Improper Fractions and Mixed Numbers
Meet our gang of fraction friends: proper fractions, improper fractions, and mixed numbers. Learn how to convert improper fractions to and from mixed numbers. Warning: even though some of these numbers may be tiny, they’ve got big personalities.
|Fractions and Decimals||Mixed Numbers|
...and others are a bit fractured.
As far as fractions go, it's a mixed bag.
Some fractions are proper...
...some are improper...
...and then there are those that are just a little mixed up.
Proper fractions have a numerator that's smaller than the denominator.
Which means they're always less than 1.
Proper fractions also donate to charities and volunteer in soup kitchens.
They know they're not greater than anyone else around them.
Improper fractions, on the other hand, are a little full of themselves.
They've got big heads... well, big numerators, anyway.
In improper fractions, the numerator is bigger than the denominator...
...which means they're greater than 1.
Since fractions aren't supposed to be greater than 1, we call these guys improper.
They're a bit on the rude side.
But if they get on our nerves...
... we can change them into mixed numbers.
Mixed numbers are combinations of whole numbers and fractions...
... so they may be a bit confused at times.
Maybe they're going through an identity crisis or something, we don't really know.
We can change improper fractions into mixed numbers
by dividing the numerator by the denominator.
That's what fractions are, right? Division.
We'll end up with a number and a remainder.
The number is the whole number in front,
and the remainder goes in the numerator of the fraction that follows it.
If we're sick of being mixed up by mixed numbers...
... we can change them back into improper fractions, too.
Since we divided to change them, let's multiply to change them back.
First, we multiply the denominator by the whole number.
Once we find that product, we add it to the numerator of our mixed number's fraction.
Then, we put that number all over the original denominator...
...to get our improper fraction.
So in the end, mixed numbers and improper fractions
can express the same number 2 different ways.
It's up to you to decide which is better: improper... or mixed.