考试成绩（百分比）

Converting Your Test Score to a Percentage

There are a few ways to go about converting your test score (in fraction form) to a percentage of a number.

Scenario 1

If the score is already a fraction out of $100,$ the percentage is just the numerator of this fraction! For example, say you got a $\frac{75}{100}$ on your test. What percent out of $100$ is this? All you have to do is add a $\%$ sign to the numerator! $\frac{75}{100}\longrightarrow 75\%.$ In other words, we are multiplying the fraction by $100$ and adding on a $\%$ sign.

Scenario 2

If the denominator (the number of points your score is out of) is a factor of $100,$ multiply the numerator and denominator by the same number so that the denominator becomes $100.$ For example, say you got a $\frac{13}{25}$ on your test, and you want to figure out what percent out of $100$ this is. Notice that $25$ is a factor of $100,$ because $25\times 4=100.$ So, we just have to multiply the numerator and denominator of our fraction by $4$ to get a denominator of $100:$ $\frac{13}{25} = \frac{13}{25} \times \frac{4}{4} = \frac{52}{100}.$ From Scenario 1, we know this is the same as $52\%$.

Scenario 3

If the denominator cannot be easily multiplied by another number to get $100,$ you can use long division to get a decimal, then convert the decimal to a percent by moving the decimal point. This takes a few more steps than our first two scenarios.

For example, say you got a $\frac{15}{16}$ on your test. First, perform long division:

So $\frac{15}{16} = 0.9375.$ If we convert this fraction to a percentage and remember our strategy from Scenario 1, we get $$0.9375 \longrightarrow \frac{93.75}{100} = 93.75\%$$

Below is a graphic with some more examples. The original number is written as a fraction, and then we convert it to a percentage.

Another Method

To convert $\frac{60}{75}$ to a percentage, you could also simplify the fraction by putting it in simplest form. Then use the method in Scenario 2 to convert to a percentage. Here's how it works.

First simplify $\dfrac{60}{75}$ by dividing the numerator and denominator by $15:$ $$\begin{align} \dfrac{60}{75} = \dfrac{4}{5} \end{align}$$

Next, notice that $5,$ the denominator of the new fraction, is a factor of $100,$ since $5\times 20=100.$ So, using the same steps as Scenario 2, multiply the numerator and denominator of our new fraction by $20:$ $$\begin{align} \dfrac{4}{5} \times \dfrac{20}{20} = \dfrac{80}{100} \longrightarrow 80\% \end{align}$$

(Video) How to Convert a Test Score to a Percent

by Helpful DIY

This video by Helpful DIY explains how to calculate a percentage out of any test score. This is a special example of finding $\%$ of a number. If you think this sounds a lot like converting a fraction to a percent... that's because it is!

$\large{\text{Summary}}$

The steps are:

1. Divide the number of questions you got right by the total number of questions.
2. Multiply the number you got from Step 1 by $100\%$.

And you'll have your percent score!

Let's look at an example.

How to Find a Percent from a Fraction

Suppose you get $10$ questions out of $16$ correct. Step one tells us to divide the two numbers. $$\frac{10}{16}=0.625$$ Then, we multiply by $100\%$. $$0.625\times100\%=\boxed{62.5\%}$$

If you got $55$ questions right on a $67$ question test, you scored an $82\%$.

$\text{Divide: } \ \frac{55}{67} = 0.82089552\\$

$\text{Multiply: } \ 0.82089552 \times 100 = 82.089552\\$

$\text{Round: } \ 82.089552 \rightarrow 82\%\\$

$\text{Done! } \ \boxed{82\%}$

Your class just got their scores back for the math test from last week, and you and your friends are talking about your scores. One of your friends says they got $100\%$ on their test and asks you what percentage you got, perhaps to rub it in. Well they're not a good friend. Anyway, you know that you got a $44$ out of $48$ on it. How do you find the percentage?

Step 1 - Proportions

First, you need to figure out what you got out of $100$. We can set up a proportion to figure it out: $$\frac{44}{48}=\frac{x}{100}$$

We can then cross-multiply to get: $$4400=48x$$

Finally, we can divide by $48$ on both sides to get $91.66666...$, which is a repeating decimal around $92$. So you got a $92$ out of $100$! But wait, we're not done yet$\dots$

Step 2 - Decimal to Percent

The decimal form of $\frac{92}{100}$ is $0.92$. To convert a decimal to a percent, shift the decimal point $2$ places to the right and put a percent sign on the end. This turns $0.92$ into $92\%$, so now you know you got a $92\%$ on the test. (Nice job!)

NOTE: You can also divide the percentage by $100$ and remove the $\%$ sign to check your work. For this problem we would get

$$\frac{92}{100}\cancel{\%} = \boxed{.92},$$

which is the decimal we started with. This process is dividing by $100$ and removing the percent sign. The final answer is a decimal.

SIDE COMMENT: If you increase or decrease your score, this will be clear regardless of whether the score is a fraction, decimal, or percent. In other words, if a fraction increases, so do the equivalent decimal and percentage.