Mainly Maths - Test your Browser

 
Use this page to check that your web browser, such as Internet Explorer, displays maths correctly.

The Mainly Maths site uses three methods to display maths.

Example

Here's a straightforward calculation to show the three methods. The example is a division, normally written as numerator over denominator:

divide 6 by the product of 2 and 3

Method 1 uses an in-line text layout:  6 ⁄ (2×3) = 1

Method 3 is similar to 2 - but uses a maths markup language:   $${6 \over 2 \times 3}$$  = 1

Method 1 should work in any browser.

Method 2 does not work with old versions of Internet Explorer or using Internet Explorer in Compatibility View.

If Method 3 works then the result should look almost identical to Method 2. If instead you see something like:

$${6 \over 2 \times 3}$$

then your browser does not support Method 3. However, you can see that 6 \over 2 \times 3  means numerator 6 over denominator 2 times 3.

Method 1 uses a forward slash / for the division sign, mainly because it is easier to type than the ÷ sign.

Methods 2 and 3 use the standard horizontal dividing line to separate numerator and denominator.

Click here to see how five typical GCSE maths examples display in your browser.

These methods are used in the Mainly Maths online test questions. It is important that:

• they work in your browser.
• you can read and understand the maths.
• you can type basic maths using Method 1.

In-line Text Layout

In Method 1 the maths is typed in a single line, just like normal text, as in 6×2 = 12 and 6 ⁄ 2 = 3. You probably use this method yourself. It is very similar to typing a calculation into a pocket calculator or typing a formula in a spreadsheet cell.

Mainly Maths online tests include short answer calculation questions. To answer, you type the calculation into the answer box using in-line maths. See Writing GCSE Maths Calculations. The in-line method is versatile and is well suited to basic GCSE calculations - but has limitations.
More Info If you have ever included maths in a text message, posted to a maths forum or typed a maths assignment, you probably used in-line maths.

Historically, few maths characters were available on typewriters and, more recently, computer keyboards. Typewriters and computer keyboards were designed to communicate using text. Mobile phone text messaging is an extension of this. Text is typed in lines and it was natural to use the same in-line approach for typing maths.

Originally, very few of the characters needed were available on a keyboard. There was no plus sign and no equal sign. Even now there is no traditional division ÷ sign and no multiplication × sign on a standard keyboard. For multiplication the lower case x is normally used, although in computing the * is common.

The forward slash / was, and still is, used both for a division sign (a division slash) and as a separator between a numerator and denominator (a fraction slash). As a result the ÷ sign has almost disappeared from maths, except in arithmetic, pocket calculators and, of course, GCSE level maths.

This in-line method for communicating maths is more common than ever - possibly because of the widespread use of forums and blogs. A web page can be persuaded to display properly formatted maths equations - but the in-line approach is still the most versatile method for typing basic maths, for example, in emails, forums and online tests.

Method 1 uses the forward slash  ⁄  for division. For example, 6 ⁄ 2 means 6 divided by 2. The slash  ⁄  is the in-line equivalent of the horizontal dividing line (the fraction bar) used in methods 2 and 3. As you will know, the fraction bar means both 'divided by' and 'over' as in 6 divided by 2 and 6 over 2.

There is a problem with using a  ⁄  dividing line. Unlike a horizontal line, the numerator and the denominator may not be clear. In the example 6 ⁄ 2×3, is the denominator 2 or is it 2×3? The 2×3 is written in brackets as in 6 ⁄ (2×3), to show that the denominator is the product 2×3.

What does the calculation mean without the brackets? Most people, as well as spreadsheets, calculators and this website, interpret the calculation 6 ⁄ 2×3 to mean divide 6 by 2 and then multiply the result by 3. The denominator is 2 and not 2×3. The result of that calculation is 9, not 1.
More Info The use of / for a division sign has replaced the traditional ÷ sign in computing. So, for example, in a spreadsheet formula, 6/2 is used and not 6÷2. In spreadsheets and other computer applications a star * is used for multiplication and so, in a spreadsheet, 6/2×3 is written 6/2*3. In this website type a lower case x for multiplication in test questions.

The use of / for division conflicts slightly with the other use of / to represent the fraction bar. A fraction bar separates the numerator from the denominator and so the calculation 2/1+1 should mean 2 over the sum of 1 and 1. The result is 1. Unfortunately, if / is a division sign, then 2/1+1 means divide 2 by 1 and then add 1. The result is 3. This website follows the second interpretation. Brackets are used, for example 2/(1+1)=1, to show that the 1+1 is the denominator. Some would say that 2/1+1=3 should be written with brackets as in (2/1)+1=3. Certainly that avoids any uncertainty but seems unnecessary. If you treat a / as division then, using BODMAS or any variation of that rule, the division is completed before the addition.

What about the example above: 6/2×3. Some would say that should be written (6/2)×3=9 to show that 6 is first divided by 2. However, you cannot expect students to use brackets in that situation. The spreadsheet does not require them, neither does a pocket calculator. The rule is, if in doubt, multiplication and division is done from "left to right", in the order it is written. Applying that rule, the 6 is first divided by 2 to give 3, Then 3×3=9.

If you are not convinced that the in-line maths expressions work, then test them on your calculator. For example, try the 2/(1+1) calculation but replace the slash / with the calculator's ÷ sign. On your calculator type 2÷(1+1)= . You should get 1.

Method 3

Internet Explorer (versions 8 and 9) on Windows XP and Windows 7 does supports Method 3. Browsers that include MathML (a maths markup language) should display Method 3 better. Firefox does. Firefox has built-in MathML support but Internet Explorer does not. You can download a free MathML plugin for Internet Explorer, called MathPlayer, from here. Install the plugin - Internet Explorer will then load a Method 3 maths page more quickly.

As of Oct 2012, for Internet Explorer 9 (on Windows 7) you should download MathPlayer 3.0 (Preview Release 1). Internet Explorer 10 on Windows 8 does not, as yet, support Method 3.

Mobile and Tablet Browsers Some browsers do not support Method 3 - for example, Opera 10 for mobile does not and so, if possible, use a later version. Method 3 works well with Firefox for Android - and Firefox has the advantage of built-in support for MathML.

An important difference between Methods 2 and 3 is that Method 3 is interactive. Right click on the Method 3 calculation (on the 6 over 2×3 bit) shown below and try out the menu options. For example, try setting the Zoom Trigger to Click:

• point at the Math Settings option.
• point at Zoom Trigger.
• click the Click option.

With the Zoom Trigger now set to Click, do a normal click on any Method 3 calculation to make it zoom.

Method 3:   $${6 \over 2 \times 3}$$  = 1

The Math Renderer option is important. If you use Internet Explorer, install the MathPlayer plugin. The maths may look better and the maths web page will load faster - but you first have to select the MathML renderer.

Firefox should use MathML by default - but check. To select MathML or check that you are using MathML, right click the Method 3 example, then:

Point at Math Settings > Point at Math Renderer > Click MathML

To select the HTML-CSS rendering:

Point at Math Settings > Point at Math Renderer > Click HTML-CSS

Method 1 Examples: Using Normal Text Layout

These examples should display correctly in all browsers. Examples (c) to (g) below are compared using the three methods in the Comparison Table. Click here.

(a)  b² − 4ac or b^2 − 4ac

In the 2nd example above the caret ^ is used to represent raised to the power of.

(b)  4 ⁄ 3

The above uses the forward slash  ⁄  to show division. It is both a fraction, 4 over 3, and a division, 4 divided by 3.

(c)  24 ⁄ 3 = 8

The meaning of the above should be clear. The numerator 24 is divided by the denominator 3. The result of the calculation is 8.

Another similar example: 11 ⁄ 3  means both 11 divided by 3 and eleven-thirds. Do not confuse it with the fraction one and one-third. You could type one and one-third with a space, as in 1 1 ⁄ 3  but that can still be confused with 11 ⁄ 3. Of course, with extra formatting, one and one-third can be written 1¹⁄₃

(d)  24 ⁄ √3 = 8√3

The square root sign  √  is used to show root 3.

(e)  x ⁄ (1−x)

In the above, the algebraic fraction x over 1−x uses the slash  ⁄  to separate the numerator x from the denominator 1−x. The 1−x is in brackets to make clear that the x is divided by 1−x.

(f)  (3.6 − 2.4) ⁄ (2.6 + 1.4)

The above fraction is written with the numerator 3.6−2.4 and the denominator 2.6+1.4 in brackets. Your calculator should 'understand' the calculation. Try it out. Include the brackets but replace the slash with the calculator's division sign, as in:  (3.6 − 2.4) ÷ (2.6 + 1.4). The result is 0.3

The next example is more complicated and is pushing in-line text layout to its limits. It may be difficult to interpret but it has the advantage that it should display correctly.

(g)  (−b ± √b^2 − 4ac ) ⁄ 2a

In the above the term in brackets is the numerator and that term is divided by the denominator 2a. For simplicity b^2 is used instead of b².

Examples (a) to (f) use text characters only and so are pure text. The maths can be typed, copied and pasted as with any chunk of text. Example (g) is slightly different - it contains some formatting to create the horizontal line that completes the square root sign. An alternative pure text approach using extra brackets is acceptable:  (−b ± √(b^2 − 4ac) ) ⁄ 2a

Comparison Table

Methods 2 and 3 separate the numerator and denominator in the standard way, using a horizontal dividing line. The line is called a vinculum, a division bar or a fraction bar.

Method 2 uses a simplified maths layout that should work with all up-to-date browsers on desktops, laptops and mobiles and so should display correctly for you.

Method 3 uses a standard maths markup language. It will not work with all browsers. For instance, it will not work using Opera Mobile 10 on a Windows Mobile 6 operating system. It works well with Firefox for Android.

If Method 3 works for you, try tweaking the settings. For example, if you use Firefox you should notice an improvement if you switch to MathML rendering. Right click a calculation in the Method 3 column, then check the setting:
Math Settings > Math Renderer > and check that MathML is selected. With Internet Explorer the web page should load faster with MathML - but you have to install MathPlayer.

Method 1 In-line Text Layout	Method 2 Simplified Maths Layout	Method 3 Standard Maths Markup
24 ⁄ 3 = 8	24 / 3  =  8	$${{{24} \over 3}\small\ =\ \small8}$$
24 ⁄ √3 = 8√3	24 / √3  =  8√3	$${{{24} \over {\sf√}3}\small\ =\ \small{8{\sf√}3}}$$
x ⁄ (1−x)	x / 1−x	$${{x \over {1-x}}}$$
(3.6 − 2.4) ⁄ (2.6 + 1.4)	3.6 − 2.4 / 2.6 + 1.4	$${{{3.6-2.4} \over {2.6+1.4}}}$$
(−b ± √b^2 − 4ac ) ⁄ 2a	−b ± √b^2 − 4ac / 2a	$${{\frac{-b \pm \sqrt{b^2-4ac}}{2a}}}$$

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