I organized an ocean cleanup and we collected a total of 25 pounds of garbage.16 pounds of garbage consisted of plastic.What percent of the garbage was plastic?

Feb 22, 2018

The answer is 64%.

Explanation:

In order to find out the percentage from a situation, we must set up two ratios.

$\frac{16}{25} = \text{? %"/"100%}$

is the equation you will have to use to find the percentage of how much is made out of plastic. The first way is to use cross-multiply. Meaning you will have to multiply $16$ by $100$ to gain $1600$ as your product. Dividing $1600$ by $25$ gives you 64%.

The second way to see if it's correct is by dividing $16$ by $25$. This gives you a decimal of $0.64$. By doing $0.64 \times 100$, it gives you $64$. Therefore, 64% of the trash collected was plastic.

Feb 23, 2018

64%

Explanation:

$\textcolor{b l u e}{\text{Preamble}}$

Percentage can be written in two ways. Although they look different they both mean the same thing.

Example: 30 percent -> 30% -> 30/100

Percentage really is a special fraction. What makes it special is that the bottom number (denominator) is ALWAYS 100.
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$\textcolor{b l u e}{\text{Answering the question}}$

All the plastic collected weighed 25 pounds
Of this there was 16 pound of plastic

The amount of plastic expressed as a fraction of the whole is $\frac{16}{25}$

We need to change this to percentage so the bottom number (denominator) has to end up as being 100.

Multiply by 1 and you do not change the value. However, 1 comes in many forms.

$\textcolor{g r e e n}{\frac{16}{25} \textcolor{red}{\times 1} \textcolor{w h i t e}{\text{d") ->color(white)("d}} \frac{16}{25} \textcolor{red}{\times \frac{4}{4}}}$

$\textcolor{g r e e n}{\textcolor{w h i t e}{\text{ddddddd")->color(white)("d}} \frac{16 \times 4}{25 \times 4}}$

$\textcolor{g r e e n}{\textcolor{w h i t e}{\text{ddddddd")->color(white)("dd}} \frac{64}{100}}$
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Think of this as $64 \times \frac{1}{100}$

Think of % as being the same as $\times \frac{1}{100}$

So 64xx1/100 ->64%