Question

Express $\$ 2.00$ as a percentage of $\$ 8.00$?

Answer 1

Hint:First let's think about a normal percentage as a ratio. If we wanted to think about $4\% $ as a ratio, we would say well, that's $4$ parts of $100\% $ or $\dfrac{4}{{100}}$ and from there I could simplify the fraction into $\dfrac{1}{{25}}$ and now I have a mathematical representation of $4\% $. Anything that we multiply by $\dfrac{1}{{25}}$ will give me $4\% $ of that thing. We will use this concept to find how much percentage of $\$ 8.00$ is $\$ 2.00$. So, let us see how to solve this problem.


Complete step by step solution:
Let us think about $\$ 8.00$ as our $100\% $ and we want to find $\$ 2.00$ parts of $\$ 8.00$, so using what we just learned we say that "$\$ 2.00$ parts of $\$ 8.00$ is the same as $\dfrac{2}{8}$."
To turn $\dfrac{2}{8}$ into a percentage we just need the denominator to equal $100$ since earlier we said that $\$ 8.00$ is our $100\% $.
We could use an equation for this, so let's use an equation for this.
We know that, $8\times\left( {{\text{some number}}} \right) = 100$
So, let the number be $x$.
$8x = 100$
Dividing both sides by $8$, we get,
$ \Rightarrow x = \dfrac{{100}}{8}$
Simplifying the fraction, by dividing both numerator and denominator by $4$, we get,
$ \Rightarrow x = \dfrac{{25}}{2}$
Now we know that if we multiply the denominator by $\dfrac{{25}}{2}$ we will get $100$ in the ratio of $\dfrac{2}{8}$ and if we multiply the numerator by $\dfrac{{25}}{2}$ we will get a ratio with $100$ as the denominator, so our percentage must be the numerator.
$\dfrac{{2.\dfrac{{25}}{2}}}{{8.\dfrac{{25}}{2}}}$
$ = \dfrac{{25}}{{100}}$
This is the fraction obtained from $\dfrac{2}{8}$ after converting $8$ into $100$.
Therefore, the percentage is,
$\dfrac{{25}}{{100}} \times 100 = 25\% $
Therefore, $\$ 2.00$ is $25\% $ of $\$ 8.00$.

Note:
 This method is more elaborate and easier to understand. But there is also a shorter and faster method to solve the problem. We can just find the ratio of the number with the total of the number and multiply the ratio with \[100\] and it gives us the percentage.
For example: ratio of $\$ 2.00$and $\$ 8.00$ is $\$ 2.00:$ $\$8.00=1:4$
Then, we multiply this ratio by 100% to get the required percentage as $\dfrac{{25}}{{100}}\times100\%$. Hence, we get the required percentage as \[25\%\].