Improper Fractions

At times you may end up with a strange looking fraction that has a numerator that is larger than a denominator. This is called an improper fraction. In general, you don’t want this, but don’t worry! There’s an easy way to fix it—you turn it into a mixed number. When you have a fraction that looks like this: 9/7, simply divide the numerator by the denominator (divide the top number by the bottom number).

Instead of writing your remainder as r 2, turn it into a fraction by putting the remainder over the divisor (7).

Now, your answer is 1 2/7. Make sure you don’t need to reduce it (this one is already reduced) and you’re done!

Let’s try this one more time. Let’s say you have a fraction that looks like this:

Now, we would set up normal long division, which would look like this:

Once you get your answer as a mixed number, check the fraction to make sure that it does not need to be reduced. (This one does not.)

Thus, your final answer is 24 3/5.

Note: there are some times where you need to use improper fractions, such as when you’re subtracting mixed numbers. Take a look at this example:

First, we found common denominators so that we can do subtraction, however, the top fraction is smaller than the bottom fraction, so we have to borrow from the whole number so that we can subtract. We cross out the 4 and make it a 3, and then add “1” (in its fraction form) to the top fraction, like this:

Notice the red fraction. After we borrow and add 1 in its fraction form, we end up with an improper fraction. However, that’s okay, because in this case we need an improper fraction so that we can do the subtraction. Our final answer is 1 13/15. Check and make sure it’s reduced all the way (this one is) and we’re done!

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