A Percent comes from the New Latin word, Per Centum which means by the 100. In order to understand what is a percent and how it is related to a fraction, please watch the following video.
Again note that the symbol '%' is used to represent the word percent. Fraction and decimals are closely related to percents. Once you have watched the above video, go to the following section to understand this relationship with conversion tips with examples.
Now that you understand what a percent is, let's take a look at how to convert a percent to a fraction or a decimal as well as a fraction or a decimal to a percent. Please watch the following video.
Here is a quick tip for conversions which we also talked about in the video.
Percent to decimal/fraction conversion | Divide by 100 |
Fraction/Decimal to Percent conversion | Multiply by 100 |
There are keywords in percent word problems that relate to a specific mathematical operation.
Keyword in Percent Word Problems "Of" translates to multiplication \(\times\). "Is" translates to equal \(=\). "What" translates to any letter or variable. "\(\%\)" translates to divide by \(100\) or multiply by \(\frac{1}{100}\) or \(0.01\). |
Example 1
\(23\%\) of 5 is what?
Solution
We can translate each part of the question:
\(\%=\times \frac{1}{100}\)
of translates to \(\times\)
is translates to \(=\)
what translates to any variable, let's use \(x\)
Therefore, \(23\%\) of 5 is what? translates to
\[\left(23\times \frac{1}{100}\right) \times 5 = x\]
Solving for the equation gives us \(x=1.15\).
Example 2
45% of what is 23?
Solution
Performing the translations we get
\[\left(45\times \frac{1}{100}\right) \times x = 23\]
To solve for \(x\), we need to multiply the fraction and divide it out to the other side
\begin{align} (0.45) \times x &= 23\\ \frac{(0.45) \times x}{0.45} &= \frac{23}{0.45}\\ x &= 51.\bar{1} \end{align}
Example 3
374,000 is what percent of 561,000?
Solution
\begin{align} 374,000 &= p \times 561,000 \\ \frac{374,000}{561,000} &= \frac{p \times 561,000}{561,000} \\ 0.666666 &= p\\ 0.666666\times 100\% &= p \\ p &= 66.6\% (nearest\,tenth\,percent) \end{align}