**Struggling with Improper Fractions? Call my helpline, now available 24/7**

That was voted “Best Maths Pun of 2014” by The Aperiodical website. I thought it was pretty funny, too.

If you, or anyone you know, has been affected by the issues raised in this post you might find the following of use:

]]>Not an easy problem. Its often easier to start with something simple and work from there. So, what fraction of these triangles are shaded in (click on each image to get a bigger view):

Perhaps you can use your answers to those above to help you solve the more difficult problem at the top of this blog post.

I’ve put them all together for you on a Triangle Fractions Worksheet and you can find the Triangle Fractions Answers

Another version of the same question, Below is an image of all nine triangles (again, click on the image to enlarge it). There are two pairs of the triangles that have the same fraction shaded (each pair has a different amount shaded in, if that makes sense?!) Can you find the pairs? Can you convince someone else that you are right?

**Teaching Tip: **Have the image of all nine triangles projected onto your interactive whiteboard as the pupils enter the class room. Let the discussion and debate begin!

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With the advent of the calculator, with the ability to do fraction calculations in a snap, I often hear the anguished cry of “what’s the point of this, why can’t I just use my calculator?”

And it is, perhaps, true that the need to do fraction ‘sums’ manually has diminished enormously since the advent of the scientific calculator.

But, as September has come and gone and we find ourselves in mid- October and Year 12 (the lower-sixth in old money) settle down to enjoy the rigours of AS and A-Level maths, one is reminded of the need for A-Level students to be fluent in the manipulation of algebraic fractions. And this is made so much easier if they have met and mastered the four rules (adding, subtracting, multiplying and dividing) fractions with numbers earlier in there mathematical journey.

So, whilst it may not be everybody’s favourite topic, it is an important skill to master.

And to help pupils master it, they need to practise it. And to help them practice, I’ve produced some worksheets for adding, multiplying and dividing fractions.

And if you want a worksheet that contains all three types of problems, you can make one using my custom worksheet page (or click here, for one I prepared earlier!)

As with all my worksheets, they generate an unlimited number of different questions, are optimised for printing (so you don’t waste loads of ink), look great on an interactive whiteboard and come complete with the answers – hidden behind a ‘click’ if you’re projecting them onto your board, or printed on a separate sheet if you are printing them out. Oh, and they are entirely free, too!

And the answer to the question at the top of the page? Well it is, of course …

(remember: when multiplying fractions, its top x top, bottom x bottom)

]]>Just like these limbo -ing Lego figures, I like to imagine fractions seeing how low they can go. Whenever they can, fractions should be simplified, cancelled down, put in their lowest terms … basically, make the top and bottom numbers the smallest they can be.

Remember the mantra: “Whatever you do to the top, you must do to the bottom.” To cancel down a fraction, try and find a number that divides into both the top number (the numerator) and the bottom number (the denominator).

Need some practice in cancelling down fractions? Then you could use my Equivalent Fractions Worksheet

Like all my worksheets, it can be used to generate an unlimited amount of different questions.

And there’s more fractions worksheets like:

Converting Mixed Numbers to Top Heavy Fractions

and more, to be found at my worksheets page

The worksheets work well when projected onto an interactive whiteboard for the whole class to try – the answers are hidden but can be shown by clicking the strip towards the bottom of the page.

*And*** **they’ve been optimised for printing – the questions and answers are printed on different sheets and they print out in black and white, with no extra images or ‘bumph’ on the printed page that you see on the screen, making them great for photocopying and saving you ink when you print.

With more worksheets being added all the time I hope you find my maths worksheet page a useful resource for home or school.

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Percentages – Its all in the name: *Per* as in ‘out of’ and *cent* as in ‘century’ ‘dollars (or Euros) and cents’ ‘Centurion’ and ‘hundred’ in French. Percent means: ‘out of 100’

So to turn a percentage into a fraction, just shove it over one hundred:

**58% = ^{58}⁄_{100}** …

… but don’t forget to CANCEL DOWN the fraction, to become ** ^{29}⁄_{50}**. Easy!

Percentages to decimals is just as easy – remember what percent means? Yep, out of one hundred, so simply divide your percent by 100 to convert it into a decimal:

**58% ÷ 100 = 0.58**

Going the other way is just as easy – to turn a decimal into a percentage simply multiply a decimal by 100:

**0.27 x 100 = 27%**

Turning a fraction into a percentage can be tough, but remember – percent means out of 100, so just ‘cancel up’ the fraction until its out of 100 and your done:

^{13}⁄_{20} We need to make the bottom number 100 so: multiply the bottom by 5 to turn it into 100, and then multiply the top by 5 as well (“whatever we do to the bottom, we do to the top”)to give:

^{13}⁄_{20} = ^{65}⁄_{100} = 65%

Easy! Follow these simple steps and you, too, will soon be getting 100%!

If you want to find out how to find the percentage of a number – e.g. what is 65% of 180 – you need to read this.

]]>Pick up any dictionary and you will find ‘Vulgar’ defined along the lines of:

- Lacking sophistication or good taste; unrefined
- indecent; obscene; lewd

… and I’ve often wondered what the poor old fraction has done to deserve such a reputation.

I have visions of unruly fractions, burping and belching and generally terrorising the more gentle and sophisticated numbers. I have an image of a gang of fractions, probably with a top heavy fraction like ^{14}⁄_{5} as the gang leader, nipping behind the bike shed for an illicit smoke. I picture some mutton-chopped Victorian mathematician so incensed by the decadent form of these fractions that he describes them as “vulgar little numbers”.

But, alas, the story of the vulgar fraction is much less colourful. The vulgar in this context is:

- common

and our vulgar fractions are nothing more than common fractions – fractions whose top number* and bottom number* are both integers (whole numbers.)

Although the average schoolboy (or girl) may not agree, fractions are actually pretty useful things and actually make maths a whole lot easier – when we encounter the delights of (harder) algebra, using fractions makes life much, much more simple than dealing with decimals. So even if they are little vulgar and swear and curse a little, you’ve got to love vulgar fractions.

**A Maths Teacher**

*I much prefer to use the words “top number” and “bottom number” than numerator and denominator – why confuse things further with fancy words that are easily forgotten.

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