# How can we convert percentage to fraction

### Fractions and percentages

Lisa and Jannis train for a sports badge.
Lisa has already met 80 percent of the requirements for a gold badge. Jannis has not yet achieved a fifth of the required performance.

Confusing? Which of the two is now the bigger sports fan? This is so difficult to say because the proportions are given once as a fraction and once as a percentage.

You can state proportions not only as fractions, but also as a percentage. How are these two statements related?

### What does percent \$\$% \$\$ actually mean?

In order to be able to compare proportions more easily, there is this trick with \$\$% \$\$: You divide the whole thing into \$\$ 100 \$\$ equal parts, no matter how big the whole thing is. One part is then a hundredth.

One hundredth is one percent.
In short: \$\$ 1/100 = 1 \$\$ \$\$% \$\$

As a picture: You color 1 box out of 100 boxes.

What if you ink more boxes?

Here 43 boxes out of 100 boxes are colored. These are \$\$ 43/100 \$\$ or \$\$ 43 \$\$ \$\$% \$\$.

You can specify proportions as a fraction or with percent \$\$% \$\$.
You can easily convert hundredths of a fraction into percent.
The following applies: \$\$ 1/100 = 1 \$\$ \$\$% \$\$

percent (lat.):

Per: of
centus: hundred

Percentages always relate to the whole. 43% of 100 students are different from 43% of 1000 students. You will learn how this is all connected later. :)

### Which fraction is the same as 80%?

\$ 80% \$ means nothing else than \$ 80 \$ from \$ 100 \$ or \$ 80/100 \$.

Actually, you don't need to convert anything here. You just write the percentage on the fraction line (in the numerator) and a \$\$ 100 \$\$ below it (in the denominator). If possible, trim the fraction.

So:

\$\$80/100 = 8/10 = 4/5\$\$

So if Lisa has met \$\$ 80% \$\$ of the requirements,
then there are always \$\$ 4 \$\$ of each \$\$ 5 \$\$ athletic achievements.
So she was pretty good there, wasn't she?

How to convert a percentage to a fraction:

1. Write the percentage in the numerator and 100 in the denominator.
2. Brevity.

Example: \$\$ 10% = 10/100 = 1/10 \$\$

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### What percentage is \$\$ 1/5 \$\$?

The reverse is not much more difficult either. You only need to expand or reduce the fraction until the denominator is \$\$ 100 \$\$. Then the numerator is your percentage.

At \$\$ 1/5 \$\$ you expand with \$\$ 20 \$\$ and get \$\$ 20/100 \$\$.

So:

\$\$ 1/5 stackrel (20) = (1 * 20) / (5 * 20) = 20/100 = 20% \$\$

So you can read the percentage directly in the meter.
So Jannis has not yet provided \$\$ 20% \$\$ of the required services.

### Can you think of what?

Lisa did \$\$ 80% \$\$,

Jannis are still missing \$\$ 20% \$\$.

\$\$ 100% \$\$ always means "everything".
In this case "all the services to get the sports badge".
If Lisa has achieved \$\$ 80% \$\$, then she automatically lacks \$\$ 20% \$\$ of the achievements.
Lisa and Jannis are both equally well prepared for the sports badge.

It didn't sound like that at first.

How to convert a fraction to a percentage:

1. Extend the fraction to a fraction of a hundred.
2. The numerator is the percentage you are looking for.

Example: \$\$ 3/5 stackrel (20) = 60/100 = 60% \$\$

### Is it always that easy?

Actually already. However, there are denominators that cannot easily be expanded or reduced to \$\$ 100 \$\$. In this case, you take a few more steps to get the result.

Example 1:

Enter the fraction \$\$ 42/60 \$\$ as a percentage.

Because \$\$ 100 \$\$ is not a multiple of \$\$ 60 \$\$, you cannot simply expand to \$\$ 100 \$\$ here. But you can reduce the fraction with \$\$ 6 \$\$. That gives \$ 7/10 \$.

\$\$42/60 = (42 : 6)/(60 : 6) = 7/10\$\$

You can expand this fraction with \$\$ 10 \$\$ and get \$\$ 70/100 \$\$, i.e. \$\$ 70% \$\$.

\$\$7/10 = (7 * 10)/(10 * 10) = 70/100 = 70 %\$\$

Example 2:

What percentage is \$\$ 27/45 \$\$?

It's best to shorten it with \$\$ 9 \$\$. Then you have \$\$ 3/5 \$\$. Now you only need to expand with \$\$ 20 \$\$ and you get \$\$ 60/100 \$\$ or \$\$ 60% \$\$ as the result.

\$\$27/45 = (27 : 9)/(45 : 9) = 3/5\$\$

\$\$ 3/5 = (3 * 20)/(5*20) = 60/100 = 60 %\$\$

Unfortunately, it doesn't work so well with all fractions ... For example, you cannot expand \$\$ 1/3 \$\$ to a 100 fraction. But you don't have to be interested in that at first, you'll learn that later.