How do you express the share of two or more things in numbers? How do you indicate how big or small a quantity as compared to the other? Wondering what the answers are! In mathematical terms, the ratio is used to compare two quantities relatively. The division is used for the comparison. Find out some facts and concepts about ratios in the article further.
What is a ratio?
The ratio is defined as the comparison of two quantities. The units of both quantities must be the same. It is used to indicate the share of one quantity concerning the other.
For instance, the ratio of two quantities a and b is their division such that a/b is denoted as a:b. It is read as a is to b.
For example, consider a string with four red beads and seven yellow beads. Then the ratio of red beads to yellow beads is 4:7, expressed as 4/7. Here four is known as the ‘antecedent,’ and seven is known as the ‘consequent.’
Classification of ratios
Ratios can be broadly categorized into two types. The first is the part-to-part ratio, and the other is the part-to-whole ratio.
- the part-to-part ratio shows the relation between two distinct groups or entities.
For example, there are 20 girls and 25 boys in a class. So the part-to-part ratio of boys to girls is 25:20.
- Part-to-whole ratio: This type shows the relation between a specific group to a whole.
For example, in 20 people, if 12 like to read, then the part-to-whole ratio is 12:20.
Calculation of ratios
Calculating the ratio is an easy task. Follow the steps given below to do that.
Consider an example where a flower bouquet requires 15 yellow roses and 20 red roses.
Step 1: Determine the quantities of both scenarios. For the considered example, they are 15 and 20.
Step 2: Write the quantities in the fraction form. Here it comes to 15/20.
Step 3: Try to simplify ratios. This article further discusses how to simplify ratios.
Step 4: Simplifying ratios express the ratio in the lowest possible number. For the example considered here, the simplified ratio is 3/4.
What does it mean to simplify ratios?
Huge numerical figures often tend to increase complexity. Higher values seem to be difficult to understand. It is, therefore, to express values in lower numbers.
Higher values of ratios will also create confusion. It is, therefore, better to express ratios in the lowest possible numbers. The conversion of higher values of ratios into lower values is what is termed simplifying ratios.
How do you simplify ratios?
Now that we know simplified ratios let us see how to simplify ratios. Later in this article, we will discuss concepts like ratio simplifiers and simplifying ratio calculators.
To simplify ratios is to write a ratio in the lowest possible form. Like fractions, ratios can also be simplified. Below are the two steps that help you answer the question ‘how do you simplify ratios?’
Step 1: Find the greatest common factor. Find the numbers that divide both sides of the ratio completely. Select the highest number from the list of the numbers that divide the numbers. This highest number is the greatest common factor.
Step 2: Divide both sides of the ratio by the greatest common factor. Dividing both sides of the ratio by the greatest common factor will reduce the ratio to its smallest form. For example: Consider a ratio of 12:8 to be simplified. The factors that will completely divide the numbers 12 and 8 are 2 and 4. The greatest of the two factors is 4. Divide both sides of the ratio by 4. The ratio you get after simplifying is 3/2. This is the simplified form of the ratio.
How to simplify a ratio with three numbers?
Simplifying a ratio with three numbers is similar to that of two numbers. The only difference is that you need to find the greatest common factor for all three numbers. For example, if you have to simplify a ratio. 20:5:30, then first find the common factors that will divide all three numbers in the given ratio. The only factor that will come in this case is 5. Divide all three numbers by 5. The simplified ratio is 4:1:6. You can also use a ratio simplifier for the purpose.
How do simplify a ratio with large numbers?
Simplifying a ratio for large numbers is more required as working with large numbers increases complexity. Simplify ratios with large numbers for ease in working with them. First, list all the factors for all the numbers on the ratio. Then divide the numbers by the common factors. Repeat these steps till you get the smallest numbers in the ratio. Consider an example of a ratio of 200:150. Divide both the numbers first by 10. You will get 20/15. Now find the greatest common factor, which is 5. Dividing both sides of the ratio by 5. The simplified form of the ratio is 4:3. Simplifying ratios which have large numbers can be a long process. Simplifying ratio calculators can help you do it easily.
How do you simplify ratios that have fractions involved?
To simplify ratios involving fractions, you need first to simplify fractions. Convert the fractions into equivalent fractions to make their denominators equal. Write the ratios with only the denominator. Then simplify this ratio with only the numerators by dividing them by the greatest common factor. For example, if the ratio to be simplified is ⅔:¾ Then make these fractions equivalent by making their denominators the same. In this case, it will come to 8/12:9/12. Then, you can write the ratio as 8:9. You can now simplify this resultant ratio. A ratio simplifier calculator will do the job more easily.
How do you simplify a ratio involving decimals?
To simplify a ratio with decimals, convert the numbers into whole numbers by multiplying them by 10, 100, 1000, or whatever is applicable.
Divide the numbers by the greatest common factor, and you will get the simplified ratio. Converting the decimals into whole numbers might result in large numbers in the ratio. In that case, follow the steps to simplify ratios with large numbers. Using a ratio simplifier will reduce the efforts to simplify the ratios with decimals. Consider a ratio of 0.4:1.2. Multiply both sides of the ratio by 10 to convert them to whole numbers, and the new ratio is 4:12. Now simplify this ratio by finding the greatest common factor and dividing the numbers by that factor. The simplified ratio is 1:3.
Why simplify ratios?
It is always easier to work with smaller numbers. Simplifying ratios will give you smaller numbers to be worked on. Simplified ratios allow you to perform various mathematical operations on them. Simplified ratios are also convenient as they do not contain decimals or fractions. It is, therefore, necessary to simplify ratios.
What are ratio simplifiers?
We have already learned what is meant by simplifying ratios and how to simplify ratios. Simplifying ratios is necessary for the easy work they provide with all the mathematical stuff. Though simplifying ratios manually is not a tough process, it can be tiring at times. Simplifying ratios with fractions, decimals, or ratios that have larger numbers can be a long process. Therefore, it is advisable to use ratio simplifiers or simplify calculators to simplify ratios.
Ratio simplifiers are specially designed software that works on simplifying ratios. These ratios simplify calculators that are available online, and you can use them for free. There are various websites where you can simplify ratios.
They are designed to work on all types of ratios. Ratio simplifiers are provided with functions that enable you to work on all types of ratios, including ratios that have decimals, fractions, large numbers, and two or more two numbers.
You have to give the required input data and sit back while you get the desired output.
How does the ratio simplify calculators work?
There are many ratio amplifiers or simplified calculators available online which can be used for free. They are very user-friendly. These calculators give the simplified form of the ratios you want. A few of them are also engineered to give a detailed description of how the result is calculated. Follow the below steps to use a ratio simplifier.
- Type the input ratio in the designated slots. Input the data in whatever form it is. The input ratios can have decimals in fractions as well.
- Click on the calculate option.
- Sit back and wait for the resultant ratio.
A simplified ratio calculator can be used to simplify a ratio even if one side of the ratio has a decimal and the other has a fraction.
The calculators also follow the same process, which you will follow manually to simplify a ratio. However, it would give you faster results.