Division Notation
So far we have explored addition, subtraction, and multiplication. Now let’s consider division. Suppose you have the 12 cookies in the figure below and want to package them in bags with 4 cookies in each bag. How many bags would we need? You might put ...
By the end of this lesson and the next few, you should be able to:
- Use division notation
- Model division of whole numbers
- Divide whole numbers
- Translate word phrases to math notation
- Divide whole numbers in applications
Image credit: Public Domain
Using Division Notation
So far we have explored addition, subtraction, and multiplication. Now let’s consider division. Suppose you have the \(12\) cookies in the figure below and want to package them in bags with \(4\) cookies in each bag. How many bags would we need?
You might put \(4\) cookies in first bag, \(4\) in the second bag, and so on until you run out of cookies. Doing it this way, you would fill \(3\) bags.
In other words, starting with the \(12\) cookies, you would take away, or subtract, \(4\) cookies at a time. Division is a way to represent repeated subtraction just as multiplication represents repeated addition.
Instead of subtracting \(4\) repeatedly, we can write
We read this as twelve divided by four and the result is the quotient of \(12\) and \(4.\) The quotient is \(3\) because we can subtract \(4\) from \(12\) exactly \(3\) times. We call the number being divided the dividend and the number dividing it the divisor. In this case, the dividend is \(12\) and the divisor is \(4.\)
In the past you may have used the notation \(4\overline{)12}\), but this division also can be written as .\(12÷4,\phantom{\rule{0.2em}{0ex}}12\text{/}4,\frac{12}{4}.\) In each case the \(12\) is the dividend and the \(4\) is the divisor.
Operation Symbols for Division:
To represent and describe division, we can use symbols and words.
| Operation | Notation | Expression | Read as | Result |
|---|---|---|---|---|
| \(\text{Division}\) | \(÷\)
|
\(12÷4\)
|
\(\text{Twelve divided by four}\) | \(\text{the quotient of 12 and 4}\) |
Division is performed on two numbers at a time. When translating from math notation to English words, or English words to math notation, look for the words of and and to identify the numbers.
Example
Translate from math notation to words.
(a) \(64÷8\) (b) \(\frac{42}{7}\) (c) \(4\overline{)28}\)
Solution
- We read this as sixty-four divided by eight and the result is the quotient of sixty-four and eight.
- We read this as forty-two divided by seven and the result is the quotient of forty-two and seven.
- We read this as twenty-eight divided by four and the result is the quotient of twenty-eight and four.
Extra:
Translate from math notation to words:
(a) \(84÷7\) (b) \(\frac{18}{6}\) (c) \(8\overline{)24}\)
Solution
- eighty-four divided by seven; the quotient of eighty-four and seven
- eighteen divided by six; the quotient of eighteen and six.
- twenty-four divided by eight; the quotient of twenty-four and eight
Extra:
Translate from math notation to words:
(a) \(72÷9\) (b) \(\frac{21}{3}\) (c) \(6\overline{)54}\)
Solution
- seventy-two divided by nine; the quotient of seventy-two and nine
- twenty-one divided by three; the quotient of twenty-one and three
- fifty-four divided by six; the quotient of fifty-four and six
Optional Video: Dividing Whole Numbers
This video below by Mathispower4u explains how to perform division using whole numbers.
This lesson is part of:
Introducing Numbers