Long division facts for kids

Long division is a special way to divide big numbers. It uses a mix of multiplication and subtraction steps. This method is often taught in schools because it helps you break down a tough division problem into smaller, easier parts. You can even use long division for polynomials, which are types of math expressions.

How Long Division Works

When you divide numbers, you usually have three main parts:

• The dividend is the total number you want to divide.
• The divisor is the number you are dividing by.
• The quotient is your answer.

Long division is like a step-by-step recipe, also called an algorithm. It helps you find the answer by following clear instructions:

• First, you look at the dividend one digit at a time, starting from the left.
• Then, you divide that part of the dividend by the divisor.
• If there's a leftover (a remainder), you carry it over to the next digit.
• If the part of the dividend is too small to divide by the divisor, you carry that number over instead.
• You keep doing this until you've used all the digits in the dividend.
• Finally, you put all your answers (quotients) together to get the final result. Any leftover remainders become the decimal part of your answer.

Examples of Long Division

Basic Division

Let's try to divide 780 by 4. We'll break 780 into its digits: 7, 8, and 0. Then we divide each by 4.

• 7 divided by 4 is 1 with a remainder of 3. We carry the 3.
• Now we have 38 divided by 4. That's 9 with a remainder of 2. We carry the 2.
• Next, 20 divided by 4 is 5 with no remainder (0). We're done!

So, 780 divided by 4 equals 195.

More Complex Division

Let's try dividing 468 by 12. This is a bit trickier because the divisor is a two-digit number.

• 4 divided by 12 is 0. Since 4 is smaller than 12, we carry the 4.
• Now we have 46 divided by 12. That's 3 with a remainder of 10. We carry the 10.
• Next, 108 divided by 12 is 9 with no remainder (0). We've reached the end.

So, 468 divided by 12 equals 39.

Getting Decimal Answers

Sometimes, numbers don't divide perfectly. Let's divide 123 by 8.

• 1 divided by 8 is 0. We carry the 1.
• Now we have 12 divided by 8. That's 1 with a remainder of 4. We carry the 4.
• Next, 43 divided by 8 is 5 with a remainder of 3.

We have a remainder of 3. This means 123 divided by 8 is 15 with a remainder of 3. To get a decimal answer, we can think of 3/8. So, 123 divided by 8 is 15.375.

Related pages

• Chunking, a different type of long division done in the UK.
• Divisor, a number which evenly divides another number
• Short division, a faster version of long division done with smaller numbers.
• Synthetic division, an alternate algorithm for polynomial long division

Images for kids

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  An example of long division performed without a calculator.

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  Animated example of multi-digit long division

See also

In Spanish: División larga para niños