How To Add Fractions Easily And Simply For Non-Mathemagicians

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I figured I’d try and learn to program. I’m finding it harder than I thought. But that’s for another blog post. But something interesting came my way while trying to learn how to program, and that is, I found out that I’m not 100% stupid at math.

My biggest problem is that I just didn’t care enough to learn. Now admittedly, I am more comfortable with word swashbuckling than I am with with math-a-magics. But it’s never too late to start, and I’ve learned how to add fractions easily and simply.

I wanted to brush up on my math skills because most of the programming courses I’ve been taking seem to think you need a good grasp of mathematics. I’m not necessarily convinced that’s the case. Again, a topic for another blog post.

But what I did find out was that learning how to add fractions is actually not that hard. In fact I’ve found it to be pretty easy. And I almost failed high school math. So how do you do it?

Simples. We all know how to add fractions with a common denominator. You’ll recall that the numerator is the number on the top of the fraction and the denominator is the number at the bottom of the fraction.

In this fraction $\frac{3}{4}$ the number 4 is the denominator and the number 3 is the numerator. The way I’ve always found to remember this is that denominator starts with d as does down! The bottom number is also known as the divisor. Some of you might remember that from high school. So, what does that mean? It means that in the above example, 3 (numerator) is being divided by 4 (denominator). So in essence $\frac{3}{4}$ is also 0.75 which is ${3}\div{4}$.

Anyway, that is an aside. Most of us know how to add $\frac{3}{4}+\frac{1}{4}$. $\frac{3}{4}+\frac{1}{4}$ is $\frac{4}{4}$. This is also equal to 1, because ${4}\div{4}$ is 1. So what is happening here is that when the denominator is the same – Denominator is the number down under the fraction line – you just add both numerators. Easy right?

But what happens when you have two fractions with different denominators? How do you add $\frac{3}{4}+\frac{2}{5}$? Well, when you multiply the two different denominators (4 and 5) together, you get a common divisor. So you end up with this $\frac{3}{20}+\frac{2}{20}$. But this is not quite correct because if you added the 3 and the 2, you’d get $\frac{5}{20}$ which simplified would be $\frac{1}{4}$ right? ‘Cos you divide 5 (numerator) into itself and you get 1, you divide it into the 20 (denominator) and you get $\frac{1}{4}$. This is how you simplify the fraction.

But you can intuitively feel that $\frac{1}{4}$ is not the right answer to the question of $\frac{3}{4}+\frac{2}{5}$. I mean even $\frac{3}{4}$ is bigger than $\frac{1}{4}$ and we’ve got to add $\frac{2}{5}$ to it, so how can adding two things together make the answer smaller? It can’t. At least not in adding simple fractions like these.

But with fractions, you have to treat the numerator and the denominator like Siamese twins. What you do to the denominator you have to do to the numerator and vice versa. So what did we do to $\frac{3}{4}$ to turn the denominator into 20? We multiplied it by the other fraction’s ($\frac{2}{5}$) denominator which in this case was 5. Cool, so what we do to the denominator (4) we have to do to the numerator (3). Et voila, we now get $\frac{15}{20}$ which you’ll agree is the same as $\frac{3}{4}$. We know it is, because if we now divide both the numerator and denominator in $\frac{15}{20}$ by 5 we’ll get our original fraction of $\frac{3}{4}$.

Excellent, outstanding work. So, what do you think we should do with the second fraction we want to add to the first fraction. Well, we’re trying to get them to have the same denominator which we’ve learned is 20. So, how did we get $\frac{2}{5}$ to have a denominator of 20? We multiplied it by the first fraction’s ($\frac{3}{4}$) denominator which is 4. Okay, so let’s do that, but let’s multiply both the numerator and denominator of this fraction ($\frac{2}{5}$) by 4. What do we get? $\frac{8}{20}$. And we can verify this is correct by dividing both the numerator and denominator by 4, and if we do this to $\frac{8}{20}$ we get $\frac{2}{5}$.

This is not so hard, non? Okay, so we’ve found the common denominator which is 20 and we’ve now ended up with our two original fractions ($\frac{3}{4}$ and $\frac{2}{5}$) being equivalent to $\frac{15}{20}$ and $\frac{8}{20}$ respectively. Now we can easily add them together. Let’s do that. Remember, when adding fractions, you only add the numerators when you have the same denominators. So ${15}+{8}=23$.

In other words $\frac{15}{20}+\frac{8}{20}$ becomes $\frac{23}{20}$ which in this case can be reduced to ${1}\frac{3}{20}$ by dividing the numerator by the denominator.

I hope you found that helpful. I’m not a math wiz by any stretch of the imagination, but when I figured out how to add fractions this easily I was hooked. In summary. When you are adding two fractions with the same denominator you just add the numerators and put that number over the common denominator. So $\frac{5}{7}+\frac{3}{7}$ becomes $\frac{8}{7}$ and if the numerator is bigger than the denominator you know you have a whole number with a fraction so you divide the numerator by the denominator and in our case you get ${1}\frac{1}{7}$ from $\frac{8}{7}$.

When the denominators of the fractions you are trying to add are different, just multiply the two denominators by each other to find the common denominator. Once you have that, then multiply fraction A’s numerator by fraction B’s denominator and vice versa. Now go practice!