What’s 847 ÷ 4?
Even adults might reach for the calculator when they have to divide big numbers like this one.
But guess what?
We don’t need it at all.
With the long division method, we can break down even the most difficult numbers just by following a clear set of steps!
Whether you’re just starting to learn about long division, prepping for an exam, or need a refresher, this guide is for you.
Read on to find simple definitions, easy-to-follow instructions, solved examples, and practice exercises to help you master long division!
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Before we jump into long division, let’s take a moment to revisit what division means on its own.
Simply put, division is counting how many of "these" are inside of "that."
For example, if we take a division like 15 ÷ 5, what we're actually doing is figuring out how many whole 5s are inside 15.
If we count 5, 10, 15, we see that three whole 5s fit into 15.
So, 15 ÷ 5 = 3.
That’s division at its core.
Long division is a process, typically used for bigger numbers, that breaks division down into simpler steps to follow.
The components of long division are the same as those in regular division.
When numbers divide evenly, like 15 ÷ 5 = 3, we have three key components:
When numbers don't divide evenly, like 16 ÷ 5 = 3 with a remainder of 1, we have four main components:
In long division, we use the long division symbol (⟌) instead of the standard division sign (÷). The dividend is placed inside the symbol, while the divisor is written outside.
In many cases, we can solve a division task using mental math.
Let’s say we want to divide 12 by 2.
Start with a simple question: How many 2s are there inside of 12?
Picture 12 lemons and imagine grouping them into sets of 2. You’d get 2, 4, 6, 8, 10, 12—counting up by twos. That’s 6 groups. So, there are 6 twos inside of 12.
Now, compare that to division: 12 ÷ 2. Dividing 12 by 2 is just asking, How many times does 2 fit into 12?
The answer is 6, which matches our counting.
What about 10 ÷ 3?
How many 3s are inside 10?
Imagine 10 lemons and group them into sets of 3. Counting up by threes: 3, 6, 9. That’s three full groups, which makes 9. But 10 is one more than 9, so there's 1 left over.
Now, compare that to division: 10 ÷ 3 asks, How many times does 3 fit into 10? The answer is 3 with a remainder of 1.
But what if we need to solve 89 ÷ 3 or 743 ÷ 3?
That’s where long division helps!
To do long division, we break it down into manageable steps:
We repeat this process until the division is complete.
For now, let’s just remember the order—in the next section, we’ll go through each step and show you how it works!
To understand the long division process, let’s start with a basic example: a two-digit number divided by a one-digit number.
Say we want to divide 43 by 7.
What we do first is place 43 (the dividend) under the division symbol and 7 (the divisor) outside to the left like so:
Now, we can follow the steps.
Step 1: Divide
Check how many whole 7s go into 43 without going over.
Since 7 × 6 = 42, we see that 6 whole 7s fit into 43.
Write 6 on top of the division symbol, right above 3.
Step 2: Multiply & Subtract
Find the product of 7 and 6.
7 x 6 = 42
Write the result (42) below 43 and subtract it from 43.
43 - 42 = 1
Write the result (1) below.
The difference is the remainder, which must be less than the divisor (otherwise you didn’t divide enough) and can be written as R1 or as a fraction where we put the remainder over the divisor, \(\displaystyle\frac{1}{7}\).
We can write the final result as:
43 ÷ 7 = 6 R1 or \(\displaystyle6\frac{1}{7}\).
Now that we understand how long division works, let’s explore more examples and handle different scenarios.
Now, let’s look at a case where we divide a three-digit number by a one-digit number.
Say we want to divide 157 by 4.
Before we start to divide, we place 157 (the dividend) under the division symbol and 4 (the divisor) outside to the left.
Then, we follow the steps:
Step 1: Divide
Check how many whole 4s are inside of 1. Since 4 can’t fit into 1, we move to the next digit.
How many whole 4s are inside of 15?
Since 4 × 3 = 12, we know that 4 fits into 15 three times.
Write 3 in the quotient, right above 5 in 157.
Step 2: Multiply & Subtract
Find the product of 4 and 3.
4 x 3 = 12
Write the result (12) below 15 and subtract it from 15.
15 - 12 = 3
Write the result (3) below.
Step 3: Bring Down
Now bring down 7, creating a new number with what was left from the previous step.
Step 4: Divide Again
Check how many whole 4s are inside of 37.
Since 4 × 9 = 36, we know that 4 fits into 37 nine times.
Write 9 in the quotient, right above 7 in 157.
Step 5: Multiply & Subtract
Find the product of 4 and 9.
4 x 9 = 36
Write the result (36) below 37 and subtract it from 37.
37 - 36 = 1
Write the result (1) below.
The difference is the remainder, which must be less than the divisor and can be written as R1 or as a fraction where we put the remainder over the divisor, \(\displaystyle\frac{1}{4}\).
We can write the final result as:
157 ÷ 4 = 39 R1 or \(39\displaystyle\frac{1}{4}\).
Long division isn’t just for whole numbers. It can also be used in other cases, like:
Learn and master all types of long division with top-rated math tutors near you.
Let’s practice what we’ve learned with a few more examples!
Let’s use the long division method to solve 95 ÷ 7.
Before we start dividing, we write 95 (the dividend) under the division symbol and 7 (the divisor) outside to the left.
Step 1: Divide
Check how many whole 7s are inside of 9.
Since 7 × 1 = 7, we know that 7 fits into 9 one time.
Write 1 in the quotient, right above 9 in 95.
Step 2: Multiply & Subtract
Find the product of 7 and 1.
7 x 1 = 7
Write the result (7) below 9 and subtract it from 9.
9 - 7 = 2
Write the result (2) below.
Step 3: Bring Down
Now, bring down 5, creating a new number with what was left from the previous step.
Step 4: Divide Again
Check how many whole 7s are inside of 25.
Since 7 × 3 = 21, we see that three whole 7s fit into 25.
Write 3 above on top of the division symbol, right above 5 in 95.
Step 5: Multiply & Subtract
Find the product of 7 and 3.
7 x 3 = 21
Write the result (21) below 25 and subtract it from 25.
25 - 21 = 4
Write the result (4) below.
Since there are no more digits to bring down, this is our remainder. The remainder must be less than the divisor and can be written as R3 or as a fraction where we put the remainder over the divisor, \(\displaystyle\frac{4}{7}\).
We can write the final result as:
95 ÷ 7 = 13 R4 or \(13\displaystyle\frac{4}{7}\).
Next, let's solve 437 ÷ 6.
Before we begin, we write 437 (the dividend) under the division symbol and 6 (the divisor) outside to the left.
Step 1: Divide
Find how many whole 6s fit into 4. Since 6 can't fit into 4, we move to the next digit.
How many whole 6s are inside of 43?
Since 6 × 7 = 42, we know that 6 fits into 43 seven times.
Write 7 in the quotient, right above 3 in 437.
Step 2: Multiply & Subtract
Find the product of 6 and 7.
6 x 7 = 42
Write the result (42) below 43 and subtract it from 43.
43 - 42 = 1
Write the result (1) below.
Step 3: Bring Down
Now, bring down 7, creating a new number with what was left from the previous step.
Step 4: Divide Again
Check how many whole 6s are inside of 17.
Since 6 × 2 = 12, we see that 2 whole 6s fit into 17.
Write 2 on top of the division symbol, right above 7 in 437.
Step 5: Multiply & Subtract Again
Find the product of 6 and 2.
6 x 2 = 12
Write the result (12) below 17 and subtract it from 17.
17 - 12 = 5
Write the result (5) below.
Since there are no more digits to bring down, this is our remainder. The remainder must be less than the divisor and can be written as R5 or as a fraction where we put the remainder over the divisor \(\displaystyle\frac{5}{6}\).
We can write the final result as:
437 ÷ 6 = 72 R5 or \(72\displaystyle\frac{5}{6}\).
Now it’s time to put your long division skills into action! Below are a few tasks to challenge what you've learned.
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Learning long division comes with its challenges. Here are some common questions we hear from students at Mathnasium, along with answers to guide you through!
Students typically learn about long division in 4th or 5th grade, depending on the curriculum.
They usually start with long division without remainders in 4th grade. By 5th grade, they tackle long division with remainders and decimals.
Long division with polynomials is introduced in middle school, around 7th or 8th grade, as students advance in algebra.
If the divisor is larger than the dividend, you can add a decimal point with a 0 and continue dividing.
Yes! Long division can be used for negative numbers. Just remember that dividing a negative by a positive will give a negative quotient, while dividing two negatives results in a positive quotient.
Yes, we can divide decimals! Think about something like 5.6 ÷ 0.8.
Applying a bit of proportional reasoning tells us that 5.6 ÷ 0.8 is the same as 56 ÷ 8.
Proportional reasoning also helps you understand how long division with decimals works.
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