Adding, subtracting, multiplying, and dividing – it gets a lot harder when you’re dealing with fractions. Here’s how to understand fractions in no time.
If you stink at math, don’t feel bad. Americans don’t have the best reputation when it comes to math. In other words, you’re not an outsider.
Unfortunately, we have some bad news for you:
You have to learn some basic math principles and concepts to get by in the business world. One of those concepts happens to be fractions.
Fortunately, we have a good handle on fractions here at We Are Augustines and are going to pass on our knowledge to you.
So sit back, relax, and enjoy this brief guide on how to understand fractions:
What Is a Fraction?
Before we go much further, let’s first discuss what fractions are. This discussion might seem trivial, but we believe it will help you in the long run.
Simply put, a fraction is a value that doesn’t represent a whole number. Some examples of whole numbers include:
A fraction, on the other hand, isn’t quite “complete.” It consists of two separate parts: a numerator and a denominator. The numerator is the number on top whereas the denominator is the number on the bottom.
Take the fraction 5/6 for example. There are six possible parts, but only five of those parts exist. The numerator is five while the denominator is six.
To put it another way:
Imagine that one LEGO set contains six blocks. If you only have five blocks, you don’t have one entire set. You instead have a fraction of a set.
But fractions aren’t technically partial numbers. That’s because we can represent every number as a fraction.
Remember those whole numbers we listed earlier? Well, we can represent them as fractions by writing:
This representation is redundant. Even so, it can help you when you performing mathematical operations on fractions.
What Mathematical Operations Can You Use on Fractions?
You can use most (if not all) of the same mathematical operations on fractions that you can use on whole numbers. These operations include addition, subtraction, multiplication, and division.
Those only encompass the elementary operations. You’ll frequently see fractions used in high-level math.
For the purposes of this lesson, however, we’ll only focus on the four simple operations we listed earlier. Let’s start with addition:
How to Add Fractions
Adding whole numbers is simple, right? If you want to know the sum of seven and five, write and solve the following equation:
7 + 5 = x
Unfortunately, adding fractions isn’t that simple. Let’s look at an example which illustrates how to add fractions. We’ll add the following values:
Let’s break both of these values down. The first fraction has a numerator of three and a denominator of five. The second fraction has a numerator of two and a denominator of ten.
The most important thing to note is that these fractions have different denominators. When fractions have different denominators, you must find the least common denominator (LCM).
In order to find the least common denominator, list out the multiples of both denominators.
The multiples of 5 include 5, 10, 15, 20, etc.
The multiples of 10 include 10, 20, 30, 40, etc.
The LCM is the smallest multiple both denominators have in common. As you can see, we’ve highlighted the number 10, as it’s the smallest common number on both lists.
Once you have the common denominator, you must find a way to make the smaller denominator equal that common denominator. Our smaller denominator is 5 in this case. That means that we have to multiply it by 2 if we want to make that denominator equal 10.
But here’s the deal:
You must multiply the entire fraction by that number. So (3/5) x 2 is equal to 6/10, which means you replace 3/5 with 6/10.
Now you’re ready to add your fractions together. You write:
6/10 + 2/10
Since both fractions have the same denominator, you can add them together. Note that you don’t add the denominators together, only the numerators. So your final answer should be 8/10.
How to Subtract Fractions
We’ve got some great news:
The process of subtracting fractions mirrors that of adding fractions. We’ll use the same two fractions we used above here to showcase the similarities. That means we’re solving the
3/5 – 2/10
We first start by finding the least common denominator. As we established before, the least common denominator is 10. As we did above, we’ll replace 3/5 with 6/10.
Now we have the following problem:
6/10 – 2/10
Remember that you don’t subtract the denominators. Just subtract the numerators, which leaves you with 4/10.
How to Multiply Fractions
Multiplying fractions is much simpler than adding and subtracting them. We’ll again use the fractions we used above:
3/5 x 2/10
In this case, you don’t have to find the least common denominator. You just have to multiply the numerators and multiply the denominators. The product of the numerators is your answer’s numerator while the product of the denominators is your answer’s denominator.
So 3/5 x 2/10 becomes (3 x 2)/(5 x 10), which equals 6/50.
How to Divide Fractions
Dividing fractions isn’t as simple as multiplying them, but it’s still easy.
Let’s take our example fractions and attempt to divide them:
In order to solve this problem, think about what dividing by a number means. If, for example, we wanted to instead divide 3/5 by 2, what would we be doing to the fraction?
Multiplying it by 1/2.
We must apply this same logic when we’re dividing fractions. Thus, we can write the expression (3/5)/(2/10) as (3/5) x (10/2). As we said above, multiplying fractions is simple:
So (3/5) x (10/2) becomes 30/10.
The only thing we’ve done here is to swap the second fraction’s numerator and denominator. We refer to this inverted fraction as the original fraction’s reciprocal.
Every number has a reciprocal, even whole numbers. The reciprocal of 3 is 1/3. The reciprocal of 100 is 1/100. We summarize this rule as:
The reciprocal of n is 1/n.
Does that sound too complex for you? Just use a fraction calculator. CalcuNation, for example, offers a nifty one.
The Secret to Figuring Out How to Understand Fractions
The secret to figuring out how to understand fractions is patience. With enough time and practice, you’ll warm up to fractions.
Don’t stress yourself out if the process takes longer than expected. There’s nothing intuitive about going from working with whole numbers to working with partial numbers.
In any case, if you’re looking to educate yourself in other ways, feel free to browse our blog. You can also contact us if there’s anything you’d like to see covered in a future blog post.