How do you simplify fractions? Or, how do you reduce fractions?

In most cases, when fractions are introduced to students as a new topic in the classroom, the initial reaction is: "Here's another complex subject we have to deal with." But then, reactions change and fractions are seen as a kind of enjoyable game that is more of a technical challenge. So, what's particularly important about fractions? Understanding their meaning, the division of roles between the numerator and the denominator, and how to reduce them. Is it difficult to reduce fractions? Not really.

So, when will you need to reduce the given fractions?

The main motivation for reducing fractions is primarily to establish more favorable working conditions. The more you can reduce a fraction, the easier it will be for you to work with it and use it as a given. Therefore, you should practice this topic as much as possible and remember: the main arithmetic operation in reducing fractions is division.

It's not difficult, it's actually easy!

Reducing Fractions: How Is It Done in Practice?

To reduce a fraction, you must divide both the numerator and the denominator by the same number. The big question is: To which number do you reduce the fraction? And the answer is quite simple: the smallest number possible! Sometimes, a fraction won't reduce in just one step (a characteristic of very large fractions), but rather in several different stages until you get to the smallest possible fraction. Here are some examples of what reduced fractions look like:

The fraction $\frac{4}{10}$ becomes $\frac{2}{5}$ after dividing the numerator and the denominator by $2$.

The fraction $\frac{5}{25}$ becomes $\frac{1}{5}$ after dividing the numerator and the denominator by $5$.

The fraction $\frac{3}{24}$ becomes $\frac{1}{8}$ after dividing the numerator and the denominator by $3$.

The fraction $\frac{30}{180}$ becomes $\frac{1}{6}$ after dividing the numerator and the denominator by $30$.

More examples: How hard is it to reduce fractions? Not hard at all! Keep in mind that, unlike other topics of study which require you to perform different mental processes, here you must stick solely to the technique of division. How do you approach reducing a fraction?

Divide the numerator and the denominator by the same number

Choose the smallest possible number for reduction

Here are some more examples of how to reduce fractions:

$\frac{25}{1000}$ becomes $\frac{1}{40}$, after dividing the numerator and the denominator by $25$

$\frac{6}{18}$ becomes $\frac{1}{3}$, after dividing the numerator and the denominator by $6$

$\frac{20}{60}$ becomes $\frac{1}{3}$, after dividing the numerator and the denominator by $20$

$\frac{8}{32}$ becomes $\frac{1}{4}$ after dividing the numerator and the denominator by $8$

Examples and exercises with solutions for reducing fractions

Exercise #1

Simplify the following fraction:

$\frac{1}{1}=$

Video Solution

Step-by-Step Solution

Let's reduce as follows, we'll divide both the numerator and denominator by 1:

$\frac{1:1}{1:1}=\frac{1}{1}$

Answer

$\frac{1}{1}$

Exercise #2

Simplify the following fraction:

$\frac{12}{4}=$

Video Solution

Step-by-Step Solution

Let's reduce as follows, divide the numerator by 4 and the denominator by 4:

$\frac{12:4}{4:4}=\frac{3}{1}$

Answer

$\frac{3}{1}$

Exercise #3

Simplify the following fraction:

$\frac{12}{8}=$

Video Solution

Step-by-Step Solution

Let's simplify as follows, we'll divide both the numerator by 2 and the denominator by 2:

$\frac{12:2}{8:2}=\frac{6}{4}$

Answer

$\frac{6}{4}$

Exercise #4

Simplify the following fraction:

$\frac{16}{8}=$

Video Solution

Step-by-Step Solution

Let's simplify as follows, we'll divide both the numerator by 2 and the denominator by 2:

$\frac{16:2}{8:2}=\frac{8}{4}$

Answer

$\frac{8}{4}$

Exercise #5

Simplify the following fraction:

$\frac{2}{10}=$

Video Solution

Step-by-Step Solution

Let's simplify as follows, we'll divide both the numerator by 2 and the denominator by 2:

$\frac{2:2}{10:2}=\frac{1}{5}$

Answer

$\frac{1}{5}$

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A golden tip for tackling a test question: Start with the easy questions!

What is an easy question? An easy question for you. Naturally, there are subjects where you're stronger and those where you take a bit more time, which is fine. To start your test with a success experience, you should always begin with topics you feel more comfortable with and that give you confidence. So how do you do that?

Quickly skim through the exam to become familiar with the types of questions and topics.

First, answer the problems that you feel you have total control over.

Remember: you can start answering the test on page $4$ or page $1$; the order of solving doesnβt matter.

So, what do you get from this?

You start the exam with a successful and pleasant experience.

Your self-confidence rises, stress and tension decrease.

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You kick off the exam with "safe" points.

3 Myths About Math Class That Need to Be Shattered

Sometimes, what prevents you from achieving the success you desire isn't your knowledge but your mental barriers. Here are 3 different myths about the subject of math that you probably believe as well:

"Math is a subject for the wise" - Not true! Math is a subject for students who understand that success is based on perseverance. It's no coincidence that there are students whose average in math is $60$, and after a period of investing in a private tutor, the average has risen to $85$. It's not that they've become wise, but that theyβve chosen to invest the effort. The key to success in the subject is perseverance: preparing assignments, participating and attending classes, and serious studying for exams.

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The Connection Between Homework Preparation and Success in Mathematics

At the end of every math class, your teacher probably also asks you to do your homework and not to give up. Beyond being your duty as a student, it's also aimed at strengthening your understanding and competence in the subjects taught. Simplifying fractions is an example of a problem based on technique, relying solely on a division operation. At first, it might take you a few minutes to simplify a fraction. The more you practice, the more you'll see for yourself how those minutes turn into seconds.

A faster solution to questions gives you an advantage in exams. Why?

Take the test without fear of not having enough time to answer all the questions.

They have time to retake the entire test before submitting it.

Without doing your homework and practicing the topics taught in class, it's unlikely that you'll be able to reduce the average time it takes to answer a question.

Online Lesson: Simplifying Fractions Step by Step!

The most significant benefit of an online private math lesson is the tremendous time savings. As a student, you have to juggle multiple tasks at once, without wanting to neglect any subject. More than once, there are students who spend about thirty minutes traveling in each direction within the city to get to their private tutor. What about you? You can save this hour!

An online class is a lesson that takes place right in your room! How does it work?

You select a teacher from our group of math tutors.

The tutor prepares a lesson plan with the topics you want to learn. For example: reducing fractions.

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Start learning! During the session, you can ask questions, solve exercises, and even get ahead on the topic before the class.