# Whats 80 of 400?

Have you ever been in a situation where someone asks you what’s the percentage of 80 out of 400 and your mind just goes blank? It can be embarrassing, but fear not my friend, because today I am going to explain this simple math problem in a way that even your grandma will understand. So sit back, relax and let’s dive into it!

## Understanding Percentages

Before we get into how to calculate the percentage of two numbers, let’s first look at what percentages are. A percentage is simply another way to express a number as part of 100.

For example, if I say I got an A+ on my math test and scored 97%, that means that out of every hundred possible marks to score from my exam paper; I was able to successfully complete 97 questions which were correct marking me with an impressive grade.

In simpler terms; Percentage = (Part / Whole) × 100%.

## Finding the Percentage

Now that we know what percentages are let’s focus on finding them between two given numbers. Whether you’re calculating your savings or figuring out the tax rate on your latest purchase – understanding this mathematical concept makes everything easy-peasy lemon squeeze-y!

To find percent values between any two numerical figures through arithmetic calculation;

Percentage Value (P) = (Number One(n1) ÷ Number Two(n2)) × Total-possible-value(TPV)

Here,

`P`: Is The Required Percentage Value That We Are Trying To Find Out.
`n1`: Denotes Number-First(In Our Case: `80`).
`n2`: Represents Number-Second(Which In Our Scenario Will Be: `400`).

`TPV`: Total Possible Value Which Typically Is Always Converted To Hundred(Thus Presumed As =”100%”).

Plug-In The Numerical Values:

`P`= (80/400)×100%

`P`= 20%

So the answer to our original question, “What’s 80 of 400?” is 20%. It means that eighty represents twenty-percent of four-hundred numerical values.

## Quick Calculation Methods

However as mathematicians have been working day and night to simplify life out for us. There are shortcut formulas that can ease up calculations and make them simpler;

1. Dividing First Number By Second And Multiplying Result By Hundred Directly divides first number by second – this makes it far easier compared to long equations such as those above(but let’s check if these short-cuts actually saves time or not)

`33.33= ((HTV/n2)100)`

Above equation would looks something like this;

Divide `80` with `400`: `(80/400)=0.2`

Multiply result with hundred: `0.2100 = 20%`

Moving on,

Although division-multiplication will remain the same in all calculation methods no matter what you choose, but still having more than one way open always plays a good move while resolving conflicts(another math pun>). So read-on((in-case any illuminati-encrypted message towards simplifying maths pops-up));

### Formula Method

The smarty pants who helped eliminate multiple steps, gave formula method which follows;

Find Percentage:
`(n1 x 100) ÷ n2 %`

In case you want percentage value represented in decimal whereas excluding % sign

`(n1 x 100) ÷ n2!) //---> Output provides Decimal Value (useful for learning but not practical).`

Another Mathematical Solution Is That You Can Take The Following Steps To Reach The Answer:

``````n1 / n2 = Result
Result  100 = Percentage Value
``````

Applying Above Formula;

80 ÷ 400 = 0.2

0.2 x 100= 20%

Expecting you to have memorized all conventional methods above, let’s move onto the next(impossible-to-recall-method). But before that a quick reminder:

A ratio is simply the comparison of two quantities by division. Unlike Percent formulae, Ratios are used when both numbers are not complete within themselves but still they want mathematicians to get this headache sorted and chalked out for them.

Okay; enough small-talking: To calculate percentage using ratio method multiply given number(n1) with hundred and divide it by quantity of number itself in numerator Nomenclature(‘-`/`-‘).

For instance here’s how it would work-out equation wise;

(80 ×100 )/400

In simpler terms, do `Number one` times `Hundred`, then forwards-divide said answer from denominator value(`Number-two`)and voila!(Still NO!?? okay moving on)

So following our rulebook which says percentage=(part÷whole)×100%

We can substitue like,

`percentage`: represents answered percent value(in our case P=20%)
`Part`: represents first-mentioned number(value we’re finding percentage-of)

`Whole`: denotes Second specific-defined-figure

Then `P`= `(n_1 10^n /n_2 10^m)` (this is where you yawn and exit screen)

where m+n<=5

Let me make it more simple with an example;

CASE I

Calculate percentage(%) if part i.e (first mentioned numerical figure)=`80`, and whole (second numerical figure)=`400`.

So, plug-in the values;

P=(80/400)100%

dividing numerator with denominator:

`````` P= (0.2)×(100%)
``````

Simplifying further;

`````` P =20%
``````

Yayyyy! we have finally arrived at the answer.

CASE II
To be more chaotic – this time let’s choose another random pair of digits as part-whole combo

Calculate percentage(%): if part`(first-number)`=`31` and while `number(second-one)`=`99`; using Ratio Concept I just taught you

``````     P=((3110^2)/(99))%
``````

Now modifying;

``````   3100/99
``````

And our final percentage calculation?

``````  30.3030303.... %
``````

Yes, that’s right! it represents ~30~%%of all possible values aka Numerical Digits in Given-Quantity(Binary or Decimal)

## Why Is It Important To Know Percentages?

Knowing how to calculate percentages might sound similar to solving high-school math problems but doing so provides an array of advantages in several real-world applications such as-

### Financial Planning

Managing your finances efficiently requires understanding percent notation which helps track spending habits by dividing expenses into groups by category or even set a budget for a specific event.

### Voting Trends

Percentages are the most vital component when predicting voting outcomes based on opinion polls conducted by Governments; therefore they hold extensive value within the political language-space.

### Fitness Goals

Understanding body-weight fluctuations over specified periods allows for improved health especially where consistency is required between dietary intake against results obtained from regular exercise patterns pursued.

## Summary

Calculating percentages may sometimes feel daunting, but it doesn’t always have to be like that. With proper knowledge about authentic mathematical techniques tailored through algorithms that ensure constant answers without any-errors, a few tricks up your sleeve and some practice –you got this!