Adding fractions is probably the first difficult bit of maths we come across at school. For example, to work out you first need to figure out that the lowest common multiple of 6 and 10 is 30, and that in order to get 30 in the denominator of both fractions you need to multiply the numerator 5 by 5 and the numerator 7 by 3. This gives

You then need to get rid of the common factors of 46 and 30, giving the final result which bears no resemblance whatsoever to the original two fractions. Doing this as a ten-year-old who has never seen it before is pretty tough.

Here is an alternative recipe that *always* works and doesn't involve faffing around with lowest common denominators. Writing "top" for numerator and "bottom" for denominator, the idea is to do:

(top left x bottom right + top right x bottom left) / (bottom left x bottom right).

Applied to our example this gives:

The difference to the standard way of adding fractions is that you are not bothered with finding the *lowest* common denominator. You simply use the product of the two denominators as *a* common denominator. Then, in order to bring both fractions on that common denominator you only need to multiply the numerator of each by the denominator of the other. Easy!

Apparently this is how Vedic mathematicians in ancient India added up fractions. If you happen to speak German, you can also explore this method in musical form in this maths rap by DorFuchs. And even if you don't speak German, it's cute!

## Comments

## Why work any other way?

I was taught this method at school (London, late 60s). Why on earth anyone would think that making it more complicated by chucking in this unnecessary LCD business is entirely beyond me. Now I'm thinking I should check that my kids haven't been polluted by this nonsense!

## How to add fractions

...its also the way I was taught to do it 52 years ago in a junior school in Swindon!

## Adding Fractions

Remember doing it this way at school - 50+ years ago.

## ditto

ditto

## stupid math trick

abundantly obvious.

same process as lcm

just figuring the lcm the way i always did it.

but then i am incapable of learning and incapable of remembering. without 90 days practice lol.

so i figure what i deal with all over again one second at a time; boring things i practice so i no longer notice them they become habits.

## It gets more complicated

Try adding

1/2 + 1/3 + 5/6 + 4/9

without looking for the lowest common denominator. The numbers get large fairly fast using the crude method touted here.

Since when are kids too stupid to comprehend lowest common denominator?

## How I was taught as well

Method I was taught in Florida in the late 80s. Next year moved to Atlanta and was "corrected" and forced to use LCD method. Yeck.

## Umm.. Yeah, I was taught this in the US 20 years ago.

Nothing new.

## same way I was taught in 1975

Same way I was taught in 1975, this does not deserve an article in 2014.

## Because

Mathematical short-cuts are often traps.

The student who learns to work fractions this way and never learns LCD will struggle in algebra and fail at calculus.

The goal IS NOT to teach easy computation--we have computers and calculators for that.

The goal IS to teach mathematical theory that can be generalized and used to learn more complex ideas.

## exactly this method works for

exactly

this method works for here and now BUT

without the skills to do it properly youll run into trouble later in high school maths

## Impressed^(-1)

Okay, so adding fractions works by using any common multiple of the denominators, not just the lowest... Doesn't seem ground-breaking and, frankly, what's the point?

Firstly students will also learn how to find the LCM of two numbers anyway.

Secondly, they need to simplify the fraction, which requires the notion common factors and it's not something that comes easy to them

Thirdly, if you try doing that to algebraic fractions or higher number fractions using this method, you'll get in trouble quickly...

Basically, uninteresting, a very particular case and not useful...

Sorry...

## There really is nothing

There really is nothing special to this method, at all. I came up with the thought in school once, I guess any student might come up with that idea, sooner or later, because finding LCDs was a pain in the ass when you could just do it this way, obviously...

## No Faffing

What a shame that +Plus magazine is suggesting that confidence-building and efficient computation techniques are 'faffing'.

Students who know their times facts (times tables) have no difficulty finding LCM, those with less confidence can try the ' 2x bigger denom, does it work for smaller? 3xbigger denom, does it work for smaller' method. Those who find LCM an issue would be better if given activities and time to understand the LCM concept and build instant recall skills in times facts. If LCM is beyond them, using bigger CMs just gives more opportunity to make computation errors with the bigger numbers - not a confidence-building approach.

Fractions techniques are brilliant tools to simplify otherwise complex calculations. Fractions are already short-cuts for multiply/division. I teach them as a step into using 'professional tools' as you would teach an apprentice the techniques of the master craftsman.

## Adding fractions without analyzing the LCM

Hi Marianne, your post is very helpful and informative about the two ways on adding fractions. Those that need LCM and those that are not. In any case, I am fun of your second method. For me, it is a proven method and very effective. So let me share my technique on solving fraction.

To add and subtract fractions successfully is to make the rules stick to your memory.

Rules for addition:

Same denominator:

Add both numerator then reduce. The result would be the final answer.

Different denominator (4 steps):

1. Multiply the numerator of first fraction to the denominator of second fraction. The result is the new numerator of first fraction.

2. Multiply the numerator of the second fraction to the denominator of first fraction. The result is the new numerator of second fraction.

3. Multiply both denominators. The result is the common denominator for two fractions.

4. Add the two new numerators. The result is the answer.

Rules for subtraction:

Same denominator:

Subtract second numerator from first then reduce. The result would be the final answer.

Different denominator (4 steps):

1. Multiply the numerator of first fraction to the denominator of second fraction. The result is the new numerator of first fraction.

2. Multiply the numerator of the second fraction to the denominator of first fraction. The result is the new numerator of second fraction.

3. Multiply both denominators. The result is the common denominator for two fractions.

4. Subtract new second numerator from first new numerator. The result is now the answer.

To make it stick to your memory:

Same numerator:

Add two fractions 50 times.

Different denominator:

Add two fractions 100 times.

To check if your answer is right and your step by step solution is correct?

Use mixed fraction calculator with button. It is important that you follow the correct steps in adding unlike fraction. Unlike fractions are those fractions with different denominator.

The key here is to make the rules implanted into the minds of the students so that they will never forget.