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Ratio to Percent
In math, the ratio to percent conversion is very useful to make comparisons of each part with the whole. A ratio compares any two parts of a whole. For example, the ratio of sugar and salt in a solution is 3:1. It is telling us that in the solution, sugar is three times that of salt. Percentages are a very specific type of ratio. A percent compares any one part of the whole against the whole, instead of making comparisons with the individual parts with each other. In the same example, the percentage of sugar in the solution is 75% and the percentage of salt is 25%. But how did we convert 3:1 into percentages? Let us learn about ratio to percent conversion in this article.
|1.||Ratio to Percent Formula|
|2.||How to Convert Ratio to Percent?|
|3.||Ratio to Percentage Table|
|4.||FAQs on Ratio to Percent|
Ratio to Percent Formula
There is a formula to convert the ratio to a percent. It can be applied directly with any values to get the required percentage. The ratio to percent formula is given below:
Percentage = Ratio × 100
It is expressed with a percentage symbol (%).
How to Convert Ratio to Percent?
Before learning about the conversion of ratio to percent, let us briefly discuss the meaning of ratios and percents first. A ratio is a relation or a comparison between two quantities of the same kind and of the same unit. There are three ways to express ratios, which are part to part ratios, part to whole ratios, and whole to part ratios. Part to part ratios compares the quantity of two parts with each other. An example of this relationship is given at the beginning of this article (the ratio of sugar and salt in a solution is 3:1). Another example could be the ratio of the number of boys and girls in the class - 2:3. Taking the same example, if we represent the ratio of the number of boys and the total number of students, the ratio would be 2:5 (as whole = total number of parts = 2 + 3= 5). This is an example of a part to whole ratio. The same ratio, if represented as 5:2, is an example of a whole-to-part relationship.
To convert the ratio to percent form, we need to first identify the ratio. And then we can apply that ratio in the above 'ratio to percent formula' to get the value of percentage. For example, if it is given that the ratio of apples to oranges in a basket is 5:8 and we have to find the percentage of apples in the basket, then we need to first find the ratio of apples to fruits in the basket. The total number of fruits in the basket is 5 + 8, which is 13 fruits. So, the ratio of apples to fruits is 5:13. Now, we can find the percentage as,
Percentage = [Ratio × 100] %
Percentage = 5/13 × 100
Percentage = 38.46%
In the same way, the ratio of oranges to fruits is 8:13. The percent of oranges in the basket is [8/13 × 100] % = 61.54%. Look at one more example of converting 1:4 to percent in the image below.
To conclude, the steps to convert a ratio to a percent are given below:
- Step 1: Identify the ratio.
- Step 2: Express the ratio a:b in the form of a fraction a/b.
- Step 3: Multiply the fraction by 100.
- Step 4: Simplify and write the answer with the percent symbol (%).
Ratio to Percentage Table
The ratio to percent table is a quick way to provide the percentage values of some commonly used ratios. Look at the ratio to percentage table given below.
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Examples on Ratio to Percent
Example 1: The primary grade students of a school are divided into two houses - red house and blue house. If the ratio of students of the blue house to the red house is 4:5, find the percentage of blue house students in the school using the ratio to percent conversion formula.
Solution: It is given that all the students of primary grades in the school are divided into two houses. The ratio of blue house students to the red house is 4:5. So,
Total parts of the whole = 4 + 5 = 9
The ratio of blue house students to the total students = 4/9
So, the percentage of blue house students in the school = 4/9 × 100% = 44.44%
Therefore, the required percentage is 44.44%.
Example 2: What will be the percentage of orange juice packets in a bucket containing juice packets, if its ratio is 3:8?
Solution: The given ratio of orange juice packets in a bucket containing juice packets of different flavors is 3:8. So, using the ratio to percent formula - percentage = [ratio × 100] %, we get, percentage = 3/8 × 100 %.
Percentage of orange juice packets = 3/8 × 100 %
= 300/8 %
Therefore, the required percentage is 37.5%.
Example 3: Convert 3:1 to percentage, using the steps of ratio to percent conversion.
Solution: The given ratio is 3:1. The steps of converting this ratio to percentage are given below:
Step 1: Write the ratio in fractional form. So, 3:1 = 3/1.
Step 2: Multiply the fraction obtained by 100. This implies 3/1 × 100.
Step 3: Simplify it and attach a percent sign with the answer. So, 3/1 × 100 = 300%.
Therefore, 3:1 = 300%.
FAQs on Ratio to Percent
How to Convert Ratio to Percent?
To convert a ratio to percent form, there are two ways which are explained below:
- Multiply the antecedent and consequent of the given ratio by a number such that the consequent will become 100. After that, the antecedent will be the required percentage. This method is suitable for ratios in which the consequent is a factor of 100. If not, then use the method explained below.
- Write the ratio (a:b) in the fractional form (a/b) and multiply it by 100. Simplify it and attach the percent symbol.
How to Convert Percent into Ratio?
To convert a percent to ratio, follow the steps given below:
- Remove the percent sign and divide the given number by 100. So, x% = x/100.
- Simplify it, if possible.
- Write the fraction obtained in the ratio form. So, x/100 = x:100.
What are the Steps to Convert Ratio to Percent?
The steps to convert ratio to percent are given below:
- Write the ratio in fractional form.
- Multiply it by 100.
- Simplify the expression and attach a percent sign with the answer.
What is Ratio to Percent Formula?
The ratio to percent formula is Percentage = Ratio × 100%. This formula helps us to convert any ratio to percent form easily.
What Percentage is a 3 to 1 Ratio?
A 3 to 1 ratio can be written as 3:1. It can be written as fraction 3/1. Multiply it by 100. It implies, 3/1 × 100 = 300%. Therefore, the 3 to 1 ratio is equivalent to 300%.
How to Convert Ratio to Percent with Three Numbers?
When three quantities are given, let's say if the ratio of the number of apples to oranges to melons in a fruit basket is 3:2:4. Then, to find the percentage of apples in the basket, we first find the ratio of apples to the total number of fruits. The ratio of apples to the total number of fruits is 3:9 or 1:3. Now, 1:3 = 1/3 × 100% = 33.33%. This is how we convert ratio to percent with three numbers.