Whether you're shopping for a bargain, managing your finances, or interpreting statistical data, understanding how to work out percentage reduction can be incredibly useful. Let’s give it a go.
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Brief Overview of Percentage Reduction
Percentage reduction measures how much something has decreased as a percentage of its original value. It's commonly used in sales to show discounts, in finance to indicate losses, and in many other fields to compare changes over time.
Knowing how to calculate percentage reductions helps you with things like saving money on shopping, managing budgets effectively, tracking health metrics, or even understanding environmental impacts, making it a valuable tool for all sorts of things in everyday life!
Key Concepts in Percentage Reduction
Percentage reduction refers to the process of calculating how much a quantity has decreased relative to its original amount, expressed as a percentage. Here are some useful terms you’ll need before working it out for yourself:
- Original Amount: The initial value before any reduction. For example, if a product's original price before the reduction was £100, that is the original amount.
- Reduced Amount: The new value after the reduction. If the product was £100 and its price drops to £80, then £80 is the reduced amount.
- Difference: The amount by which the original amount has decreased, calculated by subtracting the reduced amount from the original amount. In this case, £100 - £80 = £20. So £20 is the difference.
Step-by-Step Guide to Calculating Percentage Reduction
Calculating percentage reduction is straightforward once you break it down into simple steps. We'll guide you through identifying the original and reduced amounts, calculating the difference, and then finding the percentage reduction.
Step 1: Identifying Original Amount and Reduced Amount
Start by identifying the original amount and the reduced amount - remember, the original amount is the starting amount before the reduction, and the reduced amount is the new amount after the reduction. Nice and simple!
Let’s try it together:
“A bicycle was being sold for £150, and is now on sale at £120. Identify the original and reduced amounts.”
We can see that the original amount is £150. This is the price before any reduction has happened.
The reduced amount is £120. This is the new price after the reduction - once the bike has been put on sale.
Straightforward, right?
Step 2: Calculate the Difference
Next, we can calculate the difference by subtracting the reduced amount from the original amount, much like you would when finding the difference between any set of numbers. Written as a formula, it will look like this:
Difference = Original Amount - Reduced Amount
Let’s go back to our example and test your new skill:
”A bicycle was originally priced at £150 and is now £120. Work out the difference between the original and reduced amounts.”
We start with the original amount we found earlier: £150.
Then we have the reduced amount, which we know is £120.
Now, we can use the formula we’ve learned: Difference = Original Amount - Reduced Amount.
Using our example, this would look like:
Difference = £150 - £120 = £30.
So, the difference is £30!
Step 3: Calculating Percentage Reduction
Together, we’ve now got everything we need to calculate the percentage reduction. This is the formula we need to use:
Percentage Reduction = (Difference / Original Amount) x 100
Now we’ll find the percentage reduction in the question we’ve been working on:
”A bicycle was originally priced at £150 and is now £120. Calculate the percentage reduction.”
To start, we divide the difference by the original amount: £30 / £150 = 0.2.
Multiply our answer by 100 to get the percentage reduction: 0.2 x 100 = 20.
So, the bicycle's price was reduced by 20%.
Let’s try another one to make sure you’re confident:
“A laptop was originally priced at £500 and is now £350. Calculate the percentage reduction.”
First, identify the original and reduced amounts: £500 and £350.
Then, we calculate the difference: £500 - £350 = £150.
Now we have what we need to calculate the percentage reduction using the formula:
Percentage Reduction = (Difference / Original Amount) x 100.
Using what we’ve already worked out, we can do 150 / 500 = 0.3.
All that we have to do now is 0.3 x 100 = 30.
So the percentage reduction of the laptop is 30%!
If you need a little practice converting decimals to percentages, check out our blog link here: Converting Between Fractions, Decimals and Percentages.
Practice Questions
Confident on how you can work out the percentage reduction between two amounts? Try out a couple of questions for yourself to test what you’ve learned so far:
Practise Questions
1. A coat is on sale for £60, down from £80. Work out the percentage reduction of the coat.
2. Between 2020 and 2023, a town’s population decreased from 1500 to 1200. By what percentage did the population fall?
Answers
1.Percentage reduction of the coat:
Answer: 25%
- Original Amount: £80
- Reduced Amount: £60
- Difference: £80 - £60 = £20
- Percentage Reduction: (£20 / £80) x 100 = 25%
2.Percentage reduction of the population:
Answer: 20%
- Original Amount: 1500
- Reduced Amount: 1200
- Difference: 1500 - 1200 = 300
- Percentage Reduction: (300 / 1500) x 100 = 20%
Understanding how to calculate percentage reduction is a valuable skill that can be applied in many areas of life. Let’s recap the key points:
- Identify the original and reduced amounts.
- Calculate the difference by subtracting the reduced amount from the original amount.
- Use the formula (Difference / Original Amount) x 100 to find the percentage reduction.
Make sure to practice these steps regularly to reinforce these steps, and build your confidence in this topic. If you want to have another go at some more examples (or go even further by exploring related topics), take a look at these worksheets to have a go at:
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