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3 Steps to Convert Mixed Numbers Into Improper Fractions

Teenager solving an equation on a blackboard

Mixed numbers are a combination of a whole number and proper fractions. Here’s an example:

Mixed numbers example

Mixed numbers show a value somewhere between two whole numbers. For example, the mixed number above is neither 1 nor 2. The one-half fraction shows it's perfectly in between.

Let's dive further into what mixed numbers are and how they can be converted into another type of fraction, improper fractions.

What Are Mixed Numbers?

Mixed numbers, which are also called mixed fractions, have a whole number part and a fraction part.

The fraction part must be a proper fraction, which means that the numerator (the top number) is smaller than the denominator (the bottom number).

3 examples of mixed numbers

Now that we've defined mixed numbers, let's learn how to convert them into improper fractions.

What Are Improper Fractions?

An improper fraction has a numerator with a larger value than the denominator:

improper fractions

Because the denominator is a larger value, the decimal quotient will always be greater than one:

improper fractions converted into decimal numbers

Converting Mixed Numbers Into Improper Fractions

Let's learn how to go from the mixed number form to the improper fraction form following these steps:

Mixed numbers example

1) Multiply the whole number by the denominator:

Converting mixed numbers step 1

2) Add the resulting number to the numerator:

Converting mixed numbers step 2

3) Place this number over the original denominator:

Converting mixed numbers step 3

Understanding Mixed Numbers and Improper Fractions

Mixed numbers are a combination of whole numbers and proper fractions. Improper fractions have a larger numerator than denominator.

Learning how to convert a mixed number into an improper fraction prepares you for the next lesson you'll probably have to learn in math: converting improper fractions into mixed numbers.

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