Maybe you're trying to solve a question like: "If the original price of a blouse was $45.00 and it was 20% off, how much would a new one cost?" Such questions ask for percentage increase/decrease and are fairly common basic math problems. With a little help, you will be able to solve similar problems easily and quickly.
Step
Method 1 of 3: Calculating Percentages
Step 1. Calculate the percentage on questions like:
"If a shirt for Rp. 40,000, 00 is discounted to Rp. 32,000, 00, what percentage of the discount is given?"
Step 2. Identify the final/new value (the number obtained after the initial value is subject to a percentage) and the initial value
In the example problem above, the percentage is unknown, IDR 40,000, 00 is the initial value, and IDR 32,000, 00 is the new value
Step 3. Divide the new value by the initial value
Make sure the new value is typed into the calculator first.
- To answer the sample problem, enter the number 32,000, press the division symbol, enter the number 40,000, and then press the equals symbol.
- The results that appear are: 0, 8 (this is not the final answer)
Step 4. Move the decimal point (comma) two place values to the right so that the decimal number turns into a percent
In the example problem, change 0, 8 to 80%.
Step 5. Compare that percentage to 100%
If the percentage is less than 100%, a decrease or discount occurs. If the percentage exceeds 100%, an increase occurs.
- In the example problem, because the new price is smaller than the initial price and what is being asked is a discount, our calculations so far are correct.
- On the other hand, if the result is 120%, surely our calculation is wrong because the question is asking for a discount so there is no way for an increase (more than 100%).
Step 6. Calculate the difference between the percentage and 100%
The difference is the final answer. In the example problem, there is a 20% difference between 80% and 100%. So, the initial price of the shirt is discounted by 20%.
Step 7. Practice by working on the following example
To understand better, study the following sample questions and how to solve them:
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Question #1: "A blouse for IDR 50,000, 00 is discounted to IDR 28,000, 00. What is the percent discount given?"
- Take a calculator. Enter the number 28,000, press the division symbol, enter the number 50,000, then press the equals symbol; appears the result of 0.56.
- Change 0.56 to 56%. Calculate the difference between 50% and 100%; 44% yield. So, the starting price of the blouse is discounted by 44%.
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Question #2: "A baseball cap for Rp. 12,000, 00 sells for Rp. 15,000, 00 after tax. What is the percentage tax charged?"
- Take a calculator. Enter the number 15,000, press the division symbol, enter the number 12,000, press the equals symbol; the result is 1.25.
- Change 1.25 to 125%. Calculate the difference between 125% and 100%; 25% yield. Thus, the starting price of a baseball cap has increased by 25%.
Method 2 of 3: Calculating New Values
Step 1. Calculate new/final grades on questions like:
"Jin pants for IDR 25,000.00 are given a 60% discount. How much is the new one?" or "A bacterial colony of 4,800 bacteria grew by 20%. How many bacteria are there now?"
Step 2. Identify whether the question involves a percentage increase or decrease
For example, a sales tax-related problem involves a percentage increase. On the other hand, problems related to discounts involve a percentage decrease.
Step 3. If the problem involves a percentage increase, add 100% to the percent
For example, change the 8% sales tax to 108% or the 12% surcharge to 112%.
Step 4. If the problem involves a percentage drop, subtract 100% from the percent
If something is reduced by 30%, do the calculation using 70%; if the price of an item is discounted 12%, do the calculation using 88%.
Step 5. Convert the result obtained from Step 3 or 4 to a decimal number
Move the decimal point two place values to the left.
- Example: change 67% to 0.67; 125% to 1.25; 108% to 1.08.
- When in doubt, divide the result from Step 3 or 4 by 100; the result will be the same as shifting the decimal sign two place values to the left.
Step 6. Multiply the decimal number by the initial value
For example, if you work on the question "Jeans for Rp. 25,000, 00 are given a 60% discount. What is the new price?", here's how to do this step:
- 25,000 x 0, 40 = ?
- Remember, 100% has been subtracted by 60% to get 40%, which is then converted to a decimal number.
Step 7. Write the correct answer sentence, then finish
In the example problem, the final calculation is:
- 25,000 x 0, 40 = ? Multiply these two numbers to get 10,000.
- However, 10,000 what? 10,000 rupiah. So, after a 60% discount, the price of the jeans becomes IDR 10,000.00.
Step 8. Practice by working on the following example
To understand better, study the following sample questions and how to solve them:
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Question #1: "Jin pants for Rp. 120,000.00 off 65%. How much is the new one?"
- Answer: 100% - 65% = 35%; change 35% to 0.35.
- 0.35 x 120,000 = 42,000. So, after 65% discount, the price of the jeans is IDR 42,000, 00 (quite cheap!)
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Problem #2: "A bacterial colony of 4,800 talents grew by 20%. How many bacteria are there now?"
- Answer: 100% + 20% = 120%; change 120% to 1, 2.
- 1, 2 x 4,800 = 5,760. So, in the colony, there are 5,760 bacteria now.
Method 3 of 3: Calculating Initial Value
Step 1. Calculate the initial value on questions such as:
"A video game is on sale at 75% for Rp. 15,000.00. What is the initial price of the video game?" or "The value of an investment increased by 22% so that it is now worth $1,525,000.00. What was the initial value of the investment?"
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To answer similar questions, understand that percentages, whether they are increasing or decreasing, are calculated by multiplying. So, the multiplication, not the increase or decrease, must be cancelled. Therefore, the following three things apply:
- The method used is "divided by percent".
- If the question involves a percentage increase, the percent still adds up to 100%.
- If the problem involves a percentage decrease, 100% is still subtracted by a percent.
Step 2. Identify whether the question involves a percentage increase or decrease
For example, a sales tax-related problem involves a percentage increase, while a discount represents a decrease; Problems related to the growth of investment value involve a percentage increase, while the decreasing population size involves a percentage decrease.
- For example, let's do this problem: "A video game is on sale at 75% for $15,000. What is the initial price of the video game?"
- A sale is the same as a discount. So, this problem involves a percentage drop.
- IDR 15,000, 00 is the new/final value because it is the price obtained after being given a discount.
Step 3. If the problem involves a percentage increase, add 100% to the percent
If the problem involves a percentage drop, subtract 100% from the percent.
Since the example problem we are working on involves a discount/percentage reduction, subtract 100% by 75% to get a 25% result
Step 4. Convert the result to a decimal number
Move the decimal point two place values to the left or divide by 100.
Change 25% to 0.25
Step 5. Divide the new value by the decimal number obtained from Step 3
This method undoes multiplication, as described in Step 1.
Step 6. In the example problem, IDR 15,000, 00 is the new value and 0, 25 is the decimal number obtained from Step 3
Take a calculator. Enter the number 15,000, press the division symbol, enter the number 0, 25, and then press the equals symbol
Step 7. Write the correct answer sentence, then finish
You have just completed a problem that asks for initial grades.
- 15,000 divided by 0.25 = 60,000. So, the starting price of the video game is IDR 60,000.00.
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To double-check your answer, multiply the discount (75% or 0.75) by the original price (Rp60,000.00). If the answer is correct, the result of the multiplication is the discount amount.
(Rp15,000, 00): 0.75 x 60,000 = 45,000; IDR 60,000, 00 (initial price) - IDR 45,000, 00 (discount amount) = IDR 15,000, 00 (new price)
Step 8. Practice by working on the following example
To understand better, study the following sample questions and how to solve them: "The value of an investment increased by 22% so that it is now worth IDR 1,525,000, 00. What was the initial value of the investment?"
- This problem involves a percentage increase. So, add up 100% by 22% to get 122%.
- Convert 122% to a decimal number: 1, 22.
- Take a calculator. Enter the number 1.525,000, press the division symbol, enter the numbers 1, 22, press the equals symbol; the result is 1,250,000.
- Write the correct answer sentence. So, the initial value of the investment is IDR 1,250,000,00.
Tips
- The new/final value is calculated by multiplication. Initial values and percentages are calculated by division.
- If the problem involves a percentage increase, add 100% to the percent. If the problem involves a percentage drop, subtract 100% from the percent. This applies to all percentage questions, whether done using the multiplication or division method.
- Don't forget to shift the decimal point if needed.
- Do not forget to write units, for example rupiah, percent, and others. If you don't or write units incorrectly, the teacher may reduce your grade.
- Practice estimating answers. Roughly estimate the final answer you will get (more than 100? More than 200? Less than 50? Less than 20?) and see if the final answer matches your rough estimate.
