# Maths help: What is a percentage? How do you work out a percent of a number? Percent = out of a 100

**What does PERCENT mean?**

Percent means parts per hundred. The word comes from the Latin phrase per centum, which means per hundred. In mathematics, we use the symbol % for percent.

**So what does this mean in maths terms?**

100% means 100 for each 100, which is to say, all. 100% of 12 is 12.

50% is another way of saying half, because 50% means 50 for each 100, which is half. 50% of 12 is 6.

25% is another way of saying a quarter (which is the same as a half of a half) because 25% means 25 for each 100. 25% of 12 is 3. (12 divided by 2 = 6 (1/2) then divide by 2 again = 3 (1/4)

38% means 38 for each 100.

Remember 100% means __all__.

Example:

100% of **80** is ^{100}/_{100} × 80 = __80__

50% means __half__.

Example:

50% of **80** is ^{50}/_{100} × 80 = __40__

5% means ^{5}/_{100ths}.

Example:

5% of **80** is ^{5}/_{100} × 80 = __4__

**Using Percent**

Because "Percent" means "per 100" you should think "this should always be divided by 100"

So **75%** really means ^{75}/_{100}

And **100%** is ^{100}/_{100}, or exactly **1 **(100% of any number is just the number, unchanged)

And **200%** is ^{200}/_{100}, or exactly **2 **(200% of any number is twice the number)

**How about some examples of questions;**

1. *100 people were surveyed, and 75 responded Yes. What percent responded Yes?*

Answer. 75% -- 75 out of 100.

2. *In a class of 40 students, all 40 came to school by bus. What percent came to school by bus?*

Answer. 100%. 100% means all.

(40 out of 40 is equivalent to 100 out of 100.)

3*. 25 children want some sweets. If there are 50 sweets and they each get one each what percentage is left? *

Answer**.** 50%. 25 out of 50

(Remember that 50% is also equivalent to one half, 1/2)

4.5 sweets were left in a bag. There were 500 in total at the start of Halloween. What percentage was left?

Answer. 1%. 5 out of 500.

## A website that will help you calculate percantages

- Percent Calculator

It is important children now how to calculate percantages by themselves but they could check themselves on here. Why not use this for some questions the children have to work out before they peer assess each others work and give themselves a mark.

## Another website that will help you find percentages of a number

- Percentage Calculator

Quickly and easily find the percentage of a number! Free online App.

**How do we calculate 50%? **

50% is the same as a half (1/2). So the way we work out 50% is to divide by 2 or halve it.

For example;

50% of 20 = 10

50% of50= 25

50% of 60 = 30

50% of 15 = 7.5

**How do we calculate 25%? **

50% is the same as a quarter (1/4). So the way we work out 25% is to divide by halve it and then halve it again. This is the same as dividing by 2 and dividing by 2 again (or just dividing by 4)

We know this because a quarter is a half of a half.

For example;

25% of 20 = 10 /2 =5

25% of50= 25 /2 = 12.5

25% of 60 = 30 /2 = 15

25% of 15 = 7.5 /2 = 3.75

**How do we find 1% of a number? **

We simply divide the number by 100.

The reason for this is because 1% is the hundreth part of 100%.

100% is made up of *one hundred* 1%'s.

For example;

1% of 300 = 300 / 100 = 3

1% of 250 = 250 / 100 = 2.5

**How do we find 10% of a number? **

We simply divide the number by 10.

The reason for this is because 10% is the tenth part of 100%. 100% is made up of *ten* 10%'s.

For example;

10% of 50 = 50 / 10 = 5

10% of 350 = 350 / 10 = 35

**How do we find 5% of a number? **

We simply divide the number by 10 then divide this by 2.

The reason for this is because 10% is the tenth part of 100%. 100% is made up of *ten* 10%'s. And 5% is half of this. Another way to think of this is that there are 20 5^{th} in 100%.

For example;

5% of 20 = (20/10) /2 = 2/2 = 1

5% of 50 = (50 / 10) / 2 = 5/2 = 2.5

5% of 350 = (350 / 10) /2 = 35/2 = 17.5

**Can we use this knowledge? **

From this knowledge we can work out any kind of percentage. To do this you must think of the percentage in terms of tenths and units. So in maths terms, partition them.

For example;

16% of 160

10% of 160 = 16

5% 0f 160 = 8

1% of 160 = 1.6

So 16% = 10% + 5% + 1%

So 16% = 16+8+1.6 = 25.6

Another example;

75% of 200

50% of 200 = 100

25% of 200 = 50

75% of 200 = 50% + 25% = 100 + 50 = 150

Example number 3;

87% of 300 =

50% of 300 = 150

25% 0f 300 = 75

10% of 300 = 30

1% of 300 = 3

87% of 300 = 50% + 25% + 10% + 1% + 1% = 150 + 75 + 30 + 3 + 3 = 261

## Of course there is a far easier way to do it, far easier, but children need to learn the maths before using a calulator

Yes using a calculator is easier but children do need to learn how to do it using the best calculator they have at their disposal - their brain. They need to understand what they are doing and why it works in order to be successful with a calculator. They also need to have the knowledge to be able to check their work even if they have done it using a calculator.

All this means that I only ever teach this method to those students who have understood the basic mental and written methods first. I teach it last or when ever some student mentions it in lessons.

I tend to use it as a plenary in lesson:

They work through their calculations using the written method and then to peer assess I show them how to use the calculator and then they mark each others work.

## So how can we use a calculator?

It is simple once you convert the percentage into a decimal. This in itself is easy to as you only need to divide it by 100. Once you have that you just multiply the number to get the answer.

**Example 1:**

47% of 395

- First we divide the percentage by 100. 47 ÷ 100 = 0.47
- Next we multiply this by the number
- 0.47 x 395 = 185.65

**Example 2:**

(When a value is increased by a certain percentage - petrol!)

Petrol prices at the pump are to rise by 15% today. They are £1.32 per litre at the moment. What is the price after the rise?

So we have a rise - that means it will be more than the price now. You have two options here:

Option 1: To work out the percentage rise and add this to the original price:

- Divide the percentage by 100. ( 15 ÷ 100 = 0.15 )
- 0.15 x 1.32 = 0.198
- This then needs to be added onto the original price
- 1.32 + 0.198 = £1.518

Option 2: Work out the percentage as a total i.e. 115% because you have to add the 100% on anyway.

- Divide the percentage by 100. ( 115 ÷ 100 = 1.15)
- 1.15 x 1.32 = £1.518.

Option 2 is obviously the easiest but children need to understand the maths so it is best to show them option 1 first and then show them the maths behind the quicker version of option 2 after. That way they will understand it more and be less likely to make mistakes. Plus they will be able to check their work a lot easier and more confidently.

**Example 3:**

(When a value is decreased by a certain percentage - sale)

A shop has a sale and a tshirt has come down in price by 12%. It is marked up at £15 so how much is it in the sale?

So we have a decrease- that means the price will have come down from the original. You have two options here:

Option 1: To work out the percentage decrease and take this away from the original price:

- Divide the percentage by 100. ( 12 ÷ 100 = 0.12 )
- 0.12 x 15 = 1.8
- This then needs to be took away from the original price
- 15 - 1.8 = £13.2

Option 2: Work out the percentage of the sale item that you have to pay for: i.e. a 25% discount you would end up paying for 75% of the items value.

- Take away 12% from 100. (100 - 12 = 88)
- Divide the percentage by 100. ( 88÷ 100 = 0.88)
- 0.88 x 15 = £13.2

Again Option 2 is a short cut but you need to understand the maths behind it to be able to use this confidently. Teach option 1 first and then explain option 2 so they have a good understanding of maths.

## Of course this method of turning a percent into a decimal can work for written methods too.

Some of my students have prefered to work with decimals rather than percentages so I taught them how to convert a percentage into a decimal (by dividing by 100) and then they multiplied the two numbers together.

They used methods like the grid method or the column method to do this.

One thing I have always said to my students though is that they should pick their own method, that they feel comfortable with and can understand and go with that. They need to choose the best maths for them. By the time children have come to learning about percentages of numbers they should be confident mathmaticians who can do this.

## Comments

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What number represents 5 percent of 160

5