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Improper Fractions and Mixed Numbers

Ben, Suzy, and their stuffed animal Beaver get together to work out how to convert an improper fraction to a mixed number in this fun Numberock song.  Converting one type of fraction into another type is what kids these days do instinctively, I've heard.

Either way, Suzy's brother shared the secret sauce about how to convert improper fractions and mixed numbers just yesterday!  Her brother gets no additional credit for this song, however, that there was all Suzy's improvisation.

Converting Improper Fractions To Mixed Numbers Lyrics:

Verse One:
I asked my friend, “Do you ever wonder
how to convert an improper fraction to a mixed number?”
She said, “Actually, my brother just showed me how to do that yesterday.”
Then she sang a song; it went this way…

When there's an improper fraction to convert,
divide the top by the bottom, and then insert:
the remainder as the numerator,
the divisor as the denominator.

An improper fraction has a numerator
that’s greater than or equal to the denominator.
A mixed number has a value that is greater than one,
that’s represented by a whole number and a fraction.

Verse Two:
There was a mixed number that I had to convert.
I thought so hard, my brain started to hurt.
I texted my friend for some more advice.
She sent me this song; it was clear and concise:

To convert a mixed number to an improper fraction,
three simple steps will give you that satisfaction:
Multiply the whole number by the bottom. Then add to the top.
Keep the denominator the same and let the beat drop!

Let’s take a look at these circles
and describe the amount that’s purple.
It’s four thirds, so we could write four over three;
but one and one third seems a little clearer to me.

Converting to a mixed number makes sense
when describing the amount a value represents.
For instance, consider five halves of apple pie:
two and a half seems easier to visualize.

And now let’s have a little more fun
describing why we might want an improper fraction.
They’re the best for values getting multiplied
Improper fractions are also easier to divide

Just look at "one and one half" times "one and one fourth!"
"three halves times five fourths" is easier, of course.
Or dividing “three and one third” by “one and one third”
Is harder than dividing ten thirds by four thirds.

Learn More

This song targets Common Core standards in 4th Grade. Check out the requirements of 4.NF.3 for more detail.  But I imagine you'd rather have a little more fun than parsing math standards, and if that's the case, you may find these free games and activities at splashlearn.com a bit more interesting.

If you are interested in getting ideas on how to plan a robust standards-aligned place value lesson, we recommend checking out Instructure's recommendations for teaching this concept.

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