How to Do Long Division
- Introduction
- What is Long Division?
- Parts of Long Division
- How to do Long Division
- Dividing a Whole Number by a Whole Number
- Dividing Decimals by Whole Numbers
- Dividing Decimals by Decimal Numbers
- Solved Examples
- Practice Problems
- Frequently Asked Questions
Introduction
We normally use long division to divide large numbers. We use a series of steps in long division to find the quotient and remainder. It is a systematic process where we repeat the same sequence of steps till we find the quotient and remainder. This method is quite helpful especially when we are dealing with dividing large numbers and cannot find answers through mental math.
What is Long Division?
Long division is a mathematical operation used to divide numbers with multiple digits. It's a methodical process where the divisor divides the dividend to find the quotient and remainder. This technique allows us to tackle complex division problems step by step, making it easier to manage large numerical calculations. Mastering long division is essential for various mathematical tasks and real-life applications where precise division is required.
Parts of Long Division
How to do Long Division
Dividing a Whole Number by a Whole Number
Let's consider the division problem: `245 ÷ 5`.
To solve this using long division:
- First, we divide `2` (the first digit of `245`) by `5`, which gives us `0` with a remainder of `2`.
- Next, we bring down the next digit, `4`, and write it beside `2`, to make the number `24`. We then divide `24` by `5`, which gives us `4` with no remainder.
- Finally, we bring down the last digit, `5`, making the number `5`. We divide `5` by `5`, which gives us `1` with no remainder.
So, `245 ÷ 5` equals `49`, with no remainder.
Dividing Decimals by Whole Numbers
Example: Divide `3.5` by `7`.
Solution:
Set up the division:
Write `3.5` inside the long division symbol (dividend) and `7` outside (divisor).
Ignore the decimal:
Since the dividend is a decimal, we can ignore the decimal for now and treat `3.5` as a whole number.
Divide:
Divide the whole number `35` by `7`.
Adjust the decimal:
After dividing, we place the decimal point in the quotient directly above its position in the dividend. Here, it remains in the tenth place.
Finalize:
The quotient obtained represents the result of the division. In this case, `3.5 ÷ 7 = 0.5`.
Conclude:
Therefore, when dividing `3.5` by `7`, the result is `0.5` with no remainder.
Dividing Decimal by a Decimal Number
Dividing decimals using long division follows a similar process to dividing whole numbers, with a slight adjustment for decimal placement. Here's how to do it with an example:
Example: Divide `4.56` by `0.6`.
Solution:
Set up the division:
Write `4.56` inside the long division symbol (dividend) and `0.6` outside (divisor).
Remove the decimal from the divisor:
Since the divisor is a decimal, move the decimal point to the right to make the divisor a whole number. Do the same for the dividend to keep the decimal placement consistent. So, we multiply both by `10` to eliminate the decimal in the divisor.
Divide:
Divide the dividend which is a decimal value by the whole number divisor.
Bring down:
Bring down the next digit of the dividend (if any) next to the result obtained from the division step.
Repeat:
Repeat steps `3` and `4` until there are no more digits to bring down.
Adjust the decimal:
After dividing, we place the decimal point in the quotient directly above its position in the dividend. Here, it remains in the tenth place.
Finalize:
Once all digits have been processed, the quotient obtained represents the result of the division. If there is a remainder, it can be expressed as a fraction over the divisor or as a decimal. In this case, the quotient is `7.6`.
Conclusion:
Therefore, `4.56 ÷ 0.6 = 7.6`
Solved Examples
Example `1`. A farmer has `150` apples. He wants to pack them into boxes, with each box containing `8` apples. How many boxes can the farmer fill, and how many apples will be left?
Solution:
First, set up the division statement: `150 ÷ 8`.
Next, perform the long division:
Therefore, the farmer can fill `18` boxes, with `8` apples in each box. There will be `6` apples left over.
Example `2`. Mary has `$12.25`. She wants to divide it equally among her `5` friends. How much money will each friend receive?
Solution:
First, set up the division statement: `12.25 ÷ 5`.
Next, perform the long division:
Hence, each friend will receive `$2.45`.
Example `3`. A storage tank is filled with `457.5` gallons of water. If each bucket can hold `35` gallons of water, how many buckets will be needed to store the tank water?
Solution:
First, set up the division statement: `457.5 ÷ 35`.
Next, perform the long division:
The long division yields a quotient of `13` with a remainder.
It will take `14` buckets to empty the pool. You can imagine it as `13` buckets being completely filled and the `14`th bucket being partially filled.
Example `4`. A bakery sells `24` cakes, and each cake weighs `1.2` kilograms. How many boxes are needed if each box can hold exactly `6` cakes?
Solution:
First, set up the division statement: `24 ÷ 4`.
Next, perform the long division:
`24` is completely divisible by `6` with no remainder. So exactly `4` boxes are needed.
Example `5`. Mariana baked `308` brownies for a birthday order. She wants to put them on display. If each tray can hold `12` brownies, how many such trays would Mariana need to put all her brownies on display?
Solution:
First, set up the division statement: `308 ÷ 12`.
Next, perform the long division:
The long division yields a quotient of `25` with a remainder `8`. So, Mariana would need a minimum of `26` trays to put all her brownies on display.
Practice Problems
Q`1`. Divide `675` by `25`.
- `27`
- `30`
- `25`
- `45`
Answer: a
Q`2`. Divide `5.4` by `3`.
- `1.6`
- `1.8`
- `1.2`
- `1.4`
Answer: b
Q`3`. Divide `7.28` by `0.4`.
- `17.2`
- `18.2`
- `18.8`
- `16.4`
Answer: c
Q`4`. What is the quotient and remainder when we divide `47` by `6`?
- `7` with remainder `5`
- `8` with remainder `7`
- `8` with remainder `5`
- `7` with remainder `7`
Answer: a
Q`5`. A gardener has `48` flower pots. If she wants to arrange them in rows with `6` pots in each row, how many rows will she have?
- `8`
- `6`
- `7`
- `9`
Answer: a
Frequently Asked Questions
Q`1`. What is a long division?
Answer: Long division is a method used in mathematics to divide large numbers into smaller parts. It involves a series of steps to find the quotient and remainder.
Q`2`. How do I perform long division?
Answer: First, write the dividend (the number being divided) inside the division symbol and the divisor (the number by which you are dividing) outside to perform long division. Then, follow a series of steps including dividing, multiplying, subtracting, and bringing down digits until you find the quotient and remainder.
Q`3`. When should I use long division?
Answer: Long division is used when you need to divide numbers where the divisor is a multi-digit number. It's particularly useful for dividing larger numbers or numbers with decimals.
Q`4`. What if there is a remainder in a long division?
Answer: If there is a remainder after completing the long division process, it can be expressed separately as a remainder or as a fraction over the divisor. This means that the dividend is not completely divisible by the divisor. We can also say that the divisor is not a factor in the dividend if it leaves the remainder after long division.