Calculator™ © - Free Online Calculators

Online Calculators since 2009

# Ratio Simplifier Calculator

The ratio simplifier calculator, opart of our suite of ratio calculators, is a user friendly and time saving online calculator to simplify the ratios in the form of A : B. the two constituents of the ratio can range from integers and decimals to simple and mixed fractions. The ratio values can also positive, negative and of different types where one value is an integer and the other value is a fraction.

 Ratio Simplifier Precision (Decimal Places)0123456789101112131415 Enter whole numbers or decimals or fractions Ratio Numerator : Ratio Denominator : ## What is Ratio Simplification?

Suppose you are given a ratio of 15 : 9, this means for every 15 of A, there will be 9 of B. Now, you may consider this ratio the way it is, but here's the catch; the ratio is not simplified.

The simplified version of the above ratio is 5 : 3, a number that is easier to work with.

## How to Simplify the Different Types of Ratios?

There are various methods to solve a ratio, and the method we need to choose depends upon the type of ratio. There are three different types of ratios as mentioned below:

### Basic Ratio

Suppose you are given a basic ratio of 15:21

In such a case, you need to reduce it to its smallest integral form. The first step is to see if there's any prime number in the given ratio. Here, we have 15:21, and none of them is a prime number.

So, we will begin with finding out the factors of either side:

15 = 1, 3, 5, 15v
21 = 1, 3, 7, 21

Of all the factors for each of the given numbers in the ratio, 1 & 3 are the common factors.

Now, we need to find the greatest common factor (GCF) or highest common factor (HCF), which is 3.

So, we will divide both sides by 3

15/3 : 21/3
5 : 7

So, the simplified ratio of 15 : 21 is 5 : 7.

### Simple Algebraic Ratio

When variables are included in one or both sides of the ratio, such a ratio is known as an algebraic ratio. To understand how to simplify an algebraic ratio, let's take an example of the following ratio:

18x² = 72x

To simplify the ratio, start with finding the GCF or the HCF of the numerical values of the above ratio. To that, you'll first need to find the factors of 18 and 72:

18 = 1, 2, 3, 6, 9, 18
72 = 1, 2, 3, 4, 6, 9, 12, 18, 24, 36, 72

Now, from the factors mentioned above, we can see that the GCF or the HCF is 18.

Dividing both sides by 18, we have:

x² : 4x

Dividing both sides by x for further simplification, we have,

x : 4

### Polynomial Ratio

The most complex ones amongst all the three types of ratios, both the parts of a polynomial ratio are two equations that you'd need to work on. For example:

x² - 8x + 15 : x² - 3x - 10

Now that's completely mind blowing, right? Stay with us while we simplify the polynomial ratio for you

Separate the left hand side (LHS) into factors:

x² - 3x - 5x + 15
x(x - 3) -5(x - 3)
(x - 3)(x - 5)

Similarly, we'll separate the right hand side (RHS) into factors:

x² + 2x - 5x - 10
x(x + 2) - 5(x + 2)
(x + 2)(x - 5)

Now, we'll compare LHS : RHS,

(x - 3)(x - 5) : (x + 2)(x - 5)

Taking the (x-5) common out,

The result is:

(x - 3) : (x + 2)

## How Ratio Simplifier Calculator Works?

Developed by iCalculator, the ratio simplifier calculator is a simple ratio calculator designed to simplify basic ratios.

All you need to do is simply enter the integral values of the LHS and RHS of the basic ration you want to simplify. A second box will appear, showing your results at a lightning fast speed.

## Ratio Simplification in Real Life

Whenever we compare which of the two cereal boxes is more cost effective at a grocery store, we tend to simplify ratios. Confused? Don't be, consider a box of cereal costs \$3 for 300 grams and the other box is \$4 for 500 grams. You'll immediately notice that the \$4 box gives you more value per dollar. You compared ratio in real life without realizing it.

At the same time, while calculating the mileage or the average of your car, you divide the distance travelled by the quantity of fuel used. Once again, you are calculating the ratio.

## Conclusion

With a plethora of various online ratio calculators available to you at iCalculator, you don't need to worry about doing manual calculations at all. The ratio simplifier calculator is a simple yet extremely efficient math calculator to help you focus on your work better. Let the online tool do the calculations for you.

## Math Calculators

You may also find the following Math calculators useful.