Question

The \[33\] is what percent of $120$?

Answer 1

Hint: To solve this problem we first have to find the ratio of the number whose percentage we have to find from the number that we take as $100\% $. From the ratio then we will convert the obtained ratio in such a way so that the denominator is converted to $100$, since we are calculating within percentage, that means per/every $100$. Then we will multiply the finally converted and obtained ratio with $100$ and get the final result. So, let us see how we solve this problem.

Complete step by step answer:
Let us think about $120$ as our $100\% $ and we want to find $33$ parts of $120$, so using what we just learned we say that "$33$ parts of $120$ is the same as $\dfrac{{33}}{{120}}$."To turn $\dfrac{{33}}{{120}}$ into a percentage we just need the denominator to equal $100$ since earlier we said that $120$ is our $100\% $.

We could use an equation for this, so let's use an equation for this.
We know that, $120.\left( {{\text{some number}}} \right) = 100$
So, let the number be $x$.
$120x = 100$
Dividing both sides by $120$, we get,
$ \Rightarrow x = \dfrac{{100}}{{120}}$
Simplifying the fraction, by dividing both numerator and denominator by $20$, we get,
$ \Rightarrow x = \dfrac{5}{6}$

Now we know that if we multiply the denominator by $\dfrac{5}{6}$ we will get $100$ in the ratio of $\dfrac{{33}}{{120}}$ and if we multiply the numerator by $\dfrac{5}{6}$ we will get a ratio with $100$ as the denominator, so our percentage must be the numerator.
$\dfrac{{33 \times \dfrac{5}{6}}}{{120 \times \dfrac{5}{6}}} = \dfrac{{\dfrac{{55}}{2}}}{{100}} = \dfrac{{27.5}}{{100}}$
This is the fraction obtained from $\dfrac{{33}}{{120}}$ after converting $120$ into $100$.
Therefore, the percentage is,
$\dfrac{{27.5}}{{100}} \times 100 = 27.5\% $

Therefore, $33$ is $27.5\% $ of $120$.

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. Percentage represents a share of the whole quantity, which in the given question is 120.