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Remainders, Long Division by Picture and Example

Learn how to work with remainders with our examples and pictures.

What is a remainder?


The amount left over when you divide two numbers.

For instance, let's examine $$ 11 \div 2 $$.

When you divide 11 by 2, you end up with 1 'left over' as shown in the worked out long division below:

picture of remainder with work shown

Examples

Example 1

Let's examine $$ 7 \div 2$$.

loading Logarithm equation
Example 2

Let's examine $$ 11 \div 4$$.

loading Logarithm equation
Example 3

Let's examine $$ 11 \div 3$$.

loading Logarithm equation
Example 4

Let's examine $$ 14 \div 5$$.

loading Logarithm equation

Practice Problems

Find the remainder for each problem below.

Problem 1

$$ 13 \div 5 $$

As you can see in the picture below, the remainder is 3.

picture of remainder of 3 boxes
Problem 2

$$ 11 \div 5 $$

As you can see in the picture below, the remainder is 1.

picture of remainder of 1
Problem 3

$$ 10 \div 5 $$

As you can see in the picture below, the remainder is 0.

picture of remainder of zero

When a number (like 5 up above) evenly divides the other (10 above), then there is no remainder.

Problem 4

$$ 13 \div 4 $$

As you can see in the picture below, the remainder is one.

picture of remainder of one

challenge problem icon The problems below are "next-level". See how you do!

Problem 5

$$ 4 \div 5 $$

The answer to this problem is easier to understand if you look at the long division work.

4 divided by 5 in long division
Problem 6

$$ 0 \div 3 $$

The answer to this problem is easier to understand if you look at the long division calculations. Three goes into zero, zero times and when you do the long division you'll actually see that there is not any remainder.

zero divided by 3 in long division
Problem 7

$$ 4 \div 6 $$

The answer to this problem is easier to understand if you look at the long division work.

4 divided by 6 in long division
Problem 8

$$ 0 \div 6 $$

The answer to this problem is easier to understand if you look at the long division calculations. 6 goes into zero, zero times and when you do the long division you'll actually see that there is not any remainder.

zero divided by 3 in long division
Problem 9

You are working on you homework but, as you can see below the paper is ripped almost in half! You can only read part of the problem and it says "What is the remainder when zero is divided by ...".

Now, you don't even know what the divisor is here.

Can you still answer this question? Why or why not?

what is zero divided by anything

Yes, you actually can indeed answer this question because zero divided by any number is zero and has a remainder of zero!


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