Calculator UseConvert improper fractions to mixed numbers in simplest form. This calculator also simplifies proper fractions by reducing to lowest terms and showing the work involved. Show
In order to simplify a fraction there must be:
What is an Improper Fraction?An improper fraction is any fraction where the numerator is greater than the denominator. Examples of improper fractions are 16/3, 81/9, 525/71. How to Convert an Improper Fraction to a Mixed Number
Example: Convert the improper fraction 16/3 to a mixed number.
When possible this calculator first reduces an improper fraction to lowest terms before finding the mixed number form. Example: Convert the improper fraction 45/10 to a mixed number.
Related CalculatorsFor additional explanation of factoring numbers to find the greatest common factor (GCF) see the Greatest Common Factor Calculator. If your improper fraction numbers are large you can use the Long Division with Remainders Calculator to find whole number and remainder values when simplifying fractions by hand. To perform math operations on fractions before you simplify them try our Fractions Calculator. This calculator will also simplify improper fractions into mixed numbers. An Improper Fraction has a top number larger than (or equal to) the bottom number. More Examples
See how the top number is bigger than (or equal to) the bottom number? Three Types of FractionsThere are three types of fraction: FractionsA Fraction (such as 7/4) has two numbers: NumeratorDenominator The top number (the Numerator) is the number of parts we have. Example: 7/4 means:
So we can define the three types of fractions like this:
Improper FractionSo an improper fraction is a fraction where the top number (numerator) is greater than or equal to the bottom number (denominator): it is top-heavy. 44 Can be EqualWhat about when the numerator is equal to the denominator? For example 4/4 ? Well it is the same as a whole, but it is written as a fraction, so most people agree it is a type of improper fraction. Improper Fractions or Mixed FractionsWe can use either an improper fraction or a mixed fraction to show the same amount. For example 134 = 74, as shown here: Converting Improper Fractions to Mixed FractionsTo convert an improper fraction to a mixed fraction, follow these steps:
Example: Convert 114 to a mixed fraction.Divide: 11 ÷ 4 = 2 with a remainder of 3 Write down the 2 and then write down the remainder (3) above the denominator (4). Answer: 2 34 That example can be written like this: Example: Convert 103 to a mixed fraction.Answer: 3 13 Converting Mixed Fractions to Improper FractionsTo convert a mixed fraction to an improper fraction, follow these steps:
Example: Convert 325 to an improper fraction.Multiply the whole number part by the denominator: 3 × 5 = 15 Add that to the numerator: 15 + 2 = 17 Then write that result above the denominator: 175 We can do the numerator in one go: Example: Convert 219 to an improper fraction.Are Improper Fractions Bad ?NO, they aren't bad! For mathematics they are actually better than mixed fractions. Because mixed fractions can be confusing when we write them in a formula: should the two parts be added or multiplied?
But, for everyday use, people understand mixed fractions better. Example: It is easier to say "I ate 214 sausages", than "I ate 94 sausages" We Recommend:
How do you make an improper fraction into a proper fraction?Multiply the denominator of the fraction by the whole number. Add this result to the numerator of the fraction. This answer becomes the numerator of the improper fraction. Notice that the denominator of the improper fraction is the same as the denominator that was in the fractional part of the mixed number.
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