Exams Prep Master
When comparing quantities, we commonly use the terms fractions and percent. Percentage or percent denotes the fractions of a whole, whereas percent denotes the amount of the entire and is easier to remember than a fraction. Consider a class of 38 pupils, 23 of them female, to better comprehend the notion of fraction and percent. It is 23 out of 38. In order to simplify: 23/38 = 0.60526315789473684210526315789474 or about 60%. Here, we will learn how to convert fractions to percentages, understand the fraction to percent conversion formula, and discuss some important questions.
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Key takeaways: Fraction, percentage, Percentage Formula, Convert Fraction to Percent
What is a Fraction?
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The term fraction denotes how many parts of a whole quantity are split by the whole quantity, or how many parts of a specific size are divided by the whole quantity. The Numerator, which is written above the line, and the Denominator, which is written below the line, make up a fraction.
The denominator shows how many of those parts make up a whole, while the numerator shows how many of those parts make up a whole. Because zero pieces can never make up a whole, the denominator of a fraction can never be zero.
For instance, the fraction 1/2 is a simple fraction. The numerator '1' denotes that the fraction represents one equal portion, while the denominator '2' denotes that the entire is made up of two parts.
Check also: NCERT Solutions for Class 6 Mathematics Chapter 2: Whole Numbers
What is the Percentage?
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The percentage refers to a ratio or a figure that is stated as a fraction of a whole number. The percentage sign percent is used to represent it. Here's an example to help you understand how the percent indicates a fraction of a hundred. The fraction 35/100 can be used to express 35%. In class, 50 percent of the students were male, meaning that 50 students out of every 100 were male.
Percentage Formula
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A % is a figure or a ratio that has a denominator of 100. The formula for calculating percentages is as follows:
Percentage = \(\frac{\text{Given value}}{\text{Total value}} \times 100\)
For example, if we wish to find 10% of 150, we can do so as follows:
(10/100) × 150 = 1500/100
= 15
As a result, 10% of 150 equal 15.
How Fractions and Percentages are Used for Comparing Two Quantities?
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Consider the following scenario to better comprehend this. Henna received 320 points out of 400, or 320/400, on her annual test report, whereas her buddy Mona received 350 points out of 500, or 350/500. When we compare their grades, we can see that Mona has a higher grade than Henna. However, we cannot determine who fared better in their yearly exam only based on their earned scores because the maximum marks out of which they received the marks are not the same. To do so, we must convert their obtained fractional marks into percentage equivalents.
Check also: Class 6 Important Formulas and Examples
How to Convert Fraction to Percent?
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To convert a fraction to a percent, simply multiply it by 100 and then reduce it to percent. Here are some examples that will help you learn how to convert a fraction to a percentage. Follow the steps below to convert a fraction to a percentage:
To convert a fraction to a percentage, perform these steps:
Step 1: Convert the provided fraction to the decimal equivalent (refer to Note).
Step 2: To get the required percent amount, multiply the obtained decimal number by 100.
Note: The following steps are used to convert fractions to their decimal equivalents:
Step 1: Divide the fraction's numerator by the denominator.
Step 2: The decimal equivalent of a given fraction is the quotient produced after division.
Read more: NCERT Solutions for Class 6 Math
Things to Remember
- A fraction is a number that represents a portion of something larger. A single object or a group of objects might make up the whole.
- If the numerator and denominator of a fraction have no common factor save 1, it is said to be in the simplest (or lowest) form.
- Every fraction has a number line point connected with it. A number line can be used to display fractions.
- The numerator of a valid fraction is less than the denominator. Improper fractions are those in which the numerator is higher than the denominator.
- When an improper fraction is stated as a mixture of a whole and a part, it is referred to as a mixed fraction.
- There are many comparable fractions for each proper or improper fraction. We can multiply or divide both the numerator and the denominator of a given fraction by the same number to find an equivalent fraction.
Sample Questions
Ques. A 1-liter sugar solution contains 0.8 percent sugar. Ryan wants to know how much sugar is in the solution by converting percent to fraction. (3 Marks)
Ans. We must convert 0.8 percent to a fraction in order to discover the solution. After eliminating the percent symbol, divide the supplied percentage by 100 to convert to a fraction. As a result, we get 0.8/100. Multiply both 0.8 and 100 by 10 to eliminate the decimal point. 8/1000. The GCF of 8 and 1000 is also 8. As a result, (8/8)/(1000/8) = 1/125.
As a result, 0.8 percent equals 1/125 of the total sugar in the solution.
Ques. James offers a 14 percent discount on Rs.2500 laptop. What will the discounted price be a portion of? (2 Marks)
Ans. To calculate the discount fraction, we must convert 14 percent to a fraction. To do so, we must remove the percent sign from the supplied integer and divide it by 100. We get 14/100 by deleting the percent symbol. 14 and 100 have a GCF of 2. (14/2)/(100/2) = (7/50)
As a result, 7/50 is a fraction of the discounted price.
Ques. Mia competed in a variety of sports and won 8 out of 12 of them. Can you calculate her winning % using the fraction-to-percentage formula? (2 Marks)
Ans. The number of events she won as a percentage of the total number of events she competed in is 8 out of 12.
8/12 = 8/12 × 100 %
= 2/3 × 100 %
= 66.67 percent
As a result, Mia won 66.67% of the races.
Ques. A typist's monthly wage is Rs 15625. Determine his new salary if he receives a 12% raise. (2 Marks)
Ans. Rs 15625 is the total monthly compensation.
Increase in percentage = 12%
12 % of the amount = 12 % of Rs 15625
= Rs 15625 × 12/100 = Rs 1875
New Salary = Rs 15625 + Rs 1875
= 17500 rupees
As a result, the typist's new salary is Rs 17,500.
Ques. In one examination, 72 percent of the people who took it passed. Find the total number of examinees if the number of failures is 392. (3 Marks)
Ans. Assume there were 100 people who took the exam.
The total number of candidates who passed is 72.
The number of failed candidates is equal to (100 – 72) = 28.
If 28 of the candidates fail, the total number of candidates is 100.
If 392 contestants fail, the total number of candidates is 100 / 28 × 392 = 1400.
As a result, there are 1400 examinees in total.
Ques. What is the mathematical definition of a percentage? (2 Marks)
Ans. When it comes to mathematics, the percentage can be used in a variety of ways. Consider a number or ratio that may be expressed as a fraction of 100 to define % in mathematics. If you need to determine the percentage of a number, divide it by the number it was taken from, then multiply it by 100. In other words, the percentage can be expressed as a part per hundred.
Ques. How to calculate the percentage of marks? (2 Marks)
Ans. You'll need two things to figure out the percentage of your marks: your marks and the total number of marks (or maximum marks). You can easily find the proportion of your marks once you have these two things. To begin, divide the number of marks you received by the maximum number of marks, then multiply the result by 100.
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