3 Ways to Work with Increasing or Decreasing Percentages

2024 Author: Samantha Chapman | [email protected]. Last modified: 2023-12-17 09:13

Maybe you're trying to answer a question like "If a blouse that originally costs € 45 is on sale at 20% off, what's its new price?" These types of questions are called "percentage increase / decrease" and are a fairly basic math crux. With a little help, you can solve them easily and almost instinctively.

Steps

Method 1 of 3: Method One: Perfect Percentage

Step 1. Use the perfect percentage method for the following types of problems:

"If a shirt that costs € 40 is reduced to 32, what is the discount applied?"

Step 2. Decide which number represents the original quantity and which represents the "new quantity"

The amount that exists after the percentage has been applied can also be called the "new amount".

For our question, we don't know the percentage. We know that € 40 is the original amount and that 32 is the "after"

Step 3. Divide the "after" by the original amount

Make sure the "after" quantity goes into the calculator first.

• For our example, write 32 divided by 40 and press equal.
• This division gives us 0, 8. It is not the final answer.

Step 4. Move the decimal point two places to the right to change from decimal number to percentage

For our example problem, 0.8 changes to 80%.

Step 5. Compare that percentage to 100%

If the answer is less than 100%, there is a decrease or discount; greater than 100% is an increase.

• Since the price in the example has gone down and the price we calculated is also a discount, we are on the right track.
• The price in the example dropped from € 40 to € 32: if, however, we got 120% after our calculation, we would know we did something wrong, because we are looking for a discount and would have instead gotten an increase.

Step 6. Compare the percentage to 100%

Try to figure out how much you are above or below 100% and this will be the final answer. In our problem 80% vs 100% means we got a 20% discount.

Step 7. Practice the following examples

Try to see if you can finish the following problems:

• Problem 1:

  "A € 50 blouse has now dropped to 28. What was the discount percentage?"

  • To solve it, take a calculator. Enter “28: 50 =” and the answer is 0, 56.
  • Convert 0.56 to 56%. Compare this number to 100%, subtracting 56 from 100, giving you a 44% discount.

• Problem 2:

  “A € 12 baseball cap costs € 15 before tax. What is the percentage of taxes applied?"

  • To solve it, take a calculator. Write "15: 12 =" and the answer is 1, 25.
  • Convert 1.25 to 125%. Compare this to 100%, subtracting 100 from 125 and finding a 25% increase.

  Method 2 of 3: Method Two: New Unknown Amount

  

  Step 1. Use the new method of unknown quantities for the following types of problems:

  "A pair of jeans costs € 25 and is on sale at a 60% discount. What is the selling price?" 'Or "A colony of 4,800 bacteria grows by 20%. How many bacteria are there now?"

  

  Step 2. Decide if you have an increase or decrease in the initial situation

  Something like a sales tax, for example, is an increase situation. A discount, on the other hand, is a diminishing situation.

  

  Step 3. If you have a raise situation, add your percentage to 100

  So an 8% tax becomes 108%, for example, or a 12% surcharge becomes 112%.

  

  Step 4. If you have a decrease situation, you have to subtract the percentage from 100

  If something is 30% less, you work with 70%; if something is discounted at 12%, it is 88%.

  

  Step 5. Convert the answer in Step 3 or 4 to a decimal number

  This means moving the decimal point two places to the left.

  • For example, 67% becomes 0.67; 125% becomes 1.25; 108% becomes 1.08; etc.
  • If you are unsure how to do this, you can also divide the percentage by 100. This will give you the same number.

  

  Step 6. Multiply this decimal by your original amount

  If, for example, we are working on the problem “A 25 euro pair of jeans is on sale with a 60% discount. What is the selling price? ', The following is an illustration of this step:

  • 25 x 0, 40 =?
  • Remember that we subtracted our 60% sale price from 100, obtaining 40%, and then we transformed it into a decimal number.

  

  Step 7. Label the increase or decrease appropriately and you are done

  In our example, we had:

  • 25 x 0, 40 =? Multiply the two numbers together and we got 10.
  • But 10 what? 10 euros, so let's say that the new jeans costs € 10 after the 60% discount.

  

  Step 8. Practice the following examples

  To better understand this type of problem, try to see if you understand how to finish the following problems:

  • Problem 1:

    “A 120 euro pair of jeans is on sale at a 65% discount. What is the selling price?"

    • To solve:

      100 - 65 gives 35%; 35% converts to 0.35.

    • 0.35 x 120 equals 42; the new price is € 42.

  • Problem 2:

    “A colony of 4,800 bacteria grows by 20%. How many bacteria are there now?"

    • To solve: 100 + 20 gives 120% which converts to 1, 2.
    • 1.2 x 4,800 equals 5,760; there are now 5,760 bacteria in the colony.

    Method 3 of 3: Method Three: Original Quantity Unknown

    

    Step 1. Use the original method on unknown quantity for the following types of problems:

    “A video game is on sale at 75% discount. The sale price is € 15. What was the original price? " or “An investment has grown 22% and is now worth € 1,525. How much was originally invested?"

    • To solve these questions, you need to understand that percentages are applied by multiplication. If it is an increase or decrease, it has been applied by multiplication. Your job, therefore, is to undo this multiplication. You must cancel the application of the percentage. Thus, three things will be true:
    • You will divide by the percentage.
    • If you have a raise, you will add the percentage to 100.
    • If you have a decrease, you will subtract the percentage from 100.

    

    Step 2. Decide if it is an increase or decrease situation

    Sales tax, for example, is an increase; discounts are a decrease. An investment that grows in value is an increase; a population that decreases in number is a decrease and so on.

    • Let's imagine we need to solve the following problem:

      “A video is on sale with a 75% discount. The sale price is € 15. What is the original price?"

    • Clearance is another word for discount, so we're dealing with a decrease.
    • € 15 is our "after" amount, because it is the number we have "after" the sale.

    

    Step 3. If it's an increase, add the percentage to 100

    If it's a decrease, subtract the percentage from 100.

    Since we are dealing with a reduction / discount, subtract 100 - 75, getting 25%

    

    Step 4. Convert that number to decimal

    Do this by moving the comma two places to the left or dividing the number by 100.

    25% becomes 0.25

    

    Step 5. Divide the "after" by the decimals from Step 3

    This will help you reverse the multiplication we talked about in Step 1.

    

    Step 6. Our "after amount" is € 15 and our decimal is 0.25

    Get a calculator: "15: 0, 25 =".

    

    Step 7. Label appropriately and you are done

    You just calculated the original price.

    • 15 divided by 0.25 = 60, which means the original price was € 60.
    • If you want to check your answer to make sure it is correct, multiply the selling price (75% or 0.75) by the original price (€ 60) and see if you get the selling price.

    (€ 15): 0, 75 x 60 = Sale of € 45; € 60 (original price) - € 45 (discount amount) = € 15 (sale price)

    

    Step 8. Practice the following examples

    To better understand this type of problem, try to figure out how to end the following problem: “An investment has grown by 22% and is now worth € 1,525. How much was originally invested?"

    • This is an increase situation, so calculate 100 + 22.
    • Convert the answer to a decimal number: 122% becomes 1, 22
    • On a calculator, enter “1.525: 1, 22 =”.
    • Write down your answer. For this problem, 1,525: 1, 22 = 1250, so the initial investment was € 1,250.

    Advice

    • If you don't know the new amount, you can multiply. If not, you can split.
    • Remember for example units, Euros, Dollars, Pounds or% etc. With several operations, you will always get these same units.
    • If it's an increase, add the percentage to 100; if it is a decrease, subtract it from 100. This is true regardless of whether it is multiplying or dividing.
    • Don't forget the decimal point.