottles to each of the 6 troops.
On Tuesday, he delivered 147 bottles to each of the 3 troops.
On Wednesday, he delivered 159 bottles to each of the 8 troops.
On Thursday, he delivered 58 bottles to each of the 12 troops.
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How many pairs of socks need to be delivered to each battallion?
HintsYou can start with 9 $\times$ 100, so the first step is to put 100 on the right. Now 9 $\times$ 100 = 900, so subtract 900 from 1503.
Repeat the process until your subtraction gives you 0.
9 $\times$ 60 = 540, so put 60 on the right and subtract 540.
Finally, 9 $\times$ 7 = 63, and subtracting 63 gives 0.
You can now put the last step in place, adding up all your chunks.
SolutionThe first step is to think of the biggest multiple of 10 that you can multiply by 9 to get close to 1503. In this case start with 100 $\times$ 9, so 100 goes to the right.
100 $\times$ 9 = 900, so 900 goes underneath. Subtracting leaves you with 603.
Next, think of a multiple of 10 that you can multiply by 9 to get close to 603. In this case 60 $\times$ 9 = 540, so 60 goes to the right and 540 underneath.
Subtracting leaves you with 63.
Now 9 $\times$ 7 = 63, so 7 goes on the right, and 63 underneath.
Subtracting leaves you with 0.
Finally, you can add up all of your chunks to get your final answer, 167.
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Now, the firestarters need to be shared out equally.
HintsFirst, you need to work out how many packs of firestarters will go to each of the 7 troops. Do 8330 $\div$ 7
Now you need to divide your answer by 85 to work out how many packs of firestarters each soldier in the troop receives.
SolutionFirst, you need to know 8330 $\div$ 7.
You could start with 7 $\times$ 1000 = 7000.
Subtracting 7000 leaves 1330.
Now 7 $\times$ 100 = 700.
Subtracting leaves 630.
7 $\times$ 90 = 630.
Subtracting gives 0, and 1000 + 100 + 90 = 1190 packs of firestarters to each troop.
Now, you can work out 1190 $\div$ 85.
85 $\times$ 10 = 850.
Subtracting leaves 340.
85 $\times$ 4 = 340, and subtracting 340 leaves 0.
10 + 4 = 14, so each soldier gets 14 packs of firestarters.
