I have explained percentage increase and decrease in my previous post ‘Don’t get stuck on Percentage like Sticky Jam‘.

However, in this post I’m going back to the basics and will explain how to find percent with and without a calculator.

## What is percent and how is it linked to fractions and cakes?

Percent is another way to represent a fraction.

If you have 6 cupcakes, and I eat 3 of them, I’ve just eaten 1/2 (half) of your cupcakes.

Or I could say I’ve just eaten 50% (percent) of your cupcakes…and I’m just about to eat the remaining 50%.

Similarly:

Cupcakes Eaten | Fraction | Decimal | Percent |

1 out of 4 | 1/4 | 0.25 | 25% |

3 out of 6 | 1/2 | 0.50 | 50% |

2 out of 6 | 1/3 | 0.33 (recurring) | 33.3% |

1 out of 5 | 1/5 | 0.20 | 20% |

To change a fraction to a decimal – divide the top number by the bottom number

Decimal to Percent: Multiply the decimal by 100

Decimal to Fraction: Put the number over 10, 100, or 1000 etc. depending on number of decimal places.

Percent to Fraction: Put the percent over 100 and simplify

## How to find percent without a calculator

The word percent, means ‘per cent’ which means ‘out of 100’. (cent being french for 100).

The process of finding a percent is to take the numbers you have and proportion them to be ‘out of 100’.

For example, let’s say you have a maths test and you score: 78/100.

Because 100 is the maximum number of marks, your score will be out of 100 and so is already a percentage.

78 out of 100 is the same as 78 percent, because the total possible is 100 and you scored 78 marks.

If something is already ‘out of 100’ you don’t have to do anything to the numbers, so the number or score or amount, is already a percentage.

2/100 is 2 percent or 2%

17/100 is 17%

81/100 is 81%

100/100 is 100%

And so on.

Of course, in real life, not everything we do or come across is out of 100.

So we need a process that will change the numbers to make them out of a hundred and that’s the process of how to find a percent.

When you have two numbers and you want to find the percent you need to multiply the numbers so that they are out of 100.

For example, if you have a different maths test where the total score is 50 and you score 46 out of 50, how would you find 46 out of 50 as a percent?

You can double the numbers to make it ‘out of 100’:

`\[\frac{46}{50}\ =\ \frac{92}{100}\ =\ 92\%\]`

Similarly, you can do this for any numbers that go easily into 100:

`\[\frac{13}{25}\ =\ \frac{52}{100}\ \ =\ 52\%\ \left(mulitply\ by\ 4\right)\]`

`\[\frac{16}{20}\ =\ \frac{80}{100}=\ 80\%\ \left(multiply\ by\ 5\right)\]`

`\[\frac{9}{10}\ =\ \frac{90}{100}\ =\ 90\%\ \left(multiply\ by\ 10\right)\]`

And so on.

But what about things like:

`\[\frac{20}{23}?\ or\ \frac{15}{16}?\ or\ \frac{75}{80}?\]`

How do you turn awkward fractions into a percentage?

A fraction is a divide.

So to turn a fraction into a percent, divide the numbers and then multiply the answer by 100.

This way you are turning the fraction into a fraction of 100 which is what a percent is.

E.g 1:

`\[\frac{20}{23}\ =\ 20\ divided\ by\ 23\ =\ 0.87\ \left(2\ d.p\right)\ \]`

`\[0.87\ multiplied\ by\ 100\ =\ 87\%\]`

E.g 2:

`\[\frac{15}{16}\ =\ 15\ divided\ by\ 16\ =\ 0.94\ \left(2\ d.p\right)\]`

`\[0.94\ multiplied\ by\ 100\ =\ 94\%\]`

Have a go at these:

`\[\left(a\right)\ \frac{27}{30}\]`

`\[\left(b\right)\ \frac{42}{45}\]`

`\[\left(c\right)\ \frac{10}{37}\]`

## How to find a percent of a number

So far we’ve looked at how to turn numbers into a percent. Or how to find one number as a percent of another number.

Sometimes you have a number and you need to find 1% or 5% or 20% or 32% and so on.

So how do you find a percent of a number?

If percent means out of 100.

Then to find one percent, you can divide your number by 100.

To find more than 1% you can multiply by the percent you need.

For example:

If I want to find 12% of 30

I can find 1% like this: 30/100 = 0.3

Then multiply 0.3 by 12 which gives: 3.6.

3.6 is 12% of 30.

E.g. 2 Find 15% of 200

200/100 = 2, so 2 is 1% of 200

2 multiplied by 15 = 30.

So 30 is 15% of 200.

E.g. 3

Find 17% of 54

54/100 = 0.54, so 0.54 is 1% of 54

0.54 multiplied by 17 is 9.18

So 17% of 54 is 9.18

Hope that helps. Please comment or get in touch if you need more help.

## Percent questions in exams and real life

In your GCSE maths exam you are most likely to get a wordy problem that involves percent – we all love wordy problems don’t we eh?

So let’s have a look at percentages in real life.

When you go shopping you often see signs like ‘20% off’ or ‘10% discount’

How do you work out these percent amounts?

Let’s have a look at a question:

If a shirt originally costs £40 and is in a sale with 15% off, what is the sale price of the shirt?

There are 2 steps here, you need to work out 15% of £40 and then remember to subtract it from £40 to get the new price.

So, 1% of 40 is 40/100 = 0.4

15% is 0.4 multiplied by 15 = £6

**So the discount amount is £6.** **This is not the final answer!**

This means the new price of the shirt is £40 – £6 = £34.

Example 2:

Sarah scored 85 out of 100 on her math test. What is her score as a percentage?

**Answer:** To find the score as a percentage, divide the actual score by the total possible score and multiply by 100.

Percentage Score = (Actual Score / Total Possible Score) × 100 Percentage Score = (85 / 100) × 100 = 85%

Sarah’s score on the math test is 85%.

And here are some for you to try:

**Question:** If 30% of a class of 40 students are girls, how many girls are in the class?

**Answer:** To find 30% of 40 find 1% then multiply by 30:

40/100 = 0.4

0.4 multiplied by 30 = 12.

There are 12 girls in the class.

Question: You want to tip 15% on a restaurant bill of £60. How much should you leave as a tip?

60/100 = 0.6

0.6 x 15 = £9.

The tip amount should be £9.

## How to find percent faster

Hopefully by now you understand the process of how to find percent.

There are some shortcuts you can use, which you may have already sussed.

For example if you want 10% of a number, you can simply divide by 10.

Dividing by 100 and then multiplying by 10 is the same as just dividing by 10.

Also to find other percents like 15% or 25% and so on, you can find 10% and then add on half.

Keep playing around and have fun.

If you’re ready for percentage increase and decrease head over to my other post 🙂

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