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Percentage

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The Importance of Percentages and How to Calculate Them for Your GCSE Exam

Do you ever struggle with understanding percentages for your GCSE exam? If so, you're not alone. In this article, we will cover all aspects of percentages to help you feel confident when using them. Let's start with the basics...

The word "percent" comes from the Latin words "per" and "cent," which means "per hundred." We can represent percentages using the symbol %.

For example, out of a group of students, if 91% pass their GCSE math exam, it means that 91 out of 100 students have passed. This percentage can help us evaluate the effectiveness of a school's preparation for exams by comparing it to other groups.

Percentages are also useful for making comparisons. For instance, if a student scores 51% on their math exam and 63% on their English exam, they can determine that they did better in English despite the different structures of the exams. Now, let's dive into how to calculate percentages.

The Percentage Formula

To calculate a percentage of a total, follow these steps:

  • Divide the amount (score) by the total (total available).
  • Take this number and multiply it by 100.

For example, let's say you took a math test and got 32 questions correct out of a total of 48. To determine your score as a percentage, you would divide 32 by 48, which equals 0.67. Then, multiplying it by 100 gives you a percentage score of 67%. Not bad, but if you need a 70% to pass, you may need to review a little more.

Calculating Percentages of Amounts

Sometimes, we are given a percentage and need to find the amount. This is known as finding the percentage of an amount. To do this, we can use a helpful table like the one shown below:

PercentageDecimalFraction10%0.11/1020%0.21/525%0.251/433.3%0.3331/350%0.51/266.7%0.6672/375%0.753/4

Using this table, we can calculate any percentage by combining different values. For example, to find 28%, we can do:

  • Find 30% by dividing 28 by 10.
  • Then, find 10% by dividing 2.8 by 3.
  • Finally, find 8% by dividing 0.28 by 10.

This process gives us a final answer of 28%.

Converting Between Percentages, Decimals, and Fractions

Percentages, decimals, and fractions are all ways of representing information. They can also be converted to one another. To do this, follow these rules:

  • To convert a decimal to a percentage, multiply the decimal by 100.
  • To convert a fraction to a percentage, multiply the fraction by 100.
  • To convert a percentage to a decimal, divide the percentage by 100.
  • To convert a percentage to a fraction, write the percentage over 100 and simplify.

For example, let's convert 34% to a fraction and decimal:

  • To convert 34% to a fraction, we can simply write it over 100. This gives us 34/100, which can be simplified to 17/50.
  • To convert 34% to a decimal, we divide it by 100. This gives us 0.34.

Now, let's try some more examples:

  • 50% of 0.3 can be found by converting the fraction 1/2 to a decimal, which is 0.5. Then, we multiply it by 0.3, giving us 0.15.
  • To convert 0.07 to a percentage, we can simply multiply it by 100, giving us 7%.

Understanding Percentage Changes

Percentage change is a useful tool for analyzing data and comparing different values. To find the percentage change, we use the following formula:

Percentage change = (New amount - Original amount) / Original amount

For example, if flight prices to France increased from £150 on Tuesday to £180 on Friday, we can find the percentage change by plugging in these values into the formula:

Percentage change = (£180 - £150) / £150 = 0.2

This means that the cost increased by 20% from the original amount.

We hope this article has helped you feel more confident in understanding and calculating percentages. With practice, you'll be able to calculate them without a second thought. Good luck on your GCSE exam!

Calculating Percentage Changes: Easily Determine Increases or Decreases over Time

Calculating percentage changes is a simple way to determine if there has been an increase or decrease in a certain value over a period of time. This calculation is useful for comparing data and understanding trends. Here's an easy method for calculating percentage changes.

How to Calculate Percentage Changes:

To calculate a percentage change, use the following formula: Percentage Change = (Difference/Initial Value) * 100

The difference refers to the difference between the initial value and the new value. You can calculate the difference by subtracting the larger value from the smaller value, depending on whether there has been an increase or decrease in the amount.

For example, if the price of a laptop was £500 and then increased to £550, the difference is £50. On the other hand, if the price decreased from £500 to £480, the difference is £20.

To better understand how to calculate percentage changes, let's look at some examples.

  • Example 1: On Monday, Sarah took a test and scored 56 out of 82. On Wednesday, she retook the same test and scored 78. What was her percentage change?
    Solution: The difference is 22. Thus, the percentage change is (22/82) * 100 = 26.8%. This means that Sarah scored 26.8% higher on Wednesday than she did on Monday.
  • Example 2: Bob bought a house for £296,000. He sold the house for £400,000. Calculate the percentage increase in price.
    Solution: The difference is £104,000. Therefore, the percentage change is (104,000/296,000) * 100 = 35.1%. This means that Bob made a profit of 35.1% of what he originally paid.
  • Example 3: A company sold 31,250 televisions in 2020. In 2021, they sold 29,876 televisions. Calculate the percentage decrease in the number of televisions sold.
    Solution: The difference is 1,374. Therefore, the percentage change is (1,374/31,250) * 100 = 4.4%. This means that the company sold 4.4% less televisions in 2021 than in 2020.

Percentage Increase

Suppose flights to Doha usually cost £500, but due to a sports event, the prices have increased by 50% in July. We may want to find the new cost of the flights. To calculate the new price after a percentage increase, we first need to determine the percentage of the amount that it has gone up by. In this example, we need to find 50% of £500 to determine how much the price has increased. Then, we add this amount to the original amount to find the new price.

Example: Kevin buys a house for £250,000. After refurbishing, the house is now worth 10% more. He decides to sell it. What is the new price of the house?
Solution: To determine the new price, we first need to find 10% of £250,000, which is £25,000. This means that the price has increased by £25,000. Therefore, the new price of the house is £275,000.

Percentage Decrease

Like a percentage increase, we can also have a percentage decrease. To calculate the new price after a percentage decrease, we use the same method as a percentage increase, except that we subtract the amount from the original amount instead of adding it.

Example: In a shop, all items are reduced by 30%. Sam wants to buy a t-shirt for £30 and a pair of jeans for £45. Does he have enough money to buy both items with £52?
Solution: The t-shirt is £30, and we need to decrease this by 30%. To do so, we find 30% of £30, which is £9. Therefore, the new price of the t-shirt is £21. For the jeans, we need to find 30% of £45, which is £13.50. Thus, the new price of the jeans is £31.50. Together, the cost of both items is £52.50, and Sam has enough money to buy them both.

Key Takeaways:

  • The word 'percent' comes from 'per' and 'cent', meaning one hundred.
  • To calculate a percentage, divide the amount by the total and multiply by 100.
  • Percentage changes can be used to compare data and determine increases or decreases.

Frequently Asked Questions

  • How to Calculate a Percentage?
    To calculate a percentage, divide the score by the total and then multiply by 100.
  • What is a Percentage?
    A percentage is an amount per hundred.
  • What is the Purpose of a Percentage?
    Percentages enable us to compare data and determine increases or decreases.
  • How to Find a Number as a Percentage?
    To find a number as a percentage, divide the number by the total and then multiply by 100.
  • How to Work Out Percentage?
    To work out a percentage, divide the score by the total and then multiply by 100.

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