Instructor Note: This unit would deal with the basic nuances of the ever important topic Percentage. Owing to its importance, it becomes inevitable to form a strong foundation and holistic learning of the same. Learners get to understand basic concepts of percentage and its practical usage. It would enable them to express a number, fraction or ratio out of every hundred. Participants get to learn how percentage facilitates the expression of huge data in its simplest form. Trainer is required to deliver this unit under an engaging environment by using practical examples and competitive activities.
(After explanation of concept & practice) Display/distribute handout consisting of questions. The Foundation section will compromise 4 questions. Instruct students that they will be given 8 minutes to discuss among themselves & solve these 4 questions, whichever group solves maximum problems wins maximum points on the points table (refer opening protocol). Award 5 marks for each correct answer given by a group. Move around the class to check procedures used by students to solve problems. Once time is up, provide solutions and explanations for each question.
Switch to moderate level. This section comprises 3 questions and cumulative time allotted will be 10 minutes. All other instructions remain the same.
Switch to HOTS. This section comprises 3 questions and cumulative time allotted will be 15 minutes. All other instructions remain the same. |
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Section 1: Understanding Percentages.
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Percent comes from the Latin word “per centum”. The Latin word “centum” means 100, so “per centum” means “for each hundred”. Percent is denoted with a symbol “%”. For instance, 1 percent can be written as 1%, and it is the same as the fraction 1/100, Ten percent can be written as 10%, which is the same as the fraction 10/100.
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When we say percent, we mean a part of the whole where whole is considered as hundred. Look at the grid below with 100 cells to understand better.
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Each cell is equal to 1% of the whole (the red cell is 1%).
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Two cells are equal to 2% (the green cells).
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Five cells are equal to 5% (the blue cells).
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Twenty-five cells (purple cells) are equal to 25% of the whole or one quarter (¼).
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Fifty cells (yellow cells) are equal to 50% of the whole or half (½).
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Count the white cells. There are 17 of them. Out of 100 cells, 17% are therefore white.
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Add up the number of other cells and deduct them from 100. There is one red cell, two green, five blue, twenty five purple, and fifty yellow. That adds up to 83. So, (100−83) = 17. Again, out of 100 cells, 17 are white, or 17%.
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Divide the value of white cells by total value and then multiply the resultant to 100. Percentage= (Value of white cells/Total value)×100 OR 17/100 × 100 = 0.17 × 100 = 17 or 17%.
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Percentage is textually written as, Percentage= (Part/Whole) × 100. Now, this part & whole can be any value, but when we convert this ratio in percentage, we mean to define the resultant out of every hundred. This gives us freedom to express complex calculations in simple form. For example, If I say 20% of my shirt was torn, a person listening to this will get an idea about portion of shirt that was torn without even knowing actual length of the shirt and length of the portion that was torn because when I said 20% of my shirt was torn, he considered the whole shirt as hundred cells and imagined that 20 cells out of it were torn. Therefore, we can easily communicate in terms of percentage without expressing detailed calculations.
Section 2: Conversion of fraction into percentages and vice versa.
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To convert a fraction into percentage, just multiply the given ratio by 100, the result obtained will be in terms of percentage. Example: To express 2/3 in terms of percentage, we multiply the given ratio by 100 or (2/3) × 100 = 66.66%.
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Similarly, if we want to convert a number given in terms of percentage, we divide the number by 100. Example: To express 40% in terms of ratio, we divide 40 by 100 or (40/100) = 2/5.
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Trainer’s role- Explain to the students why we multiply and divide by 100 while converting from ratio to percentage & percentage to ratio respectively through unitary method. Give a few fractions to convert into percentage & vice versa to check understanding of concept.
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Now, look at the percentage-fraction conversion chart below. This will help you solve problems quickly.
Section 3: Percentage increase or decrease.
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Let us understand this with an example. If your salary is Rs.50,000/- per month and one day your company’s HR walks in and informs you that you are promoted to senior management and your new salary will be Rs.60,000/-. What is the percentage increase or hike on your salary?
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Solution: We can clearly see that there is an increase in your salary which is Rs.10,000/- . So, what will be the percentage increase? Percentage increase as defined above can be written as (10000/50000) * 100 which is equal to 20%. So you received a 20% hike on your current salary.
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Let us understand this with an example. Last month your total expenditure was Rs.20,000/-. However, this month you have managed your expenses well and your total expenditure was Rs.15,000/- . What is the percentage decrease on your expenditure?
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Solution: We can clearly see that there is a decrease in your expenditure as compared to the previous month which is Rs.5000/-. So, what percentage will decrease? Percentage decrease as defined above can be written as (5000/20000) * 100 which is equal to 25%. So you reduce your expenses by 25%.
Section 4: Understanding the concept of multiplying factor for quick calculations.
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What do we mean when we say that a value has increased by 20%? As discussed earlier, we consider the total value of anything or it’s whole part as hundred or 100%. Now, if we say that this whole value has increased by 20%, we mean that a value which was 100% earlier has now increased by 20% or it has become 120% of the original value. 120% can be further written as 120/100 or 1.2. This “1.2” works out to be your multiplying factor. Multiplying 1.2 to your original value will give you the increased value.
Solution: According to the given question, the employee gets a hike of 20% on his salary. So, according to formula :
Value Increased × 100 = Percentage Increase
Original Value
Value increased = (20 × 24000)/ 100 or Rs.4800/- or you could simply calculate 20% of 24000= 4800 (without using formula).
New salary of the employee will be 24000+4800 = Rs.28,800/-
Did we just get the answer in a single line? How did we do that? Simple! Salary of the employee was Rs.24000/- which can be considered as 100% of his salary as this amount represents the whole part of his salary. Now according to question, his salary increased by 20% which means now his salary is 120% of the original salary or we can express it as:
(120% of 24000) or 24000 × (120/100) or 24000 × 1.2.
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Increase 5000 by 23%.
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Increase 200 by 200%.
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Increase 17400 by 12%.
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Decrease 2800 by 13%
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Decrease 5000 by 20%.
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Decrease 12000 by 15%.
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Express ¾ in terms of percentage.
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Express 7/8 in terms of percentage.
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Express 15/14 in terms of percentage (round off the value)
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Express 125% in terms of fraction.
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Express 160% in terms of fraction.
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Express 285% in terms of fraction.
Section 5: Few tricks to calculate faster
Solution: 51% of 128= (50+1)% of 128= 50% of 128 + 1% of 128 = 64 + 1.28 = 65.28
Solution: 39% of 12.5 = 12.5% of 39 = 1/8 × 39 = 4.875
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30 Minutes |
