Simplify Fractions – Definition with Examples
A fraction is a numerical representation of a part of a whole object or group of objects. It consists of two numbers which are separated by the fraction bar. The one above the bar is called the numerator, and the one below is called the denominator. You can represent one fraction differently by altering the numerator and denominator values while keeping the same result. As a result, fractions come in a complex form, which may make them cumbersome, especially when they are part of a bigger math problem. An easy way to get through dealing with fractions is by simplifying them.
What are Simplified Fractions?
Just as the name implies, simplified fractions represent fractions in their simplest forms. What this definition means in math terms is that to simplify a fraction you need to find the greatest common factor (GCF) of the numerator and denominator. For example, if you wanted to simplify 4/8, you would have to divide both by 4, and the answer would be 1/2.
Similarly, you can simplify 12/18 by dividing it by six and get 2/3. Simplifying fractions makes comparing them to other fractions and performing other math operations easily. The process of simplifying fractions is also called reducing fractions.
How to Simplify Fractions?
The first thing you have to do when you want to simplify a fraction is to find the most significant common factor(GCF) of the numerator and denominator and then divide both by that factor. The result of the fraction must end with a numerator and denominator that have the greatest common factor as 1. If you get a number where the greatest common factor is not 1, you must try again until you get the fraction to its simplest or most reduced form.
A fraction reducer or a fraction simplifier simplifies a given fraction to its simplest forms. You can simplify using a calculator, an online tool, or a software program. If you want to do it manually, you can use step-by-step instructions to reduce fractions.
Simplifying Fractions Step by Step
If you are wondering how to reduce fractions, here are the steps you can take to simplify a fraction:
- Find the GCF of the numerator and denominator. You can find the GCF of a numerator and denominator by listing the factors of both, identifying the factors that appear in both numbers more commonly, and choosing the GCF between them. For example, if you wanted to simplify the fraction 24/36, you must first find the GCF of both numbers.
The factors of 24 are 1,2,3,4,6,8,12, and 24.
The factors of 36 are 1,2,3,4,6,9,12,18, and 36.
The greatest common factor between the two numbers is 12.
- Divide the numerator and the denominator by the GCF to get the simplified fraction which should have a common factor not greater than 1.
Using the example provided in the previous point, divide it this way: 24/12=2, and 36/12=3.
The simplified fraction of 24/36= 12/3, and the common factor between 2 and 3 is 1.
Note that the fraction used in this example is relatively simple; other fractions may not come in such a simple format.
Simplifying Fractions with Variables
Simplifying fractions with variables is almost the same process as simplifying usual fractions. You will get the GCF of the numerator and denominator, then divide both by that factor. However, variables make fractions more complex, and you must include algebraic rules to simplify the expressions.
Here is a step-by-step explanation of simplifying fractions with variables:
- First, if possible, factor the numerator and denominator.
- Next, find the common factor in the numerator and denominator.
- Then divide the numerator and denominator using the GCF.
- If the resulting fraction is still complex, simplify it further.
For example, you have the fraction (6x^2y^3)/(12xy^2):
- First, factor in the numerator and the denominator. You can factor 6x^2y^3 into 23xxyyy and then 12xy^2 into 223xy*y.
- Find the common factor in the numerator and denominator 2, x, and y^2.
- Divide the numerator and denominator using the GCF, which is 2xy^2.
What you have eventually should look like this: (6x^2y^3)/(12xy^2) = (23xxyyy)/(223xyy) = (3x*y)/(2).
Now, when you look at the above fraction, it seems more complex, so you will simplify it again using the same method above. When you do that, you should have something like this: (6x^2y^3)/(12xy^2) reduced to (3xy)/2.
Simplifying Fractions with Exponents
When you want to simplify fractions with exponents, you must use the laws of exponents to simplify the numerator and denominator before simplifying the fraction. Here are some of the steps of simplifying fractions with exponents:
- Simplify the numerator and denominator separately using the laws of exponents.
- Find the common factors in the numerator and denominator.
- Divide the numerator and denominator by the common factor you got.
- Simplify the resulting expression if you find out that the resultant fraction is more complex.
For example, let’s have the problem (a^3b^4)/(a^2b^2).
To simplify the numerator and denominator separately using the laws of exponents:
Use a^3 to divide a^2 is a^(3-2) = a^1 = a.
Then use b^4 to divide b^2 is b^(4-2) = b^2.
Find the common factors in the numerator and denominator, which is ab^2.
Now divide the numerator and denominator with ab^2.
What you will get now is (a^3b^4)/(a^2b^2) = (ab^2a^2b^2)/(a^2b^2) = ab^2.
This expression above still looks complex, so simplify (a^3b^4)/(a^2b^2) to get a*b^2.
Simplifying Mixed Fractions
A mixed fraction combines a whole number and a proper fraction. Before you simplify mixed fractions, you must first convert them to improper fractions, then simplify the improper fraction, and then if possible, convert the result back to a mixed fraction.
Here are the steps to simplify mixed fractions:
- Mixed fractions usually come in whole numbers; multiply the whole numbers by the numerator and denominator.
- Add the numerator to the answer you get from the first step.
- Write the sum from step 2 as the numerator retaining the previous denominator.
- Use the simplification method you know to simplify the improper fraction.
- If possible, convert the improper fraction to a mixed fraction.
For example, we have a problem 3 ¼.
First, multiply the whole number by the denominator of the proper fraction like this: 3 x 4 = 12.
Then move to the additions: 12 + 1 = 13.
Move the numerator around to give you 13/4.
No common factors are bigger than 1 between 13 and 4, so your simple fraction is 13/4.
As 13/4 is an improper fraction, you do not need to return it to make it a mixed fraction again.
Simplifying Improper Fractions
An improper fraction is a fraction where the numerator is bigger than or equal to the denominator. To simplify improper fractions, you have to divide the denominator by the numerator to end up with a whole number and a fraction, also called a mixed fraction.
For example, if you have 25/4, the answer will be 6 with a remainder of 1. So, you move 1 to the numerator and leave 4 as the denominator, while 6 remains the whole number. Thus, your final answer for 25/4 is 6¼.
Solved Examples of the Simplifying Fraction Concept
Here are a few solved examples on simplifying fractions:
Example 1:
Simplify the fraction 16/24.
First, find the numerator and denominator’s greatest common factor (GCF). The GCF of 16 and 24 is 8. We can divide both the numerator and denominator by 8 to simplify the fraction:
16/24 = (16 ÷ 8)/(24 ÷ 8) = 2/3
So, the simplified fraction is 2/3.
Example 2:
Simplify the fraction 12/36.
Find the GCF of the numerator and denominator. The GCF of 12 and 36 is 12. We can divide both the numerator and denominator by 12 to simplify the fraction:
12/36 = (12 ÷ 12)/(36 ÷ 12) = 1/3.
So, the simplified fraction is 1/3.
Example 3:
Simplify the fraction 9/27.
The GCF of 9 and 27 is 9, so we can divide both the numerator and denominator by 9:
9/27 = (9 ÷ 9)/(27 ÷ 9) = 1/3.
So, the simplified fraction is 1/3.
Teaching the simplification of fractions to kids can be challenging if they do not have enough practice materials. Therefore, it is not enough to assign homework and class work and be done with it. You must ensure that children practice at home and with the right set of questions that will challenge them to do better. You have to use a simplifying fractions worksheet as teaching material to get your kids submerged in the topic enough to reduce fractions in their sleep.
Dear students, I recommend that you use Brighterly Worksheets for the topic Simplifying Fractions. These worksheets will help you understand the process of fractionalization and learn how to do it with ease.
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