Percentages are an essential part of our daily life, from calculating discounts at the store to determining the tax on our earnings. However, many people struggle with percentages, especially doing it without the use of a calculator. In this article, we will guide you through how to work out percentages without a calculator, making it easy for you to master this essential skill.
What are Percentages?
Percentages are a way of expressing a number as a fraction of 100. The word "percent" means "per hundred" in Latin, so when we talk about percentages, we're talking about how many parts out of 100 a number represents.
In finance, percentages are often used to express interest rates, which basically means how much extra money you have to pay for borrowing money. And in science, percentages help make experimental results easier to understand.
Percentages are also a part of our daily life too from calculating the discount you are receiving at the supermarket to paying tax on your earnings.
In this article we will break down the various techniques for working out percentages without a calculator.
How to Convert Percentage into Decimal
You may need to work out how to convert a percentage into a decimal without a calculator.
The idea here is relatively simple, we need to divide by 100. The best way to divide by 100 is to move the decimal two places to the left.
Examples of converting Percentages into Decimals
Convert 50% into decimal
50/100 = 0.50 or 0.5
Convert 63% into decimal
63/100=0.63
Convert 17.5% into decimal
17.5/100=0.175
Work out the Percentage of a Value
One of the most common things you will be asked to do is work out the percentage of an amount. While the method to do this on a calculator is straightforward, it is also helpful to be able to do this without a calculator and the method for this is very different.
The first thing we need to do is find 10% of a number, this is usually our starting point. To find 10% of any number, we divide by 10 or if you prefer move one decimal place to the left. Lets try a few
Examples of Finding Percentages of Values
Find 10% of 80
80/10=8
Find 10% of 240
240/10=24
Finding 5%
Now imagine you were asked to find 5% of an amount, what we can do is find 10% and then halve it to give us 5%
Find 5% of 80
10% of 80 = 80/10 = 8
5% of 80 = 8/2 = 4
Find 5% of 240
10% of 240 = 240/10 = 24
5% of 240 = 24/2 = 12
Finding any multiple of 5%
Using the above you should now be able to work out any percentage multiple of 5, let's try a couple.
Find 15% of 80
10% of 80 = 80/10 = 8
5% of 80 = 8/2 = 4
15% (10%+5%) of 80 = 8+4 = 12
Find 35% of 240
10% of 240 = 240/10 = 24
5% of 240 = 24/2 = 12
30% of 240 = 24 x 3 = 72
35% (30%+5%) of 240 = 72+12=84
Finding Any Percentage without a calculator
You can extend this idea to any percentage by working out the value of 1%. To find 1% we can either divide 10% by 10 or simply divide the full amount by 100.
Find 1% of 300
10% of 300 = 300/10=30
1% of 300 = 30/10 = 3
Find 7% of 200
10% of 200 = 200/10 = 20
1% of 200 = 20/10 = 2
7% of 200 = 2x7 = 14
Work out the Percentage of Two numbers
Sometimes you may want to work out the percentage of one number compared to another. An example of a situation could be doing tests, let's imagine a student scored 8 out of 10 in an English test, 17 out of 20 in a Science test and 21 out of 25 on a Maths test. What test did the student perform best at.
Here we can attempt to convert all of the amounts into percentages and then compare.
Percentage means parts per 100 so we need to rewrite each of the above scores as fractions with the denominator of 100 and then write as a percentage.
English: 8/10 = 80/100 = 80%
Science: 17/20 = 85/100 = 85%
Maths: 21/25 = 84/100 = 84%
Now that we have converted them all into percentages, we can see that the student did best in Science.
Percentage Increase
Lets look at an example where an employee receives a 15% pay rise, her annual salary was previously £30,000. This type of question requires a percentage increase, we can first rephrase the question to increase £30,000 by 15%, and think to ourselves, are we expecting a number larger or smaller than £30,000?
Increase £30,000 by 15% without a calculator
First we need to work out 15% of £30,000
10% of £30,000 = 30000/10 = £3000
5% of £30,000 = £3000/2 = £1500
15% (10%+5%) of £30,000 = 3000+1500 = £4500
Finally to increase we add this amount to the original value
Increase £30,000 by 15% = £30,000 + £4500 = £34,500
Percentage Decrease
Now lets take a look at percentage decrease, an example of where you might use this is whilst in a shop and there is a sale giving a discount on the original price.
Lets imagine a student wanted to buy an £80 jacket which was on sale and its price was reduced by 35%, how much did it cost now?
First lets rephrase the question into Decrease £80 by 35% and we can begin
Decrease £80 by 35% without a calculator
10% of £80 = 80/10 = £8
5% of £80 = £8/2 = £4
30% of £80 = £8 x 3 = £24
35% (30%+5%) of £80 = £24+£4 = £28
Finally to decrease, we subtract this from the original amount
Decrease £80 by 35% = £80-£28 = £52
Reverse Percentages
When we are asked to work out a value before a percentage increase or decrease, this is known as reverse percentage. The best way to identify one of these questions is when it asks you to work out the original value.
Let’s use the example that train tickets have increased in price by 20% to £72, we need to work out the original price. A common mistake made in these types of problem is to attempt to decrease it by 20%, this will not give the correct answer as the opposite of increasing by 20% is not deceasing by 20%.
In order to solve this problem, we first need to identify that it is a reverse percentages question.
After a 20% increase, the train ticket now costs £72, what was the original price?
Since the new price is after a 20% increase, this represents 100%+20% = 120%
120% = £72
We need to work out the value of 1%, divide both sides by 120
1% = £72/120 = £0.60
Now multiply by 100 to work out the value of 100%
100% = £0.60 x 100 = £60
The original price of the train ticket was £60. You can now check this value is correct by increasing £60 by 20%.
Now we will look at an example where a percentage decrease had taken place.
In a sale, the price of a jacket has been reduced by 25% to £60, what was the original price of the jacket?
Remember since we are working out the original amount this is a reverse percentages question and not a percentage increase question. As the current price of the jacket is £60 after a 25% decrease we can write
100%-25% = 75% = £60
Now we work out the value of 1% by dividing both sides by 75
1% = £60/75 = £0.80
To get 100% we multiply by 100
100% = £0.80 x 100 = £80
The original price of the jacket was £80, you can check this answer by decreasing £80 by 25%.
Simple Interest
Interest is the amount you pay to borrow money or the amount others pay you if they borrow your money.
If you take out a loan from a bank, they will charge you interest and this will be a percentage of the loan amount that you pay for the privilege of borrowing their money.
If you invest money into the savings account, the bank will pay you interest of a percentage amount for investing your money with the bank.
There are two main types of interest, simple interest and compound interest. In this article we will talk only about simple interest as compound interest will require the use of a calculator.
What is Simple Interest?
As the name suggests, simple interest is easy to work out, let's take a look at an example where we invest £10,000 for 8 years with an interest rate of 4%. We want to know how much our £10,000 will be worth at the end of 8 years.
First we work out 4% (interest rate) of £10,000 (capital)
1% of £10,000 =£10,000/100 = £100
4% of £10,000 = £400
We receive this amount of interest every year for 8 years, after 8 years we have received
£400 x 8 years = £3200, this is the interest received on your investment
To find the total value of the investment, we add these values together.
£10,000 + £3,200 = £13,200
Conclusion
Percentages are an integral part of our daily lives, and it's important to understand how to calculate them. While calculators are convenient, it's also essential to know how to work out percentages without them. This article has provided various techniques to help you master this skill, from converting percentages into decimals, to finding percentages of values, to working out any percentage without a calculator.
Knowing how to work with percentages can be useful in many fields, from finance to science. So, take the time to practice and improve your percentage calculation skills, and you'll be amazed at how much easier life can be.
