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(Video) What Percent is It?

by Math Antics

Here's another mathantics video that explains how to calculate percentage given two numbers.

$\large{\text{Summary}}$

Before, we learned how to find a percent of a number. For example: $$25\%\text{ of }20$$ But there are other types of percent problems we could be asked like finding out what percent $10$ is of $50$.

To help us, we're going to use the following equation to solve any percent problem we come across. $$\frac{\text{Part}}{\text{Total}}=\text{Percent}\%$$ For example, to find $25\%$ of $20$ we would set $\text{Percent}=25$ and $\text{Total}=20$. $$\begin{align} \frac{\text{Part}}{20}&=25\%\\ \text{Part}&=25\%\times20\\ \text{Part}&=5 \end{align}$$

The trick was to multiply both sides to the equation by $20$. This left the variable "Part" by itself on the left side.

Types of Problems

There are three kinds of percent problems, ones where the $\text{Part}$ is missing, ones where the $\text{Total}$ is missing, and ones where the $\text{Percent}$ is missing.

• ${\color{#29A603}{\text{What}}}\text{ is }25\%\text{ of }20\text{?}$
• $5\text{ is }{\color{#29A603}{\text{what}}}\%\text{ of }20\text{?}$
• $5\text{ is }25\%\text{ of }{\color{#29A603}{\text{what}}}\text{?}$

Finding the Percent

So, to find the percent, we just plug in the $\text{Part}$ and the $\text{Total}$ into our equation.

Let's look at an example.

You visit $35$ of the $50$ U.S. states. What percent have you visited?

In this example, $\text{Part}=35$ and $\text{Total}=50$. Plugging these into our equation, we get: $$\begin{align} \frac{35}{50}&=\text{Percent}\%\\ \frac{35}{50}&=\frac{\text{Percent}}{100}\\ \frac{35}{50}\frac{\times\,2}{\times\,2}&=\frac{\text{Percent}}{100}\\ \frac{70}{100}&=\frac{\text{Percent}}{100}\\ 70&=\text{Percent} \end{align}$$

Percent of a Number

Let's say you want to find $a\%$ of a number $x.$

Let's do another example.

We want to find $35\%$ of $90.$ If we use the variables from the graphic, that means that $a=35$ and $x=90.$ Now, all we have to do is substitute these values into our formula to find the percent of a number. $$\begin{align} 35\% \text{ of } 90 &=\dfrac{35}{100} \cdot \dfrac{90}{1}\\ &=\dfrac{35 \cdot 90}{100 \cdot 1}\\ &=\dfrac{3150}{100}\\ &=31.5 \end{align}$$

So $35\%$ of $90$ is $31.5.$

Multiply the number by $\frac{x}{100}$

First off: in this explanation, $x$ is a variable, which means you can replace it with whichever number you need to answer a question. When you say $x$ percent of something, you're basically saying $\frac{x}{100}$ of that thing.

$\frac{23}{100}$ is equal to $23$%! Now, there are two ways to multiply a number by $\frac{x}{100}$. One is to make the number a fraction, and the other is to make $\frac{x}{100}$ into a decimal.

Making the number a fraction

To make a whole number into a fraction, just put it above $1$. For example, $3$ as a fraction is $\frac{3}{1}$. This is because fractions are basically dividing the top number by the bottom number, but dividing something by $1$ doesn't change it at all. If your number is a mixed number, you'll have to convert it into an improper fraction.

Once your number is a fraction, multiply it by $\frac{x}{100}$ and then simplify it to get your answer. Let's try it:

$30$% of $50$ is $15$. We could find that by making $50$ into a fraction ($\frac{50}{1}$), then multiplying it by $\frac{30}{100}$. $$\frac{50}{1} \times \frac{30}{100} = \frac{1500}{100} = \frac{15}{1}$$

Making $\frac{x}{100}$ into a decimal.

To make $\frac{x}{100}$ into a decimal, just divide $x$ by $100$. You can do that using a calculator, or you can just move the decimal point over to the left by two digits (the number of $0$'s in $100$).

After that, just multiply your number by your new decimal! This can be a little bit tricky, since decimals can get complicated, and you may need to use your calculator. Let's try it:

$13$% of $25$ is $3.25$. We can find this by dividing $13$ by $100$ to get $0.13$, then multiplying that by $25$. $$0.13 \times 25 = 3.25$$

(Videos) The Percent Proportion

by mathman1024

Here's a video by mathman1024 that shows you how to solve percentage problems using proportions.

$\large{\text{Summary}}$

The main proportion format we use to solve these problems is: $$\frac{\text{percent}}{100}=\frac{\text{part}}{\text{whole}}$$

Say we had the question: Jones landed $45$ out of $80$ jabs. What percent is this? This can also be rewritten as What percent of $80$ is $45$? So, our goal is to place these numbers into the proportion format we have.

We want to find the percent, so that can be left as unknown. We also have $45$ jabs out of $80$. So $45$ is the part of it, and $80$ is the whole amount. Therefore, our proportion becomes: $$\begin{align} \frac{x}{100}&=\frac{45}{80}\\ 80x&=100\cdot45\\ 80x&=4{,}500\\ \frac{80x}{\color{#29A603}{80}}&=\frac{4{,}500}{\color{#29A603}{80}}\\ x&=56.25 \end{align}$$ So, Jones connected on $56.25\%$ of his jabs. In essence, we have converted a fraction to a percent.