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.
To calculate a percentage of a total, follow these steps:
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.
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:
This process gives us a final answer of 28%.
Percentages, decimals, and fractions are all ways of representing information. They can also be converted to one another. To do this, follow these rules:
For example, let's convert 34% to a fraction and decimal:
Now, let's try some more examples:
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 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.
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.
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.
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