Long Division - GCSE Maths Definition

Definition

Long division is a method for dividing large numbers by breaking the calculation into smaller, manageable steps.

Explanation

Long division is a method that allows us to tackle big division problems. Think of it as your mathematical superpower for handling numbers that are too tricky for mental maths.

The beauty of long division is that it breaks everything down into bite-sized chunks. Instead of trying to work out 756 ÷ 12 in your head, you solve it step by step.

You'll use long division throughout GCSE Maths. It can be used for converting fractions to decimals. You may need it on the non-calculator paper for finding the mean average.

The method follows a repeated process: divide, multiply, subtract, “bring down”
You repeat these four steps until you've worked through the whole number, see the example below.

Long division has been around for centuries. It's the same method your grandparents learned at school. That's because it works brilliantly and gives you the exact answer every time.

Don't worry if it feels clunky at first. Everyone finds long division tricky initially. With a bit of practice, the steps become automatic.

The key is setting everything out neatly - aligning digits makes the process easier and is less likely to lead to mistakes.

You can use long division for any division problem, but it's most useful when the numbers are too big for quick mental calculations, or when short division doesn’t help.

Example

Question: Calculate 847 ÷ 23 using long division.

Solution:

Let's set this up properly:

    ___
23 ) 847

We can quickly see that 23 will not divide into 8, so we consider 84 instead.

Step 1: How many times does 23 go into 84?
Count up in 23’s, without going past 84.
23
(23 x 2 =) 46
(23 × 3 =) = 69
(23 × 4 =) 92 (too big)
So 23 goes into 84 exactly 3 times. We do not need to consider the remainder.

Write 3 above the 4:

     3__
23 ) 847
      69
     ---
     15

Step 2: Multiply and subtract 3 × 23 = 69 84 - 69 = 15

Step 3: Bring down the next digit Bring down the 7 to make 157:

     3__
23 ) 847
     69
     ---
     157

Step 4: How many times does 23 go into 157? 23 × 6 = 138 (good) 23 × 7 = 161 (too big) So 23 goes into 157 exactly 6 times.

Write 6 next to the 3:

     36_
23 ) 847
     69
     ---
     157
     138
     ---
      19

Step 5: Final calculation 157 - 138 = 19

Since 19 is smaller than 23, we can't divide any further.

Answer: 847 ÷ 23 = 36 remainder 19

We wouldn’t write “remainder” at GCSE, we would write the answer as a mixed number

Or as a mixed number:

Common mistakes (and how to avoid them)

Mistake 1: Getting the layout muddled up

Students often write numbers in the wrong places or forget to line up their columns properly. This makes the whole calculation go wrong.

Your dividend (the number being divided) goes inside the division bracket. Your divisor (the number you're dividing by) goes outside on the left.

How to avoid this: Always set up your long division box carefully before you start. Draw neat lines and make sure your columns are straight. Take an extra few seconds to get this right.

Mistake 2: Making times table errors

Long division relies heavily on multiplication. If you get your times tables wrong, your whole answer will be incorrect.

How to avoid this: Brush up on your times tables regularly. When you're unsure, write out the times table (carefully) to double-check. For example, if you think 7 × 9 is 63 (it does!), but you’re not sure, count up in 7’s: 7, 14, 21, 28, 35, 42, 49, 56, 63. (You could count up in 9’s).

Mistake 3: Forgetting to “bring down” digits

Students sometimes miss bringing down the next digit, which completely throws off their calculation.

How to avoid this: Make this step really obvious in your working. Draw an arrow showing which digit you're bringing down. Say it out loud: "bring down the 7."

Mistake 4: Stopping too early or going too far

Some students stop when they hit a remainder, even when the question asks for a decimal answer. Others keep going when they should stop.

How to avoid this: Read the question carefully. If it asks for the exact answer, you might need to continue with decimal places. If it asks for a whole number answer, stop when you get a remainder.

Mistake 5: Misplacing the decimal point

When dividing decimal numbers, students often put the decimal point in the wrong place in their answer.

How to avoid this: Mark where the decimal point should go before you start calculating. Remember: the decimal point in your answer goes directly above the decimal point in the dividend.

Frequently asked questions

When should I use long division instead of a calculator?

Long division is brilliant when calculators aren't allowed or when you need to show your working clearly. It's also useful for understanding exactly how division works.

What if my division doesn't work out exactly?

That's totally normal. Most division problems give you a remainder. You can leave your answer as "quotient remainder something" or convert it to a decimal by adding decimal places and continuing the division.

Can I use long division with decimal numbers?

Absolutely. The method works exactly the same way. Just keep track of where your decimal points go. The decimal point in your answer sits directly above the decimal point in the number you're dividing.

What's the difference between long division and short division?

Short division is quicker and is more appropriate when you're dividing by single-digit numbers. Long division works for any size divisor, which makes it much more powerful for bigger problems.

Related GCSE Mathematics glossaries

Dividend

Mixed Numbers

Decimal