News from Mathnasium of Huntersville

So why do you need Common Denominators when adding or subtracting fractions?

The explanation is very simple when you remember that the Denominator simply means, “The name of the fraction”. It tells you what you’re dealing with. If you buy 3 apples, then you buy 2 more apples, together you bought 5 apples.

3/apples +2/apples = 5/apples

However, if you buy 3 apples and 2 bananas, you can’t add them because they aren’t the same thing. You don’t have 5 banapples! You can’t add or subtract things with different names. You have to find a common “name” for these items.

So if you change the “name” to fruit – it works!

3/fruit + 2/fruit = 5/fruit!

Fractions work the same way!

3 apples plus 2 apples equals 5 apples.

– Or – 

3 elephants plus 2 elephants equals 5 elephants.

– Or –   

3 sevenths (3/7) plus 2 sevenths (2/7) equals 5 sevenths (5/7). 

You have to think of the Denominator not as a number, but as a “name.”

But what if we are adding two things that don’t have the same name?

3 apples + 2 bananas

3 pennies + 2 nickels 

You don’t get 5 banapples or 5 pickles do you?

No, you change the names so they are the same.  You have 5 fruit and 13 cents.

So if we have 1 third plus 1 half (1/3 + 1/2), we can’t add them, because the names are different. Just like if we had 1 dime and 1 nickel, those aren't the same type of coin. But if we turn them both into cents first, we can add them together and get 15 cents! With fractions, just like with coins, when you change the name, the number changes too. With 1/3 and 1/2, the common name is sixths, and 1/3 = 2/6, while 1/2 = 3/6. So we now have 2 sixths plus 3 sixths equals 5 sixths (2/6 + 3/6 = 5/6).

This is how we teach at Mathnasium.  We break down concepts into the simplest terms and use analogies like these, so your kids can understand how and why the concepts work.  We don’t want to just teach rules and algorithms that they are going to forget.

What about Equivalent Fractions? What about Multiplying and Dividing Fractions? Reducing Fractions?

We teach these topics and concepts in a similar way so that kids understand what to do, and why they are doing it. This is the best teaching method for long term retention. It's easy to forget something you've memorized, but it's hard to forget something that you truly understand!

Mathnasium’s goal for teaching fractions is to help the student master them. This conquers the fear and builds confidence! We help them to think and process mathematical concepts the way natural mathematicians do, so that they can work confidently at a high level.