Introduction
Let’s say your teacher brings in 36 donuts one day to class and there are 14 students. How many donuts does each student get if we want to split them up evenly? How many will be left?
To solve this problem we will have to divide. There are enough donuts so that each student will get 2 and we will have a remainder of 8 extra donuts.
Division can be a tricky subject especially when we deal with big numbers. Luckily, there are a few techniques and tricks to make problems like these a lot easier.
Important Division Strategies
1  Long division
2  Estimation
3  Dividing out common factors
4  Dividing using area models
5  Divisibility rules
A divisor is a number we are dividing by. It’s important to understand that we can rewrite a division problem in many different ways.
Here’s three ways we can write 488 divided by 22:
The first way we wrote the problem is how we solve long division problems.
Long Division
Example: Solving a Long Division Problem
Let’s solve this problem using the long division method.
Step 1  Since we are dividing by a 2 digit number, we take a look at the first two digits of 488 and ask how many times we can divide 48 by 22.
Step 2  We know we can divide 48 by 22 at least two times. It is important to note that we write the 2 above our second digit since we are dividing up to the second digit. Now, we need to figure out how much will be left over. We will multiply 22 by 2 and subtract it from 48.
Step 3  Can we divide 22 by 4? No, we cannot. So we will bring down the next digit. It is important to draw the yellow line so that we can separate the remainder later.
Step 4  How many times can we divide 48 by 22? We can divide exactly twice. We will then repeat step 2 and subtract 2 times 22 from 48. Since we are left over with 4 and we can’t divide that by 22, that is our remainder.
Final Answer  Our final answer will be 22 remainder 4.
We can express our final answer as a mixed fraction of our divisor. Another way to say 22 remainder 4 in this situation is:
Long division is very useful for solving all types of problems involving big numbers.
If we are dividing by a 1 digit number, we take a look at the first digit of the problem. Can we divide 3 by 4?
Since we can't, we add the next digit and ask can we divide 39 by 4?
A useful technique for this situation is to estimate.
Estimation
39 is close to 40. We can change our numbers a little and ask what is 40 divided by 4? Our solution is going to be a number close to 10.
Since 39 is a little less than 40, we can estimate that our answer is 9.
Using long division, our answer is 9 with a remainder of 3, which is close to our original estimate.
It is important to note we write our 9 above the second digit since we are dividing up to the second digit.
Dividing Out Common Factors
A factor is a number we can divide another by and get a whole number as our answer. For example, the factors of the number 6 are 3 and 2.
We can simplify division problems by dividing common factors out of both sides.
Let’s rewrite the problem from earlier.
Example: Solving by Cancelling Factors and Long Division
Since both the numerator and denominator are even, we know they can be each divided by 2. We can rewrite 22 as 2 × 11, and 488 as 2 × 244.
Since we have a common factor of 2 on both sides of this division, they will cancel each other out.
We have now simplified our problem to 244 divided by 11, which is a more simple problem to solve.
Let's solve using long division:
Step 1  Since we are dividing by a 2 digit number, we take a look at the first two digits of 244 and ask how many times we can divide 24 by 11.
Step 2  We know we can divide 24 by 11 at least two times. It is important to note that we write the 2 above our second digit since we are dividing up to the second digit. Now, we need to figure out how much will be left over. We will multiply 11 by 2 and subtract it from 24.
Step 3  Can we divide 11 by 2? No, we cannot. So we will bring down the next digit. It is important to draw the yellow line so that we can separate the remainder later.
Step 4  How many times can we divide 24 by 11? We can divide exactly twice. We will then repeat step 2 and subtract 2 times 11 from 24. Since we are left over with 2 and we can’t divide that by 11, that is our remainder.
Final Answer  Our final answer will be 22 remainder 2.
We can express our final answer as a mixed fraction of our divisor. Another way to say 22 remainder 2 in this situation is:
This answer is equivalent to 22 remainder 4 in our first long division example.
Solving by Using Area Models
We can use number lines and area models to help estimate certain division problems.
Solving a Division Problem Using a Number Line
A number line can help us visualize the answer to many division problems.
Let's take a look at dividing 63 by 7.
Step 1  Create a number line from zero to the number being divided, with segments every 7 units. In this case, 63 is being divided so our number line will go from 0 to 63.
Step 2  Since we are dividing by 7, count up in multiples of 7.
In this case, it takes nine multiples of 7 to get to 63. This means that 63 divided by 7 is equal to 9.
We can use area models to represent different situations. Let's recall the example from the introduction where we want to split up 36 donuts between 14 students evenly.
Solving a Division Problem Using Pictures
Let's recall the example from the introduction where we want to split up 36 donuts between 14 students evenly.
Begin by drawing 36 donuts or any shape that resembles a donut.
Since we are dividing 36 by 14, circle groups of 14 donuts. We can only circle two groups of 14 donuts, and we will be left with 8 extra donuts.
This means that 36 divided by 14 is equal to 2 with a remainder of 8.
Divisibility Rules
These rules help us quickly check if big numbers can be divided by another number. We can split our rules up into 3 groups, the first group is usually the easiest to check.
Group 1
Number
Divisibility Rule
Example
2
Any even number can be divided by 2. Big numbers are even if the last digit is even.
492 is even since the last digit is even, so we know it can be divided by 2.
5
Any number ending with a 5 or 0 can be divided by 5.
25, 5450, 120, 35, 45, 455 can all be divided by 5.
10
Any number ending with a 0 can be divided by 10.
200, 3540, 4630 can all be divided by 10.
Group 2
Number
Divisibility Rule
Example
3
A number can be divided by 3 If the sum of its digits can be divided by 3 evenly.
123 can be divided by 3 since 1 + 2 + 3 = 6 and 6/3 is a whole number.
6
A number can be divided by 6 If the sum of its digits can be divided by 3 and 2.
123 can be divided by 6 since 1 + 2 + 3 = 6 and 6 can be divided by 3 and 2 to give a whole number.
9
A number can be divided by 9 If the sum of its digits can be divided by 9.
123 cannot be divided by 9 since 1 + 2 + 3 = 6 and 6 cannot be divided by 9 to give a whole number.
Group 3
Number
Divisibility Rule
Example
11
A 2 digit number can be divided by 11 if we have repeating digits
22, 33, 44, 55 can all be divided by 11.

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