How To Add Mixed Fractions With Whole Numbers

improper fractions and mixed numbers, a la shmoop. numbers come in all shapes and sizes. some are big... ...and some are little... some are whole...

How To Add Mixed Fractions With Whole 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 arejust a little mixed up. proper fractions have a numerator that's smallerthan the denominator. which means they're always less than 1. proper fractions also donate to charitiesand volunteer in soup kitchens. they know they're not greater than anyoneelse around them. improper fractions, on the other hand, area little full of themselves. they've got big heads... well, big numerators, anyway. in improper fractions, the numerator is biggerthan the denominator... ...which means they're greater than 1.

since fractions aren't supposed to be greaterthan 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 ofwhole numbers and fractions... ... so they may be a bit confused at times. maybe they're going through an identity crisisor 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 thenumerator 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 thenumerator 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.