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In this lesson, you will learn the definition of an improper fraction, as well as proper fractions and mixed fractions. You will be given examples of improper fractions to properly illustrate what they are.

Improper Fraction Definition

Have you ever seen a person with broad shoulders and chest but skinny legs? Well, you could say that person is similar in physical appearance to an improper fraction!An improper fraction is a fraction that has a larger number on the top than on the bottom. The number on the top of the fraction is a numerator and the number on the bottom is a denominator. Therefore, an improper fraction has a greater numerator than denominator.

They are different from proper fractions that have a smaller numerator and greater denominator.

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Examples of Improper Fractions

All of the examples of improper fractions have a larger numerator than denominator. It doesn’t matter how large or small the fraction is or how large and small the numerators and denominators are; if the numerator is bigger than the denominator, it is considered ‘improper’.

What Does an Improper Fraction Mean?

In an improper fraction, the numerator can be translated as the amount of parts or pieces that we have.

The denominator is the parts the whole is divided into. So if we have the improper fraction, 13/4, we have 13 pieces or parts out of 4 parts of the whole. Another way to look at this is using an example of key lime pies – 13/4 of key lime pie would mean that we have 13 pieces of 4 key lime pies.

Mixed Fractions.

In order to convert an improper fraction, like 13/4, to a mixed fraction, we must use division and divide the denominator into the numerator.

In our example, the number 4 goes into 13 a total of 3 times but has a remainder of 1. Whenever there is a remainder, we would put that number over the denominator of the improper fraction, making a mixed fraction. If there is no remainder, we just have a whole number.

Let’s look at some examples.8/3 = 8 ÷ 3 = 2 remainder 2 = 2 2/315/8 = 15 ÷ 8 = 1 remainder 7 = 1 7/820/10 = 20 ÷ 10 = 2If we want to convert a mixed fraction to an improper fraction, we would multiply the whole number by the denominator of the fraction and add the numerator. Then we would put that number on top of the denominator.

For example:1 1/2 = 1 x 2 + 1 = 3/2Let’s look at some more examples:5 5/6 = 5 x 6 + 5 = 35/610 1/2 = 10 x 2 + 1 = 21/27 4/5 = 7 x 5 + 4 = 39/5

Lesson Summary

An improper fraction is a fraction that has a larger number on the top than on the bottom. In an improper fraction, the numerator, or the number on the top, is the amount of parts or pieces that we have. The denominator, or number on the bottom, is the parts the whole is divided into. A proper fraction has a numerator that is smaller than the denominator. A mixed fraction is a whole number and a fraction put together.

In order to convert an improper fraction to a mixed fraction, we must use division to divide the denominator into the numerator. If we want to convert a mixed fraction to an improper fraction, we would multiply the whole number by the denominator of the fraction and add the numerator. Then, we would put that number on top of the denominator.

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