Editing Elementary arithmetic (section)

==Division==
{{Main|Division (mathematics)|Long division}}
[[Division (mathematics)|Division]] is an arithmetic operation, and the inverse of [[multiplication]], given that <math>c \times b = a</math>. 

Division can be written as <math>a \div b</math>, <math>\frac ab</math>, or {{frac|''a''|''b''}}. This can be read verbally as "''a'' divided by ''b''" or "''a'' over ''b''".

In some non-[[English language|English]]-speaking cultures{{Which|date=February 2024}}, "''a'' divided by ''b''" is written {{nowrap|''a'' : ''b''}}. In English usage, the [[colon (punctuation)|colon]] is restricted to the concept of [[ratio]]s ("''a'' is to ''b''").

In an equation ''<math>a \div b = c</math>, a'' is the dividend, ''b'' the divisor, and ''c'' the quotient. [[Division by zero]] is considered impossible at an elementary arithmetic level. 

Two numbers can be divided on paper using [[long division]]. An abbreviated version of long division, [[short division]], can be used for smaller divisors.

A less systematic method involves the concept of [[Chunking (division)|chunking]], involving subtracting more multiples from the partial remainder at each stage.

=== Example ===
Dividing 272 and 8, starting with the hundreds digit, 2 is not divisible by 8. Add 20 and 7 to get 27. The largest number that the divisor of 8 can be multiplied by without exceeding 27 is 3, so it is written under the tens column. Subtracting 24 (the product of 3 and 8) from 27 gives 3 as the [[remainder]].

{|style="border-collapse: collapse; border-spacing: 2px; text-align:center"
| ||2 ||7 ||2
|-
|style="border-bottom: 1px solid black;"|÷ ||style="border-bottom: 1px solid black;"| ||style="border-bottom: 1px solid black;"| ||style="border-bottom: 1px solid black;"|8
|-
| || ||3||
|}

Going to the ones digit, the number is 2. Adding 30 (the remainder, 3, times 10) and 2 gets 32. The quotient of 32 and 8 is 4, which is written under the ones column.

{|style="border-collapse: collapse; border-spacing: 2px; text-align:center"
| ||2 ||7 ||2
|-
|style="border-bottom: 1px solid black;"|÷ ||style="border-bottom: 1px solid black;"| ||style="border-bottom: 1px solid black;"| ||style="border-bottom: 1px solid black;"|8
|-
| || ||3||4
|}

The result:
<math display="block">272 \div 8 = 34</math>

==== Bus stop method ====
Another method of dividing taught in some schools is the bus stop method, sometimes notated as
           <u>&nbsp;&nbsp;result&nbsp;&nbsp;</u>
   (divisor) dividend

The steps here are shown below, using the same example as above:
     <u> <span style="color: red;">0</span><span style="color: green;">3</span><span style="color: blue;">4</span> </u>     
    8|272
      <u>0</u>        ( 8 &times;  <span style="color: red;">0</span> =  0)
      <span style="color: darkorange;">2</span>7       ( 2 -  0 =  <span style="color: darkorange;">2</span>)
      <u>24</u>       ( 8 &times;  <span style="color: green;">3</span> = 24)
       <span style="color: darkcyan;">3</span>2      (27 - 24 =  <span style="color: darkcyan;">3</span>)
       <u>32</u>      ( 8 &times;  <span style="color: blue;">4</span> = 32)
        0      (32 - 32 =  0)
The result:

<math display="block">272 \div 8 = 34</math>