什么是带分数？

(Video) Mixed Numbers

by Math Antics

Here’s a video by Math Antics that covers improper fractions, mixed numbers, converting fractions to a mixed numbers, and converting mixed numbers to fractions.

$\large{\text{Summary}}$

Mixed numbers are a way to show fractions that have a value greater than one. They are harder to work with than improper fractions but make it easier to see the true value of a fraction.

When we write an improper fraction as a combination of a whole number and a proper fraction, we get a mixed number. We leave out the plus sign when writing mixed numbers but it's implied. You can think of there being an invisible plus sign. The fraction part has a numerator and denominator. Having an integer next to it doesn't change anything there.

$$3\frac12,\,\,2\frac18$$

Pronounced three and a half, two and an eighth, respectively

The word "and" helps us remember we're doing addition.

Proper fractions have a numerator less than the denominator and cannot be written as mixed numbers.

(Video) Mixed Numbers

by mathman1024

Here’s a video by mathman1024 that explains mixed numbers, converting a mixed number to a fraction and converting a fraction to a mixed number.

$\large{\text{Summary}}$

Mixed fractions are a number represented by a whole number and a fraction. $$3\frac12,\ 77\frac12,\ 11\frac34$$

For example, the number $3\frac12$ means $3$ whole parts and then $\frac12$. If we drew a picture it would look like

If we convert all the circles to be in terms of halves we get

As you see we have $7$ halves. For each of the three whole units we have there's two halves. So, since these both represent the same value, $$3\frac12=\frac72$$ These are the mixed number and the improper fraction forms of this number.

Another important thing to note with mixed numbers is that the whole number part is being added to the fraction part. It is not multiplication! $$\begin{align} 3\frac12&=3+\frac12\\ 3\frac12&\ne3\cdot\frac12 \end{align}$$

Mixed numbers are made up of an whole number and a fraction

Mixed numbers are the combination of a whole number ($1, 2, 7, 42, 397,$ etc.) and a fraction ($\frac{1}{2}, \frac{7}{4}, \frac{2}{546}, \frac{29}{13}, \frac{4}{16},$ etc). They tend to mimic the way we speak: I'm more likely to say something like "I have one and a half ($1\frac{1}{2}$) extra bars of chocolate!" than I am to say "I have three-halves ($\frac{3}{2}$) extra of a bar of chocolate!"

In a math problem, though, those numbers mean the same thing. The whole numbers are like full, closed containers, and the fractions are like open containers that aren't necessarily full yet.

Also, while decimals are not the same as mixed numbers, some decimals bigger than $1$ can be written as mixed numbers. For example,

$$3.25 = 3 + 0.25 = 3 + \frac{1}{4} = 3\frac14$$