什么是最简形式？

Simplest Form of Decimals and Improper Fractions

You may see some problems that ask you to simplify numbers that aren't proper fractions. We're going to go through some practice problems. Don't worry if you can't get the correct answers! These are are just for practice and the answer will be explained after each question.

Simplifying Decimals

Some problems may ask you to convert decimals into a fraction in simplest form. This is also called receding a fraction to lowest terms. To do this, divide the numerator and denominator by their greatest common factor.

Remember that we can say that $0.525$ is $525$ thousandths. This means that we can write $0.525$ as the fraction $\frac{525}{1{,}000}$. We can simplify this function the same way we would simplify any other function. $$\begin{align} \frac{525}{1{,}000}&=\frac{525 \div 25}{1{,}000 \div 25}\\ \frac{525}{1{,}000}&=\frac{21}{40} \end{align}$$

Simplifying Improper Fractions

Improper fractions are simplified through the same process as proper fractions! Let's try one out.

We know that both $21$ and $9$ are divisible by $3$, so we are going to divide both numbers by $3$ to find our simplest form. $$\frac{21\div 3}{9\div 3}=\boxed{\frac73}$$

Small is simple

The simplest form of a fraction is when the top and bottom numbers are the smallest they can be without going into decimals (so, while still being whole numbers). For example, look at the pizza below:

Right, there are $2$ slices with pepperoni on them, and $8$ pieces of pizza total. So, we can say that $\frac{2}{8}$ of the pizza has pepperoni on it. But that's not the simplest way of writing the fraction: you can divide both the top and the bottom by $2$ so that the pizza essentially has $4$ slices instead of $8$ (and one slice of pepperoni):

The simplest form of the fraction is $\frac{1}{4}$! Check out this explanation to learn more about simplifying fractions.

(Video) Simplifying Fractions

by Math Antics

In this video by Math Antics, he goes over what simplifying fractions means, how you simplify them, and then some examples.

$\large{\text{Summary}}$

Simplifying a fraction means we rewrite it using the smallest top and bottom numbers we can without changing the value of the fraction.

For example, the fractions $\frac36$ and $\frac12$ both refer to the same amount.

The amount (purple shaded area) is the same in both of these. Because of this, we can say these fractions are equivalent. $$\frac36=\frac12$$ In fact, $\frac12$ is the simplest form of $\frac36$ because it has the smallest numerator and denominator possible to represent that amount.

The general procedure is as follows. Dividing the numerator and denominator of a fraction by the GCF will do the trick. GCF is short for greatest common factor.

If the numerator and denominator of a fraction have a common denominator, then the fraction can be reduced.

In our example, $\frac36$, both $3$ and $6$ share a common factor of $3$. Therefore, it can be reduced to its simplest form $\frac12$.