How to Add 3 Fractions with Different Denominators
Until now, we had not written about operations with more than 2 fractions.
In this post, you are going to learn to add 3 fractions with different denominators with help from a visual aid. That way, you can understand the mathematical process behind the calculation.
How to add 3 fractions with different denominators (two of which are multiples)
We are going to begin with the following addition problem:
To understand this problem correctly, we have graphically represented each addend:
Using a rectangle as the unit, we divide them into 2, 3, and 4 parts, and in this case, each is a different color. Now we have represented the 3 addends: 1/2, 1/3, and 1/4.
We will start by adding the first 2 addends.
First, we divide each rectangle into equal parts (adding the divisions to each rectangle):
Now you can solve it easily! The two are shown in ”sixths” and that way we get the following sum:
We can represent the sum of this equation like this:
Now all that’s left is to add the third addend, which we can do like this:
And can be graphically represented like this:
To be able to add them, we divide them into equal parts like before:
We’ve converted the 2 fractions into ”twelfths” and now have the sum:
That we can represent in the following way:
Have you seen how easy it is to add fractions?
Visualizing everything makes it much easier!
How to add 3 fractions with different prime number denominators
Now we are going to solve a problem that is a bit more difficult because the denominators are different prime numbers and we need to go through the process a bit more carefully:
But as you can see, with the visual help it makes it easier as well!
Like before, we graphically represent each fraction:
Since the sum of the first two is the same as before, we have already calculated that answer above:
And we have the following sum:
For an answer that is much easier to add, we represent 5/6 as a rectangle divided vertically and 1/5 as a rectangle divided horizontally:
We divide both representations into equal parts:
Now we have the 2 fractions in ”thirtieths” and the sum:
That can be represented like this:
You’ve solved it!
I hope that it was easy to understand how to add 3 fractions. Share this post if you like it!
And if you want more primary mathematics, sign up for Smartick and try it for free.
- Adding and Subtracting Fractions: Why Do They Need the Same Denominator?
- Adding Fractions with the Visual Aid of Rectangles
- Homogeneous and Heterogeneous Fractions
- Practice Adding Fractions with Examples
- Using Mixed Numbers to Represent Improper Fractions
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