Whole Numbers – Division
The operation of division can be expressed and written in multiple ways:
Equation Form
Fraction Form
Dividend ÷ Divisor = Quotient
Dividend
= Quotient
Divisor
Long Division Form
Quotient
Divisor Dividend
Dividend: The number being divided
Divisor: The number that the dividend is being divided by
Quotient: The number of times the divided can be divided by the divisor
Understanding Concepts: Visualizing and Verbalizing Division
Example: Evaluate 8 ÷ 2
Here are some ways to express the question in words:
How many times does 2 go into 8?
If we need to divide 8 into 2 equal parts, how many are in each part?
We can also express the question pictorially:
If we have 8 circles and want to split them equally between two people, how many circles
would each person get?
As you can see, 4 circles will go to the person on the left, and 4 circles will go to the
person on the right (i.e. each person gets 4 circles). Therefore, 8 ÷ 2 = 4
If we express this question in the fraction form, we can solve this by reducing the fraction:
8÷2
=
8
2
÷2
=
÷2
4
1
=
4
8
4
𝑟𝑒𝑝𝑟𝑒𝑠𝑒𝑛𝑡𝑠 8 𝑐𝑖𝑟𝑐𝑙𝑒𝑠 𝑓𝑜𝑟 2 𝑝𝑒𝑜𝑝𝑙𝑒. 𝑟𝑒𝑝𝑟𝑒𝑠𝑒𝑛𝑡𝑒𝑠 4 𝑐𝑖𝑟𝑐𝑙𝑒𝑠 𝑝𝑒𝑟 (𝑜𝑛𝑒) 𝑝𝑒𝑟𝑠𝑜𝑛.
2
1
Whole Numbers – Long Division
Example 1: Evaluate 624 ÷ 12 using long division.
Step 1:
How any times does 12
go into 6?
Step 3:
What is the remainder?
(6 − 0)
Step 5:
How many times does
12 go into 62?
Step 7:
What is the remainder?
(62 − 60)
Step 9:
How many times does
12 go into 24?
0
12 624
0
12 624
0
Step 2:
What is 12 × 0?
0
12 624
0
6
0
12 624
0
62
Step 4:
Bring down the next
digit in the dividend
05
12 624
0
62
05
12 624
0
62
60
2
Step 6:
What is 12 × 5?
05
12 624
0
62
60
2
05
12 624
0
62
60
24
Step 8:
Bring down the next
digit in the dividend
056
12 624
0
62
60
24
056
12 624
0
62
60
24
24
Step 10:
What is 12 × 6?
Step 11:
What is the remainder?
(24 − 24)
056
12 624
0
62
60
24
24
0
In this case, dividing
12 into 624 left no
remainder. This
means that 12 can
be divided into 624
evenly.
∴624 ÷ 12 = 56
We repeat Steps 1 to 4 until we have exhausted all
the digits in the dividend.
Tutoring and Learning Centre, George Brown College 2014
www.georgebrown.ca/tlc