MathML 3 adds several elements to handle elementary math problems. The
elementary math elements below should be inside of either an mstack or an
mlongdiv element. Both mstack and
mlongdiv make the digits of numbers contained in them be in their
own columns and their children appear in their own row; mlongdiv's
first three children are the divisor, dividend, and result and are treated
specially.
msgroup
groups rows with similar alignment; options control the position and
shifting of children (see multiplication and division examples below)
msrow
groups digits and operators into a row; options control the position of
the children
msline
draws lines between rows of the stack; options control the position,
length, thickness, and overhang of the line
mscarries
annotates the following row with optional borrows/carries and/or
crossouts; options control the default location, style, and size of the
borrows, carries, and crossouts
mscarry
a borrow/carry and/or crossout for a single digit; options control the
location, style, and size of the borrow, carry, and/or crossout
If a blank entry in a column is needed, the element none can be used.
This is shown in some of the examples below.
Addition, Subtraction, and Multiplication Problems
Here's a simple addition problem that spaces the "+" away from the operand
by using the element none:
Notice that the carry/borrow default of "n" (north/above) is changed to the "nw" (northwest)
position by mscarries, but that is overridden for the borrow and changed back to "n".
The carry/borrow can be
in any compass position. Several different styles for crossouts are possible.
Here's a multiplication problem that shows multiple rows of carries:
There are a few things to note about this example:
we specified spacing between the characters on the mstack
tag; absolute values such as "10px"
can also be given
the carries are shifted over; we could also have used an msrow and
none,
but specifying a position is simpler
the '874' uses msrow to shift the number over one column,
but a "0" could have been added and this would not have been needed;
alternatively, msgroup with shift="1" could have been used,
similar to what is done in the long division
problem below
Long Division
There are many different styles of long division used around the world.
MathML has ten named styles, but the list is open ended. All styles share how
the intermediate steps are displayed, but differ in the placement of the
divisor, result, and where lines are drawn. The default style is the style used
in the U.S., Great Britain, and elsewhere.
Below are two examples that differ only in the style and what character is
used for the decimal separator. Because the separator is typically set on the math
element, it is included in these examples.
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mlongdiv>
<mn> 12 </mn>
<mn> 16.5 </mn>
<mn> 198 </mn>
<msgroup position='1' shift='-1'>
<msgroup>
<mn> 12</mn>
<msline length='2'/>
</msgroup>
<msgroup>
<mn> 78</mn>
<mn> 72</mn>
<msline length='2'/>
<mn> 6.0</mn>
<mn> 6.0</mn>
</msgroup>
<msgroup position='-1'> <!-- extra shift to move to the right of the "." -->
<msline length='3'/>
<mn> 0</mn>
</msgroup>
</msgroup>
</mlongdiv>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML"
decimalpoint=",">
<mlongdiv longdivstyle='stackedrightright'>
<mn> 12 </mn>
<mn> 16,5 </mn>
<mn> 198 </mn>
<msgroup position='1' shift='-1'>
<msgroup>
<mn> 12</mn>
<msline length='2'/>
</msgroup>
<msgroup>
<mn> 78</mn>
<mn> 72</mn>
<msline length='2'/>
<mn> 6,0</mn>
<mn> 6,0</mn>
</msgroup>
<msgroup position='-1'> <!-- extra shift to move to the right of the "," -->
<msline length='3'/>
<mn> 0</mn>
</msgroup>
</msgroup>
</mlongdiv>
</math>
Repeating Decimal
There are two common styles for indicating a repeating decimal in a decimal
expansion of fractions like ⅓. The most common style puts a line above
the part that repeats and the other style puts dots on the first and last digits
of the part that repeats. Both are easy to write as shown below:
Examples on this page have been collected together into a
sample page.
In order to view the page properly, you need a browser that has implemented
MathML 3's elementary math elements.
MathML Makes Elementary Math Accessible
The video below shows a prototype of MathPlayer speaking and highlighting the speech for two
elementary math examples:
