Fractions are difficult—and this type of unit, similarly to most in math, usually just builds on itself. This means that if you get stuck on a concept and don’t address it right away, you might find that even after you move on to new material, you’ll continue to use the concept that you didn’t understand. 

If you’re struggling with fractions in class, you’re likely also having difficulty tackling your homework in math, which may certainly add to your stress levels. 

This may particularly apply to you if you’re a student experiencing math anxiety, which means dealing with any math concept leaves you with anxiety and doubt. 

Luckily, there are some handy methods you can implement to make nailing your fractions a bit easier. 

Adding fractions by calculating least common denominator

First things first, let’s recall what the denominator is. The denominator is the bottom number in a fraction and indicates how many equal parts the item is divided into. 

When two—or more—fractions have the same denominators, they have common denominators. Why are common denominators important?

Because in order to add fractions, our fractions must have the same denominators. 

So, why do we need the least common denominator (LCD), specifically?  You don’t actually need to use the LCD, but it will certainly make it easier to simplify and work with any given fraction—as opposed to using any common denominator.

In order to determine the LCD…

List all multiples

Let’s say you have two fractions: ⅘ and ⅔. You’ll want to list all the multiples of both denominators, which are 5 and 3, and then you’ll be able to determine the LCD. This should look something like this:

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While these aren’t all the multiples, you don’t need to list them all since you can already see that there is a common denominator: 15. This means that you want both fractions to have a denominator of 15. And since you’re looking for the least common denominator, there’s no need to keep listing them. 

Multiply both parts of fractions 

The next step is to multiply both the top and bottom of each fraction by the number you need to make the denominators equal 15. 

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So for ⅘, you’ll need to multiply the whole fraction by 3 (because the denominator is 5, and 5 x 3 = 15).  For ⅔, you’ll multiple the whole fraction by 5 (the denominator is 3, and 3 x 5 = 15). Now, both fractions have the same denominator, and you’re ready to add the two together. 

In this example, the final answer should come out to be 22/15.

Adding fractions without calculating least common multiple

If you’re not fan of the LCD method for adding fractions, you’ll be happy to know it’s not the only option. With this trick, you’ll initially be using multiplication, but the result will be the same as if you were to add the fractions through the above method. 

For a detailed explanation, check out the video below:

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Step 1: Multiply the denominators

First, you’ll multiply the denominators together. We’ll use the same fractions as in the example above: ⅘ and ⅔. 

So, 5 x 13 = 15. 

Step 2: Cross multiply fractions

This is where it gets a tad bit more complicated. Multiply the numerator of the first fraction (4) with the denominator of the second fraction (3), and then multiply the numerator of the second fraction (2) with the denominator of the first fraction (5). This is cross multiplication. 

To visualize this better, picture two diagonal lines going from each numerator to the opposite denominator. 

Next, add the two products together. In this case, you’ll be adding together 12 and 10, which are the products of both numerators multiplied by the opposite denominators. And the result is 22. When we go back to step 1, we have the denominator of 15. So, the result is 22/15, which is the same result we got using the LCD method. 

Dividing fractions by flipping

Thinking about dividing fractions—understandably—can be confusing, since you probably learned about division by seeing one number over another—which is also a fraction.

This trick may make the concept of dividing fractions much easier to comprehend. The method is simple, and really only involves a few quick steps. 

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Step 1: Change the sign

Again, we’ll use the same fractions: ⅘ ÷ ⅔.  You’ll want to change the sign from division to multiplication. So the equation becomes ⅘ x ⅔.   

Step 2: Find the reciprocal 

The next and (basically) last step is to flip the second fraction (⅔), which makes it a reciprocal—a reciprocal is simply the number you’d have to multiply another number by to come up with 1. 

In this case, you need to multiply ⅔ by 3/2 to get 1.

Step 3: Multiply the fractions 

After you’ve flipped the sign and changed the second fraction to its reciprocal, all you’ve got to do is multiply the numerators and denominators, and you’ll have the result:

⅘ x 3/2 = 12/10 

Follow the circle method to create improper fractions

The circle method is a great tool to utilize—particularly for all you visual learners out there.

You can use the circle method when you have a number and a fraction, which is a mixed number, (such as 1½)and need to transform it into an improper fraction. An improper fraction is simply a fraction that contains a numerator which is larger than the denominator. 

This is called the “circle” method, because you’re essentially traveling in a circle around the fraction. 

Let’s look at the case of 1½:

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You’ll start at the bottom, 2. From the bottom number, go around, clockwise to the next number, which is 1. 

The first step is to multiply those two numbers: 1 x 2 = 2.  Next, you keep going in the circular clockwise motion, and go to the next number, which is 1. The second step is to add the product from the previous step to the numerator of the fraction: 2 + 1 = 3

And voilà. You don’t change the denominator at all. Simply follow the circular steps, and you’ll get your improper fraction result. 

Simplify by finding the greatest common factor

Another challenge when learning fractions is nailing the simplification process. Here we’ll go over the greatest common factor (GCF) method.

With this strategy, you’ll be looking for the GCF between the numerator and denominator—once you find it, you’ll be able to efficiently simplify a fraction. 

Why do we want to simplify a fraction? The reason is simple (pun intended)! Simplifying fractions just makes the subsequent work easier for you compared to if you leave a fraction in a larger-than-simplified version.  

Step 1: Find the GCF

First you need to determine the GCF between the numerator and denominator. Let’s look at the fraction 9/12.   

For some fractions you’ll know right away what the GCF is, and for others you’ll have to do a little more brain work. This “brain work”, just refers to listing the factors of the numerator and denominator until you find the GCF

If you can’t tell right away, you can start by seeing if 9 is a common factor, and then work down from there. You should eventually determine that the GCF between 9 and 12 is 3.

For a visual explanation, check out the video below:

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Step 2: Divide by the GCF

Once you’ve found the GCF, divide both the numerator and denominator by this number. And you’re done! In the case of 9/12, after dividing by the GCF, which is 3, you should arrive at a final answer of ¾

 

If you need more help with fractions, math, or any other subjects, don’t hesitate to book a tutor at My Private Professor today. If you aren’t satisfied with your session, it’s free: the MPP Guarantee! 

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