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Ratio to Percentage is used to convert a number which is in the form of a ratio and represents it as a percentage.
- To compare two quantities of the same unit, the ratio is used.
- Percentage, on the other hand, is a type of ratio in which the value of the whole is always equal to 100.
- There are different instances when ratio and percentage come into play.
- Consider a solution with 3:1 sugar and salt constituents.
- The 3:1 is a ratio that shows that the sugar is three times that of salt.
- In the fractional form, we would say that the sugar constituent is 75% in the solution and the salt constituent is 25%.
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Key Terms: Ratio, Percentage, Whole number, Integer, Ratio to Percentage formula, Numerator, Denomination, Decimal, Fraction, Percent
Ratio
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A ratio indicates the number of times one number contains another.
- For example, if a bowl of fruit contains eight oranges and six lemons.
- The orange-to-lemon ratio is eight to six (that is, 8:6, which is equivalent to the ratio of 4:3).
- Similarly, the ratio of lemons to oranges is 6:8 (or 3:4), while the ratio of oranges to total fruit is 8:14 (or 4:7).
- A ratio can be considered as an ordered pair of numbers, a fraction with the first number in the numerator and the second in the denominator.
The ratio of numbers A and B can be represented as
\(A:B \; \;or \; \; \frac{A}{B}\)
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| Related Concepts | ||
|---|---|---|
| Integration by Partial Fraction | Fundamental Theorem of Calculus | Types of Relation |
| Determinant Formula | Differentiation and Integration Formula | Relation and Function |
Percentage
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A percentage is a number or ratio indicated as a fraction of 100.
- It is commonly denoted by the percent symbol (%).
- If we need to calculate the percentage of a number, divide it by the whole and multiply by 100.
- Therefore, the percentage denotes a part per hundred.
- The word percent means per 100.
- A proper 100% defines a whole.
To calculate the percentage, divide the number by the total value and multiply the result by 100.
Percentage formula = (Value/Total value) × 100
Conversion of Ratio to Percentage
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The conversion of ratio to percentage helps us to acquire accuracy in combinations of materials or in calculating the percentage score in a test.
- Ratios are sometimes used to represent parts of a whole.
- They can also be expressed numerically as percentages.
The process to convert the ratio into percentages is as follows:
- Step 1: Express the ratio of the form a:b to that of fraction in a/b.
- Step 2: To convert the fraction into a percentage, multiply it by 100.
- Step 3: After converting it, add the symbol % to the final value.
Ratio to Percentage Formula
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With the help of the ratio to percentage formula, the conversion becomes easy. The formula can be given by:
Percentage = Ratio × 100
The percentage is ended by the symbol %.
Ratio to Percent ExamplesExample 1: Convert the ratio of 4:5 into a percentage. To convert the ratio, follow the steps:
Therefore, the ratio of 4:5 can be converted to 80%. Example 2: Convert the ratio 2:1 into percentage. To convert the ratio, follow the steps:
Therefore, the ratio of 2:1 can be converted to 200%. |
Ratio to Percentage Table
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The percentage value for some of the most commonly used ratios is shown in the ratio to percentage table.
| Ratio | Fractional Form | Conversion | Percentage |
|---|---|---|---|
| 1:2 | 1/2 | 1/2 ×100 | 50% |
| 1:3 | 1/3 | 1/3 ×100 | 33.33% |
| 1:4 | 1/4 | 1/4 ×100 | 25% |
| 1:5 | 1/5 | 1/5 ×100 | 20% |
| 1:10 | 1/10 | 1/10 ×100 | 10% |
| 2:5 | 2/5 | 2/5 ×100 | 40% |
| 4:5 | 4/5 | 4/5 ×100 | 80% |
| 1:50 | 1/50 | 1/50 ×100 | 2% |
| 1:100 | 1/100 | 1/100 ×100 | 1% |
Solved Examples
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Ques. The angles of a triangle are in the ratio 1:1:2. Find the value of each angle. What will be the percentage of each angle?
Ans. Given the ratio of the angles of a triangle is 1:1:2
Total parts = 1 + 1 + 2 = 4 parts.
We know, the sum of angles in a triangle is 180º.
Therefore, the measure of the first angle = 1/4 x 180 = 45º
Percentage of the first angle = 1/4 x 100% = 25%
The measure of the second angle = 1/4 x 180 = 45º
Percentage of the second angle = 1/4 x 100% = 25%
The measure of the third angle = 2/4 x 180 = 90º
Percentage of the second angle = 2/4 x 100% = 50%
Ques. Convert the ratio 5:4 into a percentage.
Ans. The ratio 5:4 in fraction form can be written as 5/4.
Using the ratio-to-percentage conversion formula, we get
Percentage = Ratio x 100%
⇒ Percentage = 5/4 x 100 = 125%
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Things to Remember
- A percentage is used to represent a number as part of a whole. Percentage means ‘per hundred’.
- When anything is 100%, it means it is the whole.
- The ratio is a comparing quantity that compares two values of the same part.
- The ratio is of three forms: part-to-whole ratio, part-to-part ratio, and whole-to-part ratio.
- The three steps of converting a ratio into a percentage include representing the ratio in a fraction, multiplying it by 100, and adding the symbol of % to the final value.
- The formula for converting a ratio to a percentage is Percentage = Ratio × 100.
- To show that a value is a percentage, it is necessary to add the percentage symbol.
Sample Questions
Ques. What is the formula for the ratio to percentage conversion? (2 Marks)
Ans. The formula for the ratio to percentage conversion is given by
Percentage = Ratio x 100%
Ques. Define Ratio. (1 Mark)
Ans. A ratio indicates the number of times one number contains another.
Ques. Convert the following ratio of 1:2 into a percentage. (3 Marks)
Ans. The ratio given is 1:2
- Converting the ratio of 1:2 into a fractional form that is 1:2.
- Multiplying 1/2×100 which gives the result 50.
- Adding the symbol of percentage % after the result. The final answer would be 50%.
Therefore, the ratio of 1:2 can be converted to 50%.
Ques. Convert the following ratio of 2:5 into a percentage. (3 Marks)
Ans. The ratio given is 2:5
- Converting the ratio of 2:5 into a fractional form that is 2/5.
- Multiplying 2/5×100 which gives the result 40.
- Adding the symbol of percentage % after the result. The final answer would be 40%.
Therefore, the ratio of 2:5 can be converted to 4%.
Ques. All the angles of a triangle are given in the ratio of 1:1:4. Estimate the values of each angle. Calculate the percentage also. (3 Marks)
Ans. The angles of the given triangle are in ratio 1:1:4
Total parts= 1+1+4= 6 parts
As we know, the sum of all the angles in a triangle is 180.
Therefore, estimating the first angle= 1/6 ×180 = 30.
Estimating the second angle= 1/6 ×180 = 30.
Estimating the third angle= 4/6 ×180 = 120.
Now, converting these angles into a percentage, we get:
The first angle is 1/6 ×100 = 16.6 %.
The second angle is 1/6 ×100 = 16.6 %.
The third angle is 4/6 ×100 = 66.6 %.
Ques. The ratio of Varun’s monthly expenditure to his savings is in the ratio 7:3. Estimate the salary percentage he spent and saved. (2 Marks)
Ans. The ratio of Varun’s expenditure and savings is 7:3. Therefore, total parts= 7+3=10.
Salary spent in parts is 7/10
Salary saved in parts = 3/10
Expenditure percentage= 710 ×100 = 70%.
Saving percentage= 310 ×100 = 30%.
Ques. Estimate 75% into ratio. (2 Marks)
Ans. 75% can be written as 75/100 in the fractional form.
In the simplest form, 75/100= ¾.
Therefore, the ratio of 75% is 3:4.
Ques. In a primary school, the students are divided into two houses- the yellow house and the red house. If it is given that the ratio of students present in the yellow house to the ratio of students present in the red house is 4:5, then calculate the percentage of students in the yellow house with the help of the ratio to percentage formula. (3 Marks)
Ans. The given ratio of the yellow house to the red house is 4:5.
As the students are separated into two houses, the total parts are 4+5=9.
Therefore, the ratio of students present in the yellow house is 4/9
Now, the percentage of students present in yellow house= 4/9 ×100 = 44.44%
Henceforth, the required answer is 44.44%.
Ques. Calculate the percentage of pineapple juice packets from a bucket containing the juice packets in a ratio of 3:8. (2 Marks)
Ans. Given: The ratio of 3:8 of the pineapple juice packets to a bucket containing juice packets of several flavors.
Calculating the percentage of pineapple juice packets using the ratio to percentage conversion formula, we have:
Percentage= 3/8 ×100 = 37.5 %
Ques. Convert the given percentage into the ratio form: 25%. (2 Marks)
Ans. 25% can be written as 25/100 in the fractional form.
In the simplest form, 25/100= 1/4.
Therefore, the ratio of 25% is 1:4.
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