How To Simplify Ratios With Fractions

How To Simplify Ratios With Fractions – Ratios are used as a way of comparing values. Usually expressed in the form A:B, they tell us how much of one thing we have compared to another. For example, if we have a bowl of fruit that contains two apples and six oranges, we can express this as 2:6.

Ratios are useful because they allow us to easily scale values ​​and express quantities in a way that is easy to understand. As such, you’ll find them in everything from official statistics to grocery store labels.

How To Simplify Ratios With Fractions

How To Simplify Ratios With Fractions

When relationships appear in everyday contexts, they are usually given in their lowest form. In the numerical reasoning test, you may need to simplify the ratio. This process is easy enough when working with whole numbers, but complicated when working with ratios involving fractions.

Question Video: Forming And Converting Improper Fractions To Mixed Numbers In The Simplest Form

For example, take the ratio 1 5/12: 7/3. Since each side or term of the ratio is a fraction, we must first manipulate it and identify the common denominator that will allow us to find the lowest form of the ratio. We will walk through this process below.

How To Simplify Ratios With Fractions

If we consider the above example of the ratio 1 5/12: 7/3, we need to go through four steps to express it in its simplest form.

In our example, the previous term in the ratio is the mixed fraction 1 5/12, so we need to convert it to an improper fraction first (you can skip this step if there are no mixed fractions in the ratio).

How To Simplify Ratios With Fractions

Are Ratios And Fractions The Same?

To do this, we first multiply the whole number by the denominator of the fraction; in this case 1 x 12 = 12.

We then add this result to the numerator of the fraction, so 12 + 5 = 17. This number now becomes our new numerator, which we place above our original denominator, giving us the improper fraction 17/12.

How To Simplify Ratios With Fractions

Our ratio is now 17/12:7/30, so our next task is to find the lowest common denominator of our two fractions.

Ratio To Fraction

To keep the values ​​of our fractions the same, we need to multiply both the numerator and denominator by the same amount. For that:

How To Simplify Ratios With Fractions

Now we have a common denominator, we can leave it out and write our ratio using numerators.

In our example, the highest common factor is 1, so the ratio is already in its lowest form.

How To Simplify Ratios With Fractions

How To Solve A Proportion

Here we have two proper fractions, so we can go straight to step two and find the lowest common denominator. Since 68 is a multiple of 17, this is our answer:

Now find the highest common factor, in this case 3, and to simplify, divide both terms of the ratio:

How To Simplify Ratios With Fractions

We have a mixed fraction here, so we need to convert it to an improper fraction first. Multiply the whole number by the denominator of the fraction:

Ratio And Proportion.

Now find the lowest common denominator of the two fractions, in this case 18. Keep the value of the fractions by multiplying both the numerator and denominator by the same value:

How To Simplify Ratios With Fractions

Before working with ratios involving fractions, first master the art of simplifying ratios involving whole numbers.

You will need to understand this process in order to express the relationship in its lowest form, so make this the starting point of your review. In a numerical reasoning test, you have to work quickly, and the faster you are in this process, the faster you will be in general.

How To Simplify Ratios With Fractions

How To Add Fractions To Whole Numbers: 4 Steps (with Pictures)

A ratio that contains both mixed and real fractions can be intimidating, causing you to draw a blank and eat up your time.

This is easily avoided if you are confident about converting mixed fractions to improper fractions. All you have to remember are two simple rules: multiply the whole by the denominator and add to the numerator.

How To Simplify Ratios With Fractions

Multiplying quickly is key to finding the lowest common denominator. Knowing your time charts is also helpful in identifying the highest common factor in relationship terms.

Simplifying Ratio Fractions Worksheet

Always make sure you understand the question and watch out for costly mistakes. If your question is presented as a word problem, write it as a numerical equation and check that each part of the ratio is correctly placed.

How To Simplify Ratios With Fractions

For example, “what is 3/6 to 5/8 in simplest form?” should be written 3/6:5/8, with the first digit marked as the previous term.

Similarly, when converting fractions, check the numerators and denominators, and when writing your final answer, make sure the terms of your ratio match the question.

How To Simplify Ratios With Fractions

Math Example Fraction Properties Simplifying Fractions Example 9

Our platform is full of tests, tips, articles and videos that we are happy to share with you. All of our content is developed by industry experts who draw on decades of experience in psychometric testing.

To find out why more than 9 million people use our platform, start by taking our free practice tests.

How To Simplify Ratios With Fractions

If you are really serious about getting a top job, then your first step is to master the psychometric tests. Our platform contains 1000 questions written by industry experts, all with full explanations that will not only improve your performance but help you quickly overtake all your competitors. Upgrade to unlock our full testing platform and improve faster than ever before. To simplify a relationship means to reduce the relationship to the smallest, simplest terms. Sometimes ratios can be large numbers and difficult to work with, especially when you start doing things like adding, subtracting, dividing, or multiplying ratios.

Ratio To Fraction Calculator

Before we get into how to simplify ratios, we need to quickly review finding factors, because factors are an important part of the simplification process. What is a factor?

How To Simplify Ratios With Fractions

A factor is a number that is exactly divisible by another number without any remainder. In other words, these are the numbers that are multiplied to equal the given number. Example 1: What are the factors of 6?

Let’s identify all the numbers that can be multiplied to get the answer 6 or that can be divided evenly by 6.

How To Simplify Ratios With Fractions

Solving Ratio Problems

So the factors of 6 are 1, 2, 3 and 6. Example 2: What are the factors of 16?

For more information on how to find factors, click this link to my post and video on Finding Factors and Greatest Common Factor. A step-by-step guide to simplifying relationships

How To Simplify Ratios With Fractions

When it comes to simplifying ratios, it really doesn’t matter which of these ways you write them, they can all be simplified using the same method, so choose the one that makes the most sense to you.

How To Cross Multiply: 2 Simple Methods (with Examples)

Let’s walk through these steps using our 3 lemons to 6 limes ratio example. Step 1:  Find the factors of the numbers in our ratio

How To Simplify Ratios With Fractions

Sometimes called the greatest common divisor (GCD). Whatever you want to call it, we’re looking for the largest factor that occurs in both numbers in our ratio—3 and 6 in this example.

Our greatest common factor in our example will be 3 because 3 is the greatest factor present in both 3 and 6. Step 3:  Divide the numbers in our ratio by the greatest common factor

How To Simplify Ratios With Fractions

Question Video: Simplifying Expressions

Dividing 3 3 gives 1 and 6 3 2. The reduced or simplified ratio 3 : 6 is now 1 : 2. How to simplify ratios when the numbers are large

Since these numbers are large and likely have many factors, the easiest way to simplify is to divide both the numerator and denominator by the same numbers until they reach smaller numbers.

How To Simplify Ratios With Fractions

We’ve simplified the ratios a lot since our original ratio, but if you look at the ratio we’re left with, you can see that we could lower it even further. We see that 5 is a factor of both 5 and 15.

Equivalent Ratios Worksheet, Defintion, Examples

You can use this method when the numbers are very large. If you divide both numbers by the same amount, you can repeat this process until the numbers are small enough to be factored using normal factors.

How To Simplify Ratios With Fractions

Be sure to watch my video on how to simplify your relationships. In the video, I go over several examples, including the ones we just covered. Once you’ve watched that, watch my video below where I give you some examples to complete with the answers.

For more experience simplifying ratios, go to the additional resources page and get a free printable worksheet with the answers. Here you will find a wide variety of graded printable fraction worksheets to help your child practice converting fractions to their simplest form.

How To Simplify Ratios With Fractions

Simplifying Ratios Worksheet

It involves dividing both the numerator and denominator by a common factor to reduce the fraction to an equivalent fraction with the smallest possible numerator and denominator.

The Simplifying Fractions Calculator also shows you worked examples of how to simplify a fraction if you’re really stuck!

How To Simplify Ratios With Fractions

Fraction equivalence, converting fractions to decimals and properties of fractions are all explored in our fun games.

Simplifying Ratios No Units

At the end of the quiz, you will be able to see your results by clicking “View Score”.

How To Simplify Ratios With Fractions

This will take you to a new website where your results will be displayed. You can print a copy of your results from

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